---
abstract: 'An article usually includes an abstract, a concise summary of the work covered at length in the main body of the article. It is used for secondary publications and for information retrieval purposes.'
author:
- 'A. Author'
- 'B. Author'
- 'C. Author'
bibliography:
- 'aipsamp.bib'
nocite: '[@*]'
title: |
    Sample Title:\
    with Forced Linebreak[^1]
---

[^2]

> The “lead paragraph” is encapsulated with the LaTeX  `quotation` environment and is formatted as a single paragraph before the first section heading. (The `quotation` environment reverts to its usual meaning after the first sectioning command.) Note that numbered references are allowed in the lead paragraph. The lead paragraph will only be found in an article being prepared for the journal *Chaos*.

\[sec:level1\]First-level heading:\
The line break was forced \\\\
===================================

This sample document demonstrates proper use of REVTeX 4.2 (and ) in manuscripts prepared for submission to AIP journals. Further information can be found in the documentation included in the distribution or available at <http://authors.aip.org> and in the documentation for REVTeX 4.2 itself.

When commands are referred to in this example file, they are always shown with their required arguments, using normal TeX format. In this format, `#1`, `#2`, etc. stand for required author-supplied arguments to commands. For example, in `\section{#1}` the `#1` stands for the title text of the author’s section heading, and in `\title{#1}` the `#1` stands for the title text of the paper.

Line breaks in section headings at all levels can be introduced using \\\\. A blank input line tells TeX that the paragraph has ended.

\[sec:level2\]Second-level heading: Formatting
----------------------------------------------

This file may be formatted in both the `preprint` (the default) and `reprint` styles; the latter format may be used to mimic final journal output. Either format may be used for submission purposes; however, for peer review and production, AIP will format the article using the `preprint` class option. Hence, it is essential that authors check that their manuscripts format acceptably under `preprint`. Manuscripts submitted to AIP that do not format correctly under the `preprint` option may be delayed in both the editorial and production processes.

The `widetext` environment will make the text the width of the full page, as on page . (Note the use the `\pageref{#1}` to get the page number right automatically.) The width-changing commands only take effect in `twocolumn` formatting. It has no effect if `preprint` formatting is chosen instead.

### \[sec:level3\]Third-level heading: Citations and Footnotes

Citations in text refer to entries in the Bibliography; they use the commands `\cite{#1}` or `\onlinecite{#1}`. Because REVTeX uses the `natbib` package of Patrick Daly, its entire repertoire of commands are available in your document; see the `natbib` documentation for further details. The argument of `\cite` is a comma-separated list of *keys*; a key may consist of letters and numerals.

By default, citations are numerical; [@feyn54] author-year citations are an option. To give a textual citation, use `\onlinecite{#1}`: (Refs. ). REVTeX “collapses” lists of consecutive numerical citations when appropriate. REVTeX provides the ability to properly punctuate textual citations in author-year style; this facility works correctly with numerical citations only with `natbib`’s compress option turned off. To illustrate, we cite several together [@feyn54; @witten2001; @epr; @Berman1983], and once again (Refs. ). Note that, when numerical citations are used, the references were sorted into the same order they appear in the bibliography.

A reference within the bibliography is specified with a `\bibitem{#1}` command, where the argument is the citation key mentioned above. `\bibitem{#1}` commands may be crafted by hand or, preferably, generated by using BibTeX. The AIP styles for REVTeX 4 include BibTeX style files `aipnum.bst` and `aipauth.bst`, appropriate for numbered and author-year bibliographies, respectively. REVTeX 4 will automatically choose the style appropriate for the document’s selected class options: the default is numerical, and you obtain the author-year style by specifying a class option of `author-year`.

This sample file demonstrates a simple use of BibTeX  via a `\bibliography` command referencing the `aipsamp.bib` file. Running BibTeX (in this case `bibtex aipsamp`) after the first pass of LaTeX produces the file `aipsamp.bbl` which contains the automatically formatted `\bibitem` commands (including extra markup information via `\bibinfo` commands). If not using BibTeX, the `thebibiliography` environment should be used instead.

#### Fourth-level heading is run in.

Footnotes are produced using the `\footnote{#1}` command. Numerical style citations put footnotes into the bibliography[^3]. Author-year and numerical author-year citation styles (each for its own reason) cannot use this method. Note: due to the method used to place footnotes in the bibliography, *you must re-run BibTeX every time you change any of your document’s footnotes*.

