Hello and welcome to the session my name is Mansi and I am going to help you with the following question. The question says two dice are thrown, the events a, b and c are as follows. Event e is getting an even number on the first die, event b is getting an odd number on the first die and even c is getting the sum of the numbers on the die less than or equal to 5. Now describe the event a or b. So, let us see the solution to this question now event a or b is same as the event a union b. So, what we need to do is here first of all we need to write down the sample space for event a then we write down the sample space for event b and then we find out the sample space for a union b. Now we see that this is the sample space for event a that is getting an even number on the first die and this is the sample space for event b that is getting an odd number on the first die. Now event A union B will be all the sample points of this sample space and every sample points of this sample space. So for event A union B the sample space will be 1 1, 1 2, 1 3, 1 4 and so on we have till 6 6. So this is the sample space for the event A union B. Now we see that this is equal to the sample space when two dice are thrown because there we have all the possibilities that we get whenever two dice are thrown. So this is our answer to the question. I hope that you understood the question and enjoyed the session. Have a good day.


Okay, I think maybe we should get started as people are coming in. So welcome back everyone. So we have many nice talks today and three talks in the morning in this US morning session. So the first speaker of the day is Paola Orogero and she's going to tell us about quantum GHS. Okay, thank you. So first of all, I would like to thank the organizers for the nice invitation. And so, okay. And so, yes, today I would like to talk about my recent work on quantum generalized aerodynamics, which is in collaboration with Pasquale Calabrese, Ben Duayon and Jerome Dubai. And is in this, our recent paper. But, so even if most of people I think in this, in this conference actually know aerodynamics better than I do probably, still I would like to start with some basics of aerodynamics just to recall some basic facts. And so the key assumption underlying any hydrodynamic theory is, is the one of separation of scales. And by that, what I mean is that usually want to assume separation of land scale, meaning the, the existence, the existence of a mesoscopic scale small L, which assume to be much smaller than the mesoscopic scale so that this, this land, the system can be seen locally as homogeneous, but still a much larger than the microscopic scale usually associated the same to the inter particle distance so that still contains a large number of particles. Also one assumes a time scale separation, which basically amounts to assuming a local relaxation. And so the, the existence of such intermediate scale is actually, is actually important because it allows us to replace the complex problem of dealing with many large number of interacting particle with the particles with the simpler problems, problem of dealing instead with the fluid, just in terms of few, few local properties. And in practice, what this mean is that what one is allowed to do under the assumption is, is to replace expectation values of observables in the exact state at a given time with expectation time expectation values on on a stationary state. But this stationary state will will is taken to to be a different one for any cell in space and time so basically it will be position and time dependent in general. So what are these local feature that we want to keep track of well they are related to conservation laws that in general for a generic system are usually the mass the momentum and the energy if it's conserved them. And the other assumption of other dynamics is that they take the form of continuity equation for the associated densities. If we think to this equation as in terms of expectation values in the in the sense that I was explained before, then these are exactly what people usually mean by conventional dynamic. But now, so let's move to to integrable model instead which, which are different in that they possess an in feed number of conservation laws, and therefore for such models, conventional dynamics is not expected to apply. So first of all, what is interesting about these models is that they are exactly solvable by means of better answer. But also let me say that I would say that the answers is not what I would call a flexible technique, meaning that soon, for example, as we, as we add some in homogeneity in the system and then the, the solvability of the model breaks down. And, and therefore, this is one of the reasons why I think the these words that have been mentioned many times already now in this conference by Kassel Vared et al. and Bertine et al. are quite remarkable because so they need allow to treat these one dimensional integrable system in a more versatile way. And they do that by using a hydrodynamic approach, which is nowadays called generalized hydrodynamics. So let's see what this is about. So as before, the starting point are these conservation laws which can be shown to take the form of continuity equations also in this case. Now we have a different number of them. Let me say also that we remind also that in integrable models, eigenstates are labelled by a set of quantum numbers called the rapidities which are related to the momentum of the so called quasi particles, meaning the stable excitation of these models. And we are interested in the thermodynamic limit in which basically these states can instead be described by by now a continuous function which can be taken to be this what is called the occupation function basically is the occupation in this rapidity space.  