By considering a chain of atoms, this value for phonons in 1 dimension can be found to be the inverse of the quantity pi times the group velocity.
One algorithm used for computing this quantity relies on a random walk to produce a flat histogram; that algorithm, named after Wang and Landau, is useful when using the multicanonical ensemble, as it uses the inverse of this quantity for the sampling distribution. For a particle in a 3-dimensional box, this quantity can be visualized as the surface area of an octant of a sphere, and in N dimensional k-space it can be visualized as the shell of an N-1 dimensional sphere. (*) By considering a chain of atoms, this value for phonons in 1 dimension can be found to be the inverse of the quantity pi times the group velocity. This quantity is constant for electrons confined to two dimensions, and varies directly with the applied magnetic field within the Landau levels induced during the de Haas-van Alphen effect. The integral of the product of the distribution function with this quantity with respect to energy yields the particle number. For 10 points, name this quantity, which describes the configurational size of a region in energy space.
One algorithm used for computing this quantity relies on a random walk to produce a flat histogram; that algorithm, named after Wang and Landau, is useful when using the multicanonical ensemble, as it uses the inverse of this quantity for the sampling distribution.
density of states