Math and Equations
==================

Inline math may be typeset using the `$` delimiters. Bold math symbols may be achieved using the `bm` package and the `\bm{#1}` command it supplies. For instance, a bold $\alpha$ can be typeset as `$\bm{\alpha}$` giving $\bm{\alpha}$. Fraktur and Blackboard (or open face or double struck) characters should be typeset using the `\mathfrak{#1}` and `\mathbb{#1}` commands respectively. Both are supplied by the `amssymb` package. For example, `$\mathbb{R}$` gives $\mathbb{R}$ and `$\mathfrak{G}$` gives $\mathfrak{G}$

In LaTeX there are many different ways to display equations, and a few preferred ways are noted below. Displayed math will center by default. Use the class option `fleqn` to flush equations left.

Below we have numbered single-line equations, the most common kind: $$\begin{aligned}
\chi_+(p)\alt{\bf [}2|{\bf p}|(|{\bf p}|+p_z){\bf ]}^{-1/2}
\left(
\begin{array}{c}
|{\bf p}|+p_z\\
px+ip_y
\end{array}\right)\;,
\\
\left\{%
 \openone234567890abc123\alpha\beta\gamma\delta1234556\alpha\beta
 \frac{1\sum^{a}_{b}}{A^2}%
\right\}%
\label{eq:one}.\end{aligned}$$ Note the open one in Eq. (\[eq:one\]).

Not all numbered equations will fit within a narrow column this way. The equation number will move down automatically if it cannot fit on the same line with a one-line equation: $$\left\{
 ab12345678abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta
 \frac{1\sum^{a}_{b}}{A^2}%
\right\}.$$

When the `\label{#1}` command is used \[cf. input for Eq. (\[eq:one\])\], the equation can be referred to in text without knowing the equation number that TeX will assign to it. Just use `\ref{#1}`, where `#1` is the same name that used in the `\label{#1}` command.

Unnumbered single-line equations can be typeset using the `\[`, `\]` format: $$g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow
q^+g^+g^+ \dots ~.$$

Multiline equations
-------------------

Multiline equations are obtained by using the `eqnarray` environment. Use the `\nonumber` command at the end of each line to avoid assigning a number: $$\begin{aligned}
{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1}
\delta_{\sigma_1,-\sigma_2}
(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\
&&\times
[\epsilon_jl_i\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1),\end{aligned}$$ $$\begin{aligned}
\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2}
        (N^2-1)\nonumber \\
 & &\times \left( \sum_{i<j}\right)
  \sum_{\text{perm}}
 \frac{1}{S_{12}}
 \frac{1}{S_{12}}
 \sum_\tau c^f_\tau~.\end{aligned}$$ **Note:** Do not use `\label{#1}` on a line of a multiline equation if `\nonumber` is also used on that line. Incorrect cross-referencing will result. Notice the use `\text{#1}` for using a Roman font within a math environment.

To set a multiline equation without *any* equation numbers, use the `\begin{eqnarray*}`, `\end{eqnarray*}` format: $$\begin{aligned}
\sum \vert M^{\text{viol}}_g \vert ^2&=&g^{2n-4}_S(Q^2)~N^{n-2}
        (N^2-1)\\
 & &\times \left( \sum_{i<j}\right)
 \left(
  \sum_{\text{perm}}\frac{1}{S_{12}S_{23}S_{n1}}
 \right)
 \frac{1}{S_{12}}~.\end{aligned}$$ To obtain numbers not normally produced by the automatic numbering, use the `\tag{#1}` command, where `#1` is the desired equation number. For example, to get an equation number of (\[eq:mynum\]), $$g^+g^+ \rightarrow g^+g^+g^+g^+ \dots ~,~~q^+q^+\rightarrow
q^+g^+g^+ \dots ~. \tag{2.6$'$}\label{eq:mynum}$$

A few notes on `\tag{#1}`. `\tag{#1}` requires `amsmath`. The `\tag{#1}` must come before the `\label{#1}`, if any. The numbering set with `\tag{#1}` is *transparent* to the automatic numbering in REVTeX; therefore, the number must be known ahead of time, and it must be manually adjusted if other equations are added. `\tag{#1}` works with both single-line and multiline equations. `\tag{#1}` should only be used in exceptional case - do not use it to number all equations in a paper.

Enclosing single-line and multiline equations in `\begin{subequations}` and `\end{subequations}` will produce a set of equations that are “numbered” with letters, as shown in Eqs. (\[subeq:1\]) and (\[subeq:2\]) below:

\[eq:whole\] $$\left\{
 abc123456abcdef\alpha\beta\gamma\delta1234556\alpha\beta
 \frac{1\sum^{a}_{b}}{A^2}
\right\},\label{subeq:1}$$ $$\begin{aligned}
{\cal M}=&&ig_Z^2(4E_1E_2)^{1/2}(l_i^2)^{-1}
(g_{\sigma_2}^e)^2\chi_{-\sigma_2}(p_2)\nonumber\\
&&\times
[\epsilon_i]_{\sigma_1}\chi_{\sigma_1}(p_1).\label{subeq:2}\end{aligned}$$

Putting a `\label{#1}` command right after the `\begin{subequations}`, allows one to reference all the equations in a subequations environment. For example, the equations in the preceding subequations environment were Eqs. (\[eq:whole\]).