So we want to look at the problem from a macroscopic from a macroscopic point of view meaning in terms of expectation values which now will be given again in the stationary state but which is now described by a gg instead of a Gibbs ensemble and still preserve this, this local this, this local behavior. And if we think in this term basically what happens that in terms of these of these expectation values, this infinite number of conservation laws of continuity equation can be recast in this equation for for the occupation function. And this is what what the GHD is about. So instead of going to the details of this Paula. Yes. Paul Giuseppe. Naive question. Usually in hydrodynamics you have Navier-Stokes equation. What kind of equation you will have here in this context? What. So this I didn't get the question so if you want to this is so you basically what you are asking if I understand correctly is a relation between the usual equation of hydrodynamics meaning the one so let's say for for the density of for the other velocity and this one. Correct. I mean, well, the Navier-Stokes is the, it's about the pillars of hydrodynamics in usual sense. So I'm asking in this context, what kind of equation you will have. Well, I mean, this is the equation which described hydrodynamics in this in this case. Okay, I'm not sure I understood the question. Well, Navier-Stokes is a non-linear equation for the velocity itself. So, yes, yeah, yeah, yeah, yeah, if you want to, if you want to, okay, maybe, maybe you can come back to this question later because for a specific class of states for example, I will show that this equation become an equation for the for a set of rapidities which are if you want to relate to the moment of the particle so maybe it's closer to what you have in mind. Okay. But okay, so maybe as I was saying, instead of going to the details of this equation, I prefer to give a more intuitive picture of probably also this with help in what Giuseppe was asking for for what free models are concerned because in this case, this equation actually become very easy to understand, meaning that when we talk about free models, then these rapidities are nothing but the momentum of the particles themselves. And this occupation function becomes the occupation function in space space, also known as a Wigner function. And therefore in this case, this, this equation of GCD is nothing but the evolution equation of the function, which is something that is a routine use in some classical methods since a long time. All right. And so the other in this very brief overview, the last thing that I want to talk about is a special class of states in GHD, which are the zero, what I will call the zero entropy states. So what are they? Basically, they are states whose occupation function is of this form. So it is one within a given contour called Fermi contour, and it is zero outside. So first of all, let me mention that the states actually appear quite naturally, meaning that for example if you think to ground states within these particles of bosons within homogeneous potential, they are of this form. And what is important, what is peculiar of these states is that if we look at them locally, within a given cell, let's say, then they look like split from each other, let me see. Okay, so they basically, they can be, they can be parameterized by just a set of Fermi points, okay, that we are this theta one, theta two, two. And in this case, we see that it's clear that because of this simple form of the occupation function, basically the equation for the evolution of this occupation function can be written in terms of a finite number of equation for those Fermi points. And so in this case, we end up in a finite dimensional GHD. What I mean is that usually one can think of this occupation function as an infinite number of equation one for each theta, but now we have a finite number of them. What is also important, and I will come back to this later in the talk, is that if we are in a special case where we only have one Fermi C, meaning just two Fermi points, okay, so this J just run from one to two. Then these are those states for which generalized aerodynamics actually reduce to standard aerodynamics. This can be easily shown. Okay, so this was meant to be just really a flash of what GHD is about. Let me just mention that after the two pioneering work that I mentioned before, so a lot of activity has been going on in this field with many contribution and application from many groups in the world. Of course it is just a partial list, but just to say that many people are contributing to the development of this theory. And with that, I want to pass to the main part of this talk, which is about quantum aerodynamics. So another question which arises at this point is how to incorporate quantum effects in GHD. And by that, what I mean is that generalized aerodynamics as any theory at the hydroscale is not enough, if you want to say this way, to describe quantum phenomena as for example correlations among different fluid cells. And this is exactly what we want to do here. So again, so let me be very precise about what is the particular program that we have in mind here, in order to avoid confusion. So I mean a very common and well-known procedure in literature is that of starting from classical equations, in this case will be nothing but hydrodynamics itself and quantize them by hand in a sense. What I mean by that is that, so this path was basically the path taken by Landau for example, by the way, was the first to first quantize a liquid in his development of the theory of superfluid helium. But after that actually the very same approach was was also was also adapted to other system, including Bose-Anson condensate, where quantum fluctuation are captured by Bovellibot theory, superconductors or liquid and general liquids described by Latinger liquid theory. And so in this sense what we have in mind is nothing new I would say. Let me also emphasize that, so here we are not interested in going to higher order hydrodynamics, meaning we are not interested in correcting GHD equations for the GHD equations, which is instead a different path which was recently pursued, for example, by Maurizio. He actually mentioned that also in his talk the other day when he was talking about this Moyalex function and similar ideas also appear, for example, in this paper by Dean Ledusal Majunde Lechel. But here, this is not what we have in mind, instead what we want to do here is to look at the propagation of linear sound waves on top of hydrodynamics and quantize them. In the same sense in which all these people did for another situation. And so when here we talk about quantum fluid, so we talk about quantum fluid in the same sense in which Latinger liquid is a quantum fluid, maybe this can be more familiar to many of you. Okay, but to be more specific, to understand better what I mean, let's go to, let's be specific and let's take a model, a specific model, which is in this case the Lieblinger model describing repulsively interacting bosons. And let's focus again on zero entropy states. So again, the plan is to look at fluctuation around the GHG background at zero entropy one in this case and quantize such fluctuation in a semi-classical fashion. Right, so if we start from a zero entropy states fluctuation basically can be seen as a deformation of this of this Fermi contour. Okay. And, and from, from a local point of view, what this means is that these are nothing but fluctuation of these of the Fermi points, which in the interacting case are associated to this western number to a certain number of rapidities. But what we do next is to