<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:x="urn:schemas-microsoft-com:office:excel" xmlns:st1="urn:schemas-microsoft-com:office:smarttags" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv=Content-Type content="text/html; charset=us-ascii">
<meta name=Generator content="Microsoft Word 11 (filtered medium)">
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="PlaceType"/>
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="PlaceName"/>
<o:SmartTagType namespaceuri="urn:schemas-microsoft-com:office:smarttags"
name="place"/>
<!--[if !mso]>
<style>
st1\:*{behavior:url(#default#ieooui) }
</style>
<![endif]-->
<style>
<!--
/* Font Definitions */
@font-face
{font-family:Batang;
panose-1:2 3 6 0 0 1 1 1 1 1;}
@font-face
{font-family:"\@Batang";
panose-1:0 0 0 0 0 0 0 0 0 0;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman";}
a:link, span.MsoHyperlink
{color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{color:purple;
text-decoration:underline;}
span.EmailStyle17
{mso-style-type:personal-compose;
font-family:Arial;
color:windowtext;}
@page Section1
{size:595.3pt 841.9pt;
margin:56.7pt 42.5pt 56.7pt 85.05pt;}
div.Section1
{page:Section1;}
-->
</style>
</head>
<body lang=RU link=blue vlink=purple>
<div class=Section1>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>Hello all,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>I am trying to understand the meaning of some
variables in the source code of QE. Particularly, it is not clear what is the
meaning of the (3*nat, 3*nat) matrix u in phonon and electron-phonon
calculations. In the output file generated by the subroutine phq_summary.f90
the columns of this matrix are referred to as “phonon
polarizations” – i.e. they are supposed to be eigenvectors of the
dynamical matrix. <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>I consider the case when nat = 2 (two atoms in the
unit cell), so the eigenvectors are 6-dimentional (3*nat=6) and there are six
of them. I was told that in the case nat = 2 the components have the following
meaning: (1x, 1y, 1z, 2x, 2y, 2z) – Cartesian components of deviations
for both atoms.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>Now, in the output file generated by phq_summary.f90
for q=0, regardless of degeneracy of branches, there is always only one nonzero
component. For instance, the first eigenvector is (-1,0,0,0,0,0). Obviously,
all six eigenvectors are orthonormal, which is how it’s supposed to be.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>But here is what bothers me. For acoustic phonon
modes, the unit cell moves as a whole, i.e. both atoms must move with the same
phase. So I expect to see something like (1/sqrt(2),0,0, 1/sqrt(2),0,0),
instead of (-1,0,0,0,0,0). For optical branches on the other hand, two atoms
have the opposite phase (the center of mass of the unit cell does not move), so
I would expect to see something like (1/sqrt(2),0,0, -1/sqrt(2),0,0). My
understanding is this: if every eigenvector has only one nonzero component, it
means that in each mode, one atom is not moving at all!<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>Maybe, I misunderstood the meaning of components of
the matrix u? <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'>I apologize for this lengthy explanation. And I would
really appreciate any help.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span lang=EN-US style='font-size:
10.0pt;font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-US
style='font-size:10.0pt;font-family:Arial;color:navy'>Best regards,<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-US
style='font-size:10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-US
style='font-size:10.0pt;font-family:Arial;color:navy'>Kostyantyn Borysenko<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span lang=EN-US
style='font-size:10.0pt;font-family:Arial;color:navy'>Electrical and Computer Engineering
Department<o:p></o:p></span></font></p>
<p class=MsoNormal><st1:place w:st="on"><st1:PlaceName w:st="on"><font size=2
color=navy face=Arial><span lang=EN-US style='font-size:10.0pt;font-family:
Arial;color:navy'>North Carolina</span></font></st1:PlaceName><font size=2
color=navy face=Arial><span lang=EN-US style='font-size:10.0pt;font-family:
Arial;color:navy'> <st1:PlaceType w:st="on">State</st1:PlaceType> <st1:PlaceType
w:st="on">University</st1:PlaceType></span></font></st1:place><font size=2
color=navy face=Arial><span lang=EN-US style='font-size:10.0pt;font-family:
Arial;color:navy'><o:p></o:p></span></font></p>
</div>
</body>
</html>