### Wide equations

The equation that follows is set in a wide format, i.e., it spans across the full page. The wide format is reserved for long equations that cannot be easily broken into four lines or less:

$${\cal R}^{(\text{d})}=
 g_{\sigma_2}^e
 \left(
   \frac{[\Gamma^Z(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2}
  +\frac{[\Gamma^Z(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2}
 \right)
 + x_WQ_e
 \left(
   \frac{[\Gamma^\gamma(3,21)]_{\sigma_1}}{Q_{12}^2-M_W^2}
  +\frac{[\Gamma^\gamma(13,2)]_{\sigma_1}}{Q_{13}^2-M_W^2}
 \right)\;. \label{eq:wideeq}$$

This is typed to show the output is in wide format. (Since there is no input line between `\equation` and this paragraph, there is no paragraph indent for this paragraph.)

Cross-referencing
=================

REVTeX will automatically number sections, equations, figure captions, and tables. In order to reference them in text, use the `\label{#1}` and `\ref{#1}` commands. To reference a particular page, use the `\pageref{#1}` command.

The `\label{#1}` should appear in a section heading, within an equation, or in a table or figure caption. The `\ref{#1}` command is used in the text where the citation is to be displayed. Some examples: Section \[sec:level1\] on page , Table \[tab:table1\],

  Left[^4]    Centered[^5]    Right
  ---------- -------------- -------
  1                2              3
  10               20            30
  100             200           300

  : \[tab:table1\]This is a narrow table which fits into a text column when using `twocolumn` formatting. Note that REVTeX 4 adjusts the intercolumn spacing so that the table fills the entire width of the column. Table captions are numbered automatically. This table illustrates left-aligned, centered, and right-aligned columns.

and Fig. \[fig:epsart\].

Figures and Tables
==================

Figures and tables are typically “floats”; LaTeX determines their final position via placement rules. LaTeX isn’t always successful in automatically placing floats where you wish them.

Figures are marked up with the `figure` environment, the content of which imports the image (`\includegraphics`) followed by the figure caption (`\caption`). The argument of the latter command should itself contain a `\label` command if you wish to refer to your figure with `\ref`.

Import your image using either the `graphics` or `graphix` packages. These packages both define the `\includegraphics{#1}` command, but they differ in the optional arguments for specifying the orientation, scaling, and translation of the figure. Fig. \[fig:epsart\]

![\[fig:epsart\] A figure caption. The figure captions are automatically numbered.](fig_1)

is small enough to fit in a single column, while Fig. \[fig:wide\]

![image](fig_2)

is too wide for a single column, so instead the `figure*` environment has been used.

The analog of the `figure` environment is `table`, which uses the same `\caption` command. However, you should type your caption command first within the `table`, instead of last as you did for `figure`.

The heart of any table is the `tabular` environment, which represents the table content as a (vertical) sequence of table rows, each containing a (horizontal) sequence of table cells. Cells are separated by the `&` character; the row terminates with `\\`. The required argument for the `tabular` environment specifies how data are displayed in each of the columns. For instance, a column may be centered (`c`), left-justified (`l`), right-justified (`r`), or aligned on a decimal point (`d`). (Table \[tab:table4\]

[ccddd]{} One&Two&&&\
one&two&&&\
He&2& 2.77234 & 45672. & 0.69\
C[^6] &C[^7] & 12537.64 & 37.66345 & 86.37\

illustrates the use of decimal column alignment.)

Extra column-spacing may be be specified as well, although REVTeX 4 sets this spacing so that the columns fill the width of the table. Horizontal rules are typeset using the `\hline` command. The doubled (or Scotch) rules that appear at the top and bottom of a table can be achieved by enclosing the `tabular` environment within a `ruledtabular` environment. Rows whose columns span multiple columns can be typeset using LaTeX’s `\multicolumn{#1}{#2}{#3}` command (for example, see the first row of Table \[tab:table3\]).

  ----- ------------------- ------------------- ------------------- -------------------
                                                                    
   Ion    1st alternative     2nd alternative     lst alternative     2nd alternative
    K       $(2e)+(2f)$           $(4i)$            $(2c)+(2d)$           $(4f)$
   Mn       $(2g)$[^8]       $(a)+(b)+(c)+(d)$        $(4e)$            $(2a)+(2b)$
   Cl    $(a)+(b)+(c)+(d)$      $(2g)$[^9]       $(4e)^{\text{a}}$  
   He    $(8r)^{\text{a}}$   $(4j)^{\text{a}}$   $(4g)^{\text{a}}$  
   Ag                        $(4k)^{\text{a}}$                       $(4h)^{\text{a}}$
  ----- ------------------- ------------------- ------------------- -------------------

The tables in this document illustrate various effects. Tables that fit in a narrow column are contained in a `table` environment. Table \[tab:table3\] is a wide table, therefore set with the `table*` environment. Lengthy tables may need to break across pages. A simple way to allow this is to specify the `[H]` float placement on the `table` or `table*` environment. Alternatively, using the standard  package `longtable` gives more control over how tables break and allows headers and footers to be specified for each page of the table. An example of the use of `longtable` can be found in the file `summary.tex` that is included with the REVTeX 4 distribution.