switch to, so if you want this rapidities are not physical quantities, so we want to switch to physical momenta associated to the to the excitation of the model. And the main reason for doing that is that this contrary to this detail is PA satisfy an exact conservation laws together with this to the associated energies. And now if we were if starting from this equation we write an equation for the fluctuation delta PA we easily arrive to this equation. And if you look to this equation, what is describing is exactly sound waves linearly propagating sound waves. So it's exactly the equation we were looking for. At this point, the main, the second point is that we want to want to quantize this fluctuation. And in the, in the, in the language of sorry, in the language of quantum fields, what this means is that one user. Why one usually assume the existence of an existence of an action as whose minimum you are called as classical basically gives back them the way the equation and the whose expansion to second order instead gives the quantum fluctuations. So if we if we switch now to the Hamiltonian formalism, the main result of our work is to write down explicitly the Hamiltonian which does this job basically in fact this Hamiltonian together with together with the this commutation relation is reproduces exactly as a question of motion them, then the way the equation that was showing you before. So let me comment a bit about this Hamiltonian so first of all, not that this Hamiltonian depends explicitly on the state meaning it depends on the on the Fermi contour for this zero entropy states. But most importantly, not that this Hamiltonian is quadratic. And so what we are saying basically is that fluctuations quantum fluctuation on top of a GHD background are captured by a quadratic theory, and this should not sound very surprising if one think in terms of a Lattinger liquid theory. And in fact, what this Hamiltonian describes is exactly a Lattinger liquid, though, I mean a more complicated one meaning that we see that is explicitly time dependent, especially in homogeneous and in general multi component. So, let me also mention that what so what we did in this work was basically generalize our previous work with the Yanis Brun and the Jerome Dubai and where basically we carried out the same pro the very same program but in a specific case, if we want, which is the limit of our core bosons. Okay, so the same model, but the limit where the bosons become become our core, which is also known as the limit them. And also in the specific for specific protocol, which was a quench from seeing from a single well to another single well with different frequency. And, and this, I mean, the reason why I call this slide the quantum conventional dynamic is because basically, this is exactly the situation where GHD actually reduced to standard aerodynamics and so the problem that we face back then was to quantize in the very same sense, a standard aerodynamics. And, but the, I mean, what I wanted to underline is that also there, I mean, as expected, at this point, we went up in a theory which was nothing but the Lattinger liquid again time dependent and in homogeneous. Time with a single component. This is due to the fact that for this particular protocol we are always in the situation where only two Fermi points appear, which, as I mentioned, different times now is exactly the case where generalized aerodynamics reduced to standard aerodynamics. And so the last part, the last thing that I want to talk about is about numerical checks to so I want to show you that indeed this theory works. And so what we did basically what I show you here is a numerical check for the Lieblinger model and where I consider a particular protocol which is the following so we start in the in the in the ground state of a quartic potential and at equal zero we quench to a quadratic to our harmonic potential. So this is, I mean, this, this protocol, if you want, is interesting also from an experimental point of view because it's a simple way of modeling, for example, the currently running experiment as the or previous experiment as the quantum Newton cradle but but mainly because from this theoretical point of view, we see that if we look now at the evolution. This data show you here is basically a movie picture. If we look to the evolution of the occupation function, we see that in this protocol what happens that sometimes develops more than two Fermi points so we are in the true regime of GHD. And what I show you are basically the comparison between our theory and 10 10 dependent the energy. So this liner is just the density profile and so the gray lines are our merits while the theory is the is the orange curve. So this line is just the density. So what you see here in orange is just GHD instead of the new prediction are at the third and fourth line, which for different for different point in space show the density density correlations. So you see that. So, okay, many, many features are captured already at this, at this number of particles which that we can reach with the with the numerics, but also stronger finite size effect are visible. You have to take into account that the year so the numerics we can reach is up to 20 particles, which is quite far from the thermodynamic limit to where we expect our theory to work better. And if you want to this can be also seen as a strength of this GHD and theory in the sense that it works directly in the in the thermodynamic limit. But if you want to have a more reliable comparison, what you can do is to again to go to the to the top share the limit. Because in that limit to you can rely on on three fermion techniques for the numerics. And this is what we are we are doing. We're doing right now. And so basically, in this case, so the same is the same protocol just in this limit. So you see that you can one can look at the gain at the density density correlation. And, okay, here, there's just a small point is that you need to average over a small window because to to get rid of this free the oscillation but apart that the prediction of our theory perfectly with the with the numerics. In this case, we're also able to go beyond that and to give an analytic expression for for the entanglement entropy as a function of space and time. And, and we are also we are also proceeding with the other checks of other quantities in this case. All right, so and with that, I would like to conclude with this short summary. So, so I repeated after several talks that just the need to provide a more efficient way to describe interacting quantum particles in one day, but still it misses important quantum effects. And I hope I convinced you that GHD gives indeed a way to construct quantum fluctuation around GHD. But on the other hand, let me emphasize once again that this is not the end of the story meaning that there are far farther contribution which one can take into account by considering correction to the GHD equation for the evolution itself. And with that, I would like to thank you for the attention. Thanks a lot. Nice talk. So we have a few minutes for questions. I have a question. Yes. And it's about okay, even the summary. Okay, I read that there are GHD misses important quantum effects. So I'm wondering that in the past I always consider just generalized dynamics and I compute the time evolution of collection functions and entanglement entropies. So which are the quantum effects that I missed. So if you want, and so there are, there are, let me say in this way, at least this is my point of view. If you want, for example, also also what you did in your talk, for example, so you use indeed quite a GHD to compute the evolution of of your of your quasi part of your quasi particle to compute entanglement or whatever, but still you need some other tool to to say what are the correlation. So in my case, for example. So let me go back to the main slide, which may be so. So here, if you want to, if you from the point of view of GHD, the, the, the, the problem that we describe would just to say that just give these as initial condition, and that GHD would tell us how these initial conditions. So as far as I can understand that the initial condition is the Fermi C. So we know that is described by conformal theory that are correction that the case is power law and so on and so forth. Exactly, what I'm saying is that. So what is the, what is that I mean, what is more than that. What I'm saying is that what, what, what I would call GHD or what I would say that GHD is enough to describe is this initial condition, okay, which, which has, which has no fluctuation and nothing like that. Plus, and the GHD equation tells you how this initial condition evolves. The main thing is that now on top of that you can consider fluctuation, but not only this fluctuation, you also have to give an Hamiltonian or an action if you want, which makes them become quantum. Okay, and this is exactly what we give here. If you want, if you want, and I think that what you what what the way you would say this, and I would perfectly agree with you if you want, is that what we are doing is to transport in time initial correlations. And this I agree, but I don't agree on the fact that I don't agree on the fact that this is not what I would call a quantum theory. I was just wondering what is what I could get more with a quantum generalized aerodynamics instead of generalized aerodynamics. Yes, okay, so for example, how would you, for example, you said that in your in your talk that your quasi particle picture which already I find that I mean, already there I would not say this just a general dynamic would say this is a general dynamics plus complemented with the quasi particle picture. I mean, with. Okay, but, but apart this, you also say that, for example, you cannot, you cannot start from, from any, from any state that that you want, you know, because of the state too much entangled the chair, etc. What I'm saying is that there are correlations that that you can compute to just be in a very simple way by by the way, just because you know you know this Hamiltonian. So once you know this Hamiltonian you have a mapping for example, for example, in the free case in the unit of the tonsure are though. What happens is that you this Hamiltonian also also requires conformal invariance and so there you can you can use all the machinery to compute in a very simple, in a very simple way. I don't know any in particle density matrix correlation function or any correlation function basically computed entanglement as I showed. So I think that you do get something more in this sense. What you do you do not get is a and I stress, I think during the talk is that you are what we are not correcting that the GHD equation, but also, for example, not that these correlations that, for example, the density density correlation in the in the tonsure are though they are ordered. They contribute to they give it a correction if you, in my perspective, a quantum correction which are order order h bar square. And as you mentioned, and the other day in the non-interacting case you expect the first correction to the to the GHD equation to be to be proportional to the third derivative, right? So Okay, it's only for GHD. Then there are correlation of the state that I don't know. Exactly. No, no, exactly. No, no, exactly what I'm saying, but, but, but to say that Okay, okay, fine. I don't want to monopolize the discussions. Oh, yeah, no, no. Okay, we can discuss a little bit later, but to say that probably many situations I would expect this kind of correlation coming from the from the initial state if you want to be more important than the correction to the dynamics itself in GHD. I mean, I don't know, but So, okay, we're like a couple minutes behind, but I see we have one more question. Hopefully we can make it quick. Yeah. Should I go? Yes, yes. Okay, so just to remark on what Giuseppe asked, so the question you're writing is the Euler equation, right? The Navier-Stokes would be by adding the viscosities and this is what's required to add the diffusion. That's what Okay, okay. Sorry. I was not sure. Navier-Stokes and GHD with diffusion. I mean, it's not the moment to talk about. So for me, the question is very simple. So you're in this slide you show entanglement entropy. Yes. So actually what is, how do you define here the density entanglement? This would be the entanglement to be of a small interval at position X. This is, yes, you know, so this is this. So, if you, if you see here in each of these of this frame, the time is fixed, you see, and this is a function of X. So, yes, it's the entropy entanglement entropy from zero to X and the rest. Okay. But this doesn't grow to, I mean, it seems to From minus infinity to X. From minus infinity to X. But it remains of order one, right? You don't generate, you don't go to a No, well, no, in this case, you don't expect because basically you are starting from a ground state. So you start from the ground state of So you're starting from the ground state in the double well. And then you are quenching just the potential. So in this case, you don't expect to generate Okay, but this, so this you cannot get from quasi particle picture.   I'm not sure that is everything that is not a linear cannot be captured by what you are to a picture, I mean, a particular after this idea of working in a Carved space and whatever, but I don't think so. All right. Move on to the start though, since we have few minutes behind then we can leave question for the discussion session. So let's thank Paolo again.