There are two methods for setting footnotes within a table (these footnotes will be displayed directly below the table rather than at the bottom of the page or in the bibliography). The easiest and preferred method is just to use the `\footnote{#1}` command. This will automatically enumerate the footnotes with lowercase roman letters. However, it is sometimes necessary to have multiple entries in the table share the same footnote. In this case, create the footnotes using `\footnotemark[#1]` and `\footnotetext[#1]{#2}`. `#1` is a numeric value. Each time the same value for `#1` is used, the same mark is produced in the table. The `\footnotetext[#1]{#2}` commands are placed after the `tabular` environment. Examine the LaTeX source and output for Tables \[tab:table1\] and \[tab:table2\]

        $r_c$ (Å)   $r_0$ (Å)   $\kappa r_0$        $r_c$ (Å)   $r_0$ (Å)   $\kappa r_0$
  ---- ----------- ----------- -------------- ---- ----------- ----------- --------------
   Cu     0.800       14.10        2.550       Sn     0.680       1.870        3.700
   Ag     0.990       15.90        2.710       Pb     0.450       1.930        3.760
   Au     1.150       15.90        2.710       Ca     0.750       2.170        3.560
   Mg     0.490       17.60        3.200       Sr     0.900       2.370        3.720
   Zn     0.300       15.20        2.970       Li     0.380       1.730        2.830
   Cd     0.530       17.10        3.160       Na     0.760       2.110        3.120
   Hg     0.550       17.80        3.220       K      1.120       2.620        3.480
   Al     0.230       15.80        3.240       Rb     1.330       2.800        3.590
   Ga     0.310       16.70        3.330       Cs     1.420       3.030        3.740
   In     0.460       18.40        3.500       Ba     0.960       2.460        3.780
   Tl     0.480       18.90        3.550                                   

  : \[tab:table2\]A table with more columns still fits properly in a column. Note that several entries share the same footnote. Inspect the LaTeX input for this table to see exactly how it is done.

for an illustration.

All AIP journals require that the initial citation of figures or tables be in numerical order. LaTeX’s automatic numbering of floats is your friend here: just put each `figure` environment immediately following its first reference (`\ref`), as we have done in this example file.

We wish to acknowledge the support of the author community in using REVTeX, offering suggestions and encouragement, testing new versions, ….

Appendixes
==========

To start the appendixes, use the `\appendix` command. This signals that all following section commands refer to appendixes instead of regular sections. Therefore, the `\appendix` command should be used only once—to set up the section commands to act as appendixes. Thereafter normal section commands are used. The heading for a section can be left empty. For example,

    \appendix
    \section{}

will produce an appendix heading that says “APPENDIX A” and

    \appendix
    \section{Background}

will produce an appendix heading that says “APPENDIX A: BACKGROUND” (note that the colon is set automatically).

If there is only one appendix, then the letter “A” should not appear. This is suppressed by using the star version of the appendix command (`\appendix*` in the place of `\appendix`).

A little more on appendixes
===========================

Observe that this appendix was started by using

    \section{A little more on appendixes}

Note the equation number in an appendix: $$E=mc^2.$$

\[app:subsec\]A subsection in an appendix
-----------------------------------------

You can use a subsection or subsubsection in an appendix. Note the numbering: we are now in Appendix \[app:subsec\].

### \[app:subsubsec\]A subsubsection in an appendix

Note the equation numbers in this appendix, produced with the subequations environment:

$$\begin{aligned}
E&=&mc, \label{appa}
\\
E&=&mc^2, \label{appb}
\\
E&\agt& mc^3. \label{appc}\end{aligned}$$

They turn out to be Eqs. (\[appa\]), (\[appb\]), and (\[appc\]).

[^1]: Error!

[^2]: Footnote to title of article.

[^3]: Automatically placing footnotes into the bibliography requires using BibTeX to compile the bibliography.

[^4]: Note a.

[^5]: Note b.

[^6]: Some tables require footnotes.

[^7]: Some tables need more than one footnote.

[^8]: The $z$ parameter of these positions is $z\sim\frac{1}{4}$.

[^9]: This is a footnote in a table that spans the full page width in `twocolumn` mode. It is supposed to set on the full width of the page, just as the caption does.