What's going on everybody it stops here welcome back some other videos so in today's video We're going to be doing an overall market update taking a look at the Dow Jones the S&P 500 and the Nasdaq We're also going to be doing a trading update talking about what I did today in terms of my trades as well as talking about some stocks And ETFs that I'm personally watching and looking to trade here you guys in particular guys in this month of September in 2019 and if you guys want to skip to the you guys part for those of you guys that are not interested in the market update and Other stocks that I'm watching there's going to be a time stamp down below in the description So you can go click that and go to the part that you guys saw in the title and that you guys want to see so With that further ado guys hit that like button consider subscribing if you want to see further content for me And let's get right into the topics of today's video So the S&P 500 ended up closing the day down $20 and 19 cents today down point six nine percent closing the day briefly above 2906 or rather slightly above 2,900 rather at 2906 the Nasdaq right now guys is currently down 50 cents But this is the future if I pull up on my phone very quickly where exactly it ended up closing I can tell you guys it was down 88 points down 1.11 percent on the day the Dow Jones industrial average here down 285 points at the close down 1.08 percent closing the day at $26,100 so overall today guys the markets were affected by the tariff situation that Went live the tariffs went live between the US and China on September 1st We saw the futures go down on Sunday The futures were down on Monday, which was yesterday when the markets were closed and that kind of bled into the market today And we saw the results of the day down 1% roughly and you know all of the major Indexes that we track on this channel being the Dow the S&P and the Nasdaq so if we go back to the S&P guys to break down some technicals here and starting off on the one day actually maybe the five day five minute You guys can see we closed the day on the 30th at about let's say 26 or rather 2925 and you guys can see the gap down very clearly You know from the close on Friday to the open today on Tuesday. We gap down to about 2907 we dropped all the way down to about 2892 found a bit of a support at around 2890-2895 and then we ended up closing the day on a nice little upswing and some may argue You know the technicals don't lie here that this is a higher or low from the previous and this could be a Potential breakout spot for the S&P 500 and if we go to the 20 day one hour You guys can see that a bit more right we can see even if we extend this trend line a bit You can see actually no, that's not a good spot to start it. Let me start it down here. You can see That we kind of are holding a uptrend pattern here based on the past couple of weeks from the 15th of August We bottomed out at 2824 then we bottomed out at 2860 2875 towards the end of August right around this area this range right here And now it seems like we're bottoming out here again on the 20-day one-hour chart on top of these moving averages the 180 SMA and the 50 SMA as well as on top of that 2900 level of support and I was talking about The 2900 level of support and the group chat today and the discord chat And if you guys are not in that that is linked down below And I was talking about how this is a very critical level of support for the S&P 500 Just take a look over the past couple of months 2900 2900 was a resistance here We broke above it making it a support we pulled back we retested it We popped up we ended up breaking it here in the month of May We popped up above it held it again as a support back in June, right? We popped up to all-time highs to 3025 there and then for a little bit we held it here You know at 2900 as well until ultimately we broke down and triple bottomed at 2850 You know during the month of August and now it seems like again We're retesting that level and the fact that we closed above it despite us following below it today in the market During the trading session. That's a really good sign here that the S&P does want to potentially Rally back again. We saw in the five-day five minute You know this is looking pretty good the fact that we double bottomed here We broke above the 50 SMA. That's a good first sign now I would love to see a break out of the 180 SMA here on the five-day five minute before really Confirming that hey, we might be breaking out here. We may be pushing up maybe to 2940 again Maybe to 2950 we might be pushing for a higher high, you know, that's kind of what I'm watching here In terms of the S&P 500 if we're going over here to the NASDAQ And we start on the 184 hour you guys can see, you know Unlike the S&P actually, let me just double check that before I do make that statement Actually, no the S&P is still trading below the 180 SMA, but it's trading above the 50 SMA So it's actually trading below only one of the moving averages But the NQ right the NASDAQ is actually trading right now below both of the moving averages on the four-hour chart Both the 50 SMA and the 180 SMA So in my opinion for NASDAQ right to get back up to highs here to get above or rather just to break out at this point You know, we need to get a break above that 50 SMA and the 180 SMA that you guys see here on the 184 hour chart Overall, you can argue that we're holding this trend line as well that I just drew out for you guys You know from the sell-off in May, you know the beginning of June We started out at about 7,000 here on the NASDAQ right we pulled down 7,300 that was in the beginning of August higher low again in the middle of August another higher low towards the end of August Right and now in the beginning of September It seems like we're holding another higher low on top of this trend line again that I just drew for you guys So guys if we pop above this trend line tomorrow, let's let's say excuse me We break above the 180 SMA, you know This could be a very big breakout in terms of the NASDAQ, but the one thing that's kind of You know making me a bit skeptical that that's actually going to happen is the state of the economy that we're in The state of the trade war at the drop of a button guys literally Things can go down right if Trump tweets if more tariffs are slapped the market You know, even though the technicals are telling us hey We might be pushing up the market might dump because when things are going on in the macro economy And they're very very, you know harsh on the market like the trade war is the technicals go out the window for the most part Right, we may dump and then you know dump all the way down here to 74 30 again and be like, okay Now we're definitely not riding this trend now We're definitely not uptrending which is just honestly something to be Aware of and something to keep an eye on Especially when we're in these rocky time periods in the overall Economy and obviously in the stock market as well So that's kind of my thought here on the NQ if we break it down a little bit on some of these smaller charts You can see the trend line, you know, it's clearly riding it here as well Although it's very sloppy with all these lines everywhere. Just look at the cursor right here on the screen You know, it's riding that trend line from the longer-term chart But we're still trading below the moving averages here even on the one-hour chart And I'm sure on the five-day five-minute. We'll see a bunch of the same Yep, you guys can see under the moving averages on the five-day five-minute chart as well So what I'd look for for a breakout is a pop on the smaller time frame here the five-day five-minute Above the moving averages on the Nasdaq. So let's talk about the Dow Jones industrial average very quickly here guys Going over to the 184 hour You guys can see this is actually similar to the S&P We're trading trending above the 50 S&A, but we're still trending below the 180 S&A on the four-hour chart So we're kind of in between both of the moving averages here overall if we zoom in a bit We're holding the support at around $26,000 on the one day one minute we can see today we gap down We actually hit 26,000 and we had a triple bottom on it once twice three times That's a good sign here that hey we might be pushing up This could be a bullish move and that's exactly what we got right from there We popped on the intraday chart here the moving averages went from being resistance levels to being support levels We got the bullish cross here the 50 S&A crossing above the 180 S&A on the Dow intraday chart That is a good sign That's a good close for the Dow that hey We might potentially be filling up the gap tomorrow with the way this ended up closing and of course the futures guys are Super important watch the futures tomorrow pre-market if they're gapping up green There's a good chance the markets could run tomorrow, but let's say they're dumping right Let's say they're red that can mean the gap down might continue the downtrend that we've been on Really since today could continue right on the five day five minute you guys can see the markets have been going up But let's say you know the gap down continues tomorrow We'll most likely notice that from the futures being read in the beginning of the day and how the market Reacts and how the market goes through you know out the gate in the beginning of the day 930 a.m. Eastern Standard, and I'm sure it's obviously different time periods if you're in You know different parts of the world so Dow Jones guys, you know, we see on the five day five minute It's kind of holding this higher low here from the previous right kind of similar to the S&P on the 20 day You guys can see it's holding literally kind of the same pattern as the S&P because on the S&P We bottomed out on the 15th of August and then we made higher lows in the middle of August or towards the end of August Rather a couple of times. Let me just pull up the S&P. It's literally identical, right? Take a look at the S&P chart take a look at the Dow chart. It's literally identical So now the fact that we are breaking out of the moving averages here on the one-hour chart We're actually holding them as a support This is a pretty good sign that the Dow could end up popping and filling the gap tomorrow But we just have to watch these futures guys. We could end up popping up to 26400 that is a level of resistance that I'm seeing here, but just keep an eye on those futures So that's kind of the market breakdown for today I'd love to know what you guys have to think about the markets down below Is this a bull trap, you know, is this setting up for a potential, you know You know people might go long tomorrow and then the markets dump, you know, is this trapping us I would love to know what you guys have to think about that down below in the comment section So let's talk about very briefly what I did today and like I mentioned in my previous video I think I uploaded last on Sunday. I was in BAC Bank of America from last week I got in at around 2720 and when I saw the market futures down a pretty decent chunk on Sunday I was thinking to myself crap I'm in a bad trade right now because if the markets gap down like they did most likely BAC is going to gap down and I'm going to be red in my position. So I didn't make the smartest move by You know hopping into BAC knowing the tariffs are going to kick in that wasn't really a smart move on my part And I ended up losing a bit of money today on BAC because again, I didn't really thoroughly analyze it I didn't really think it through a hundred percent that does happen sometimes guys And if we go to the five day five minute you guys can see what I'm talking about So I got in I believe it was this day or this day whichever day that doesn't really matter But my average cost was 2720 right I got into BAC and I held it over the weekend And then boom it fell right off the cliff hitting lows at about $26 and 70 cents and you guys can see you know if my average cost is 2720 You know 2725 it's a roughly around that area You know if we're going down if we're selling off to 2672, you know I'm already down 2% at that point, but the fact that we jumped out of the gate Very aggressively selling off. I just cut my losses guys to be honest I just cut the losses right here because this was extremely aggressive. This was not even Consolidating it seems like every time it tried to consolidate and maybe pop up it got hit It got rejected even harder and the selling started to kick in very very aggressively So I just took a little bit of a loss like I said in Sunday's video I kind of predicted that I was going to do this to be honest because again the futures were down I figured BAC would be down and I would want to hop out just to be safe. That's exactly what I ended up doing I didn't lose a lot of money Right. I think I got out at about like 2690 right around here, you know 2690 up to about 2720 You can see that's about a 1.1 1.2% loss and that's okay guys You know sometimes you lose money of course sometimes you make money. It's all a part of the game here So despite me losing money on BAC, it's actually one of the stocks I'm going to be watching here on this potential pullback as a potential swing trade again Right, this could be an entry point tomorrow opening up an entry point if we do end up holding $27 holding this 180 SMA support tomorrow on this one-hour chart like we are right now at the close of the market I think this could be a very good opportunity for a reentry and that's sometimes how it works guys You know you take a little loss on a stock, right? You play it safe and then you look at the stock again for potential reentry It's not revenge trading It's making a sound decision if the stock's actually looking good again, right? If it was you know looking crappy down trending I'm not I would obviously not hop into it But the fact that it is looking like it's holding a higher low here despite the massive dip Holding you know the 180 SMA and on the smaller time frames. It's looking pretty decent as well this breakout above the 50 SMA This is giving me some signs that hey, this might be a good opportunity to re-enter But I'm going to wait and see how it goes tomorrow how it's moving pre-market. That's very very important So that's actually one that I'm watching so that's one breakdown of a stock there You guys is another one that you guys saw in the title that I'm watching very heavily and if you guys watch my video on Sunday What are we talking about with natural gas guys? It's literally coming to life right now? It's coming into fruition. We were talking about the $2 and 40 cent Resistance and we zoom in here and I'll show you guys even further here and explain what I'm talking about So we saw moving back a little bit, you know rewinding a little bit 230 was a very strong resistance on natural gas, right? We noticed how in June it was a strong resistance We dip below it then pop making it a new support and then in July the middle of July We broke 230 making it a resistance again And we actually got rejected towards the end of July again before selling off very frantically to two dollars and two cents on Natural gas and we also got rejected again at 230 in the beginning of August So there were multiple rejections in the past three four months on Natural gas really the past three months at 230 and now that we've been reversing to the upside 50 SMA is crossing the 180 SMA on the 184 hour chart. That's a bullish move there we've been making higher lows ever since we bottomed down at 202 and Again, we popped above 230 That's a good sign that we could be filling the gap back up to two dollars and forty cents here Notice how we actually pulled down was this today? Yes, this was today We pulled down and we confirmed 230 as a new support and we pushed to this high or high to 236 which is extremely Extremely important guys when I see a stock ETF future whatever it may be when it breaks out of a resistance the next thing I want to see it do is pull down and Confirm that resistance as a new support or that old resistance as a new support, right? And natural gas did exactly that today, which is making you guys honestly the most Valuable ETF in my opinion or ETN rather over these next couple of days as long as Natural gas holds the trend that it's on right now and for those of you guys I don't know what I'm talking about with natural gas and you guys will you guys as an ETF or an ETM that trades based upon Natural gas it goes up whenever natural gas is going up at a 3x rate So let's say natural gas is up 3% you guys is going to be up 9% right? That's how it works. So here we can see exactly what I'm talking about We actually double bottom triple bottom that actually maybe even a quadruple bottom here On 230 as a new support one at 9 0 5 a.m. Yesterday on Monday Another one 6 p.m. Yesterday on Monday and another one this morning 5 25 a.m This is all Eastern Standard Time on Tuesday and then another one when the market was about to open at about 8 45 a.m And that's when we shot up and pushed to that high or high really just confirming and continuing the uptrend So this is looking very juicy to me guys honestly if we go back to the 184 hour We might be pulling back a bit as you're seeing here this red candlestick We might be pulling back a bit maybe 233 whatever it may be low 230s But this could be a perfect entry point dip by on you guys if natural gas continues the trend and fills up to 240 And let's go to you guys very quickly and see You know you guys was up 8% today at one point I think it was up 10 11% so you can see how big this moves when natural gas makes You know a decent move because again, it's a 3x Leveraged ETN so you can see on the 20 day, you know from $10 up to $16 That's quite a move over the past roughly month at this point And if natural gas does make that pull back to the low 230s, you know this could go down to the low 15s Maybe maybe 15 20 maybe 15 30 and this could be a very good dip by especially if we hold the 50s to may as a Support and especially if natural gas again continues its trend So that's kind of what I'm watching here with you guys and with natural gas Let's say we pop above 240, you know We have to hold that as a support and that point in time You know if we do then the next level I'm going to be watching on natural gas is going to be around 248 to 250 which was a resistance from back in the beginning of July in 2019 so those are you know really the main Points that I wanted to get across, you know regarding to you guys and regarding to Natural gas that's what I'm watching. That's personally what I'm waiting for to get into this trade I want to see a pullback potentially on natural gas and then get in on the dip Tomorrow hopefully if everything does end up playing out So the next stock I want to talk about let me pull up my phone because I am blanking out right now and what that stock is Okay, okay, okay Apple guys a APL Apple is under pressure right now There's no lie about that because Apple has a lot of its business tied up in China the China and the US Relationship the Chinese the US relationship right now obviously isn't great That's putting a lot of a damper on Apple and I feel like it's kind of putting a cap on the stock right now On Apple right we can see you know the stock's not been doing well over the past couple of weeks It's really not been going anywhere, but judging on the 20-day one hour This could potentially be a point where we might see a little bit of a move to the Upside here and I actually drew these trend lines like a couple Like probably a week ago and it ended up playing out exactly to these trend lines. Look no joke guys I didn't draw this before this video. This was like a month or like a week ago Whatever, but just showing you guys, you know, we went down we popped up Now we could do this right we could dump here If we break the trend line that I just drew and the fact that we're holding the trend line that I just drew Into the market closed today. This could be a point in time where we potentially ride back up and retest $210 if we pop and break the 50 and the 180 SMA here on the one-hour chart This is very possible, right? We have to see if it's gapping up pre-market tomorrow if the markets are green tomorrow This is probably going to be a safe quote-unquote safe mini swing trade Back up to $210 because if the markets rally for a day or two Apple could be very very good trade a very attractive position here again Nothing safe guys. That's why I put the quotations, right? Nothing is safe in the market But this to $210 markets green Apple usually does well when the markets are green That is something that could definitely happen here But if we break the trend that I just drew, you know If we start pushing down this trend line that I drew last week might end up playing out And at that point put options could be a decent play shorting the stock Although I never short stocks that could be a good play for you, maybe and Honestly, I won't be looking to swing trade it if that does end up happening So Apple I'm watching it But certain things have to fall into place certain puzzle pieces have to line up You know for this to end up being a trade tomorrow But of course, I'll let you guys know and we'll be talking about it, you know in the discord chat So one more actually two more very quickly before I do end off this video I know this video is probably long right now, but all you loyal subscribers that are watching out there I really appreciate you guys. You guys are the best you guys are awesome in video This is actually a short term a short potential put option play a short play if this ends up breaking the You know the support of this wedge that I've drawn out here and I actually drew this out And I was thinking to myself, you know in video really could do one of two things at this point If we zoom in a bit you can see this wedge that I'm talking about right We hit a low of 130 popped up here to a high at about 176 over the past couple of months We pulled down held the higher low at 150 we popped and we made a lower high from the previous at 177 right, you know the lower high at 170 we hit another lower high at about 168 putting us in this wedge because we're making higher highs or rather we're making higher lows But at the same time we're making lower highs. So depending on which side we pop here on Nvidia If we break out of the resistance, this could be bullish right very bullish But if we break below the support here, you know if we break down into the 150s This could be a very good put option a very good short play Honestly that I'm going to be watching heavily guys, but at this point, you know Nvidia I feel like one of the moves up when it moves green It's on fire right but then when it moves down when it's red it gets bashed guys It gets bashed five percent in a day down five percent the next day It just gets killed right we can see, you know Multiple scenarios of when the stock dropped heavily and the matter of a couple of trading days, right? You know from 178 on the 23rd of July and went all the way down to 145 on the 5th of August That's like a 10-day move. It went down 30 bucks a share. That's insane, right? We can see here, you know back in May it went from 170 all the way down to 130 So this stock moves down heavily, which is why I'm thinking if it makes this downwards move here This could be a very critical, you know break and a very bearish Sign right that it might start selling off aggressively again Which we can profit on that downside if you know how to trade The downside right which is very important as well, but probably a bit more advanced, you know An advanced strategy out there, which is you know trading options and trading Short doing going short rather which I never do right. I never go short. I do put options Sometimes right on long-term positions or stocks that are looking like they have a lot of downside and in video This could definitely be one, you know, if we do get into that scenario that I just talked about So j-nug guys before I end off j-nug is one more that I want to talk about I talked about this one on sunday's video ended up playing out perfectly to the way I talked about it But I never got into it But we held that 50 sma on the four hour we popped above it now It seems like we're fiddling with 95 96, which is a resistance from last week, right? We're fiddling around that area and gold if we look at gold very quickly guys We can see gold actually popped and it's retesting that resistance level at about 15 55 15 60 that rough general area. So we might pull down on gold. We might hold that 50 sma as a support again We might hold 15 45 who knows right but gold and gdx They need to continue to move gdx is what really j-nug trades based upon right gdx goes up J-nugs going up as well So if gdx and gold continue to move if the markets get rocky, right the markets go down People are flooding to gold j-nug could continue to be a very good play And you know, honestly j-nug might be touching a hundred bucks again very very soon But be careful right if the markets go green, right? You know gold might go down a bit in the near term Which is why it's super important and as you guys probably have realized I watch stocks and I have different, you know trading strategies for different scenarios in the market So I'm thinking okay the markets go up if you know You know the trade war, you know the sentiment becomes a bit more positive Which I don't think it's going to but hypothetically speaking here You know apple could be a swing trade that I'm looking at from 205 to 210 But let's say the markets end up getting rocky volatile gold starts to push Because that's what usually happens when the markets get rocky and volatile I have j-nug right I have j-nug that I can go to and make money on the downside And of course I have market ETFs that I watch TV IX is a volatility etn Goes up when the markets go down when there's a lot of volatility So it's very important to just have a bunch of different Plans lined up strategies lined up for different scenarios in the market So you can make money when the markets are green you can make money when the markets are red That's very very important So I'm going to wrap up the video here guys if you enjoyed it If you found value in it feel free to go down below and hit that like button Consider subscribing if you want to see further content for me and drop a comment down below Let me know your thoughts on the market. What are you trading? What stocks are you watching coming up and where's the market going guys? I want to know your opinion. Is it going red right now? Is it going green? Let me know down below. So I'll catch you all in the next video I appreciate all of you guys watching you mean a lot to me. Peace out