<HTML><BODY style="word-wrap: break-word; -khtml-nbsp-mode: space; -khtml-line-break: after-white-space; ">Eric: do not be satisfied by meaningful answer to your meaningful and legitimate questions. You have to *understand* them (i.e. do not stop thinking and striving to understand, until answers given by others sound to you as YOUR answers. Keep asking yourself questions until you are sure that you can answer all of them). <DIV><BR class="khtml-block-placeholder"></DIV><DIV>Signed: Grandad<DIV><BR class="khtml-block-placeholder"></DIV><DIV>Coming now to your present doubt. You have to understand here that what is arbitrary here is the overall _phase_ of the eigenvectors. This obviously implies (in some sense) that the imaginary part is arbitrary, but *NOT* that it can (always) be neglected, as this specic case shows. What has to be nonzero is NOT the real part of the eigenvector, but its modulus.</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Is it clearer now? Could you answer similar questions by yourself in the future?</DIV><DIV><BR class="khtml-block-placeholder"></DIV><DIV>Signed: Stefano B.</DIV><DIV><BR class="khtml-block-placeholder"><DIV><BR><DIV><DIV>On Aug 31, 2006, at 6:07 AM, Eric Abel wrote:</DIV><BR class="Apple-interchange-newline"><BLOCKQUOTE type="cite"><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Hello PWSCF users,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">I have a question which is sort of a follow-up to a similar question which I asked previously.<SPAN class="Apple-converted-space"> </SPAN>Anyway, I was wondering about the imaginary part of the phonon eigenvectors, which at the time, Stefano had informed me are more or less arbitrary. <SPAN class="Apple-converted-space"> </SPAN>At the time that made sense.<SPAN class="Apple-converted-space"> </SPAN>But now I am trying to make sense of the following eigenvectors:</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">q = <SPAN class="Apple-converted-space"> </SPAN>0.0000<SPAN class="Apple-converted-space"> </SPAN>0.0563<SPAN class="Apple-converted-space"> </SPAN>0.0000</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">**************************************************************************</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-converted-space"> </SPAN>omega( 1) =<SPAN class="Apple-converted-space"> </SPAN>-0.308036 [THz] = <SPAN class="Apple-converted-space"> </SPAN>-10.275037 [cm-1]</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.142674<SPAN class="Apple-converted-space"> </SPAN>-0.338669 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.031918<SPAN class="Apple-converted-space"> </SPAN>-0.201463<SPAN class="Apple-converted-space"> </SPAN>-0.388896<SPAN class="Apple-converted-space"> </SPAN>-0.061613 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.019612<SPAN class="Apple-converted-space"> </SPAN>-0.123787<SPAN class="Apple-converted-space"> </SPAN>-0.367551<SPAN class="Apple-converted-space"> </SPAN>-0.058231 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.226888<SPAN class="Apple-converted-space"> </SPAN>-0.354765 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.036445<SPAN class="Apple-converted-space"> </SPAN>-0.230039<SPAN class="Apple-converted-space"> </SPAN>-0.328252<SPAN class="Apple-converted-space"> </SPAN>-0.052005 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.096682<SPAN class="Apple-converted-space"> </SPAN>-0.403396 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-converted-space"> </SPAN>omega( 2) = <SPAN class="Apple-converted-space"> </SPAN>0.617574 [THz] =<SPAN class="Apple-converted-space"> </SPAN>20.600196 [cm-1]</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.403925<SPAN class="Apple-converted-space"> </SPAN>-0.012145 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.397050<SPAN class="Apple-converted-space"> </SPAN>-0.075201 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.397199<SPAN class="Apple-converted-space"> </SPAN>-0.075229 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.404073<SPAN class="Apple-converted-space"> </SPAN>-0.012149 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.408949<SPAN class="Apple-converted-space"> </SPAN>-0.077455 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">( -0.416112<SPAN class="Apple-converted-space"> </SPAN>-0.012511 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><SPAN class="Apple-converted-space"> </SPAN>omega( 3) = <SPAN class="Apple-converted-space"> </SPAN>0.788199 [THz] =<SPAN class="Apple-converted-space"> </SPAN>26.291668 [cm-1]</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.389819<SPAN class="Apple-converted-space"> </SPAN>-0.233273 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.055122 <SPAN class="Apple-converted-space"> </SPAN>0.347926<SPAN class="Apple-converted-space"> </SPAN>-0.110454<SPAN class="Apple-converted-space"> </SPAN>-0.017499 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.061881 <SPAN class="Apple-converted-space"> </SPAN>0.390589<SPAN class="Apple-converted-space"> </SPAN>-0.148121<SPAN class="Apple-converted-space"> </SPAN>-0.023467 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.342277<SPAN class="Apple-converted-space"> </SPAN>-0.187111 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000<SPAN class="Apple-converted-space"> </SPAN>-0.050913 <SPAN class="Apple-converted-space"> </SPAN>0.321357<SPAN class="Apple-converted-space"> </SPAN>-0.249835<SPAN class="Apple-converted-space"> </SPAN>-0.039581 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">(<SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>0.384275<SPAN class="Apple-converted-space"> </SPAN>-0.092029 <SPAN class="Apple-converted-space"> </SPAN>0.000000 <SPAN class="Apple-converted-space"> </SPAN>)</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">These are the first 3 (accoustic) modes of the spectrum.<SPAN class="Apple-converted-space"> </SPAN>If the imaginary part doesn't matter, then it would appear that the accoustic displacement along the b-direction is practically zero.<SPAN class="Apple-converted-space"> </SPAN>However, the imaginary part is the same magnitude as the displacements in the other orthogonal directions.<SPAN class="Apple-converted-space"> </SPAN>Is there any physical meaning to this, or is it just an artifact of the calculation?</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Eric,</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Ph.D. Student, M.I.T.</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; min-height: 14px; "><BR></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">_______________________________________________</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; ">Pw_forum mailing list</DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="mailto:Pw_forum@pwscf.org">Pw_forum@pwscf.org</A></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><A href="http://www.democritos.it/mailman/listinfo/pw_forum">http://www.democritos.it/mailman/listinfo/pw_forum</A></DIV> </BLOCKQUOTE></DIV><BR><DIV> <SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><SPAN class="Apple-style-span" style="border-collapse: separate; border-spacing: 0px 0px; color: rgb(0, 0, 0); font-family: Helvetica; font-size: 14px; font-style: normal; font-variant: normal; font-weight: normal; letter-spacing: normal; line-height: normal; text-align: auto; -khtml-text-decorations-in-effect: none; text-indent: 0px; -apple-text-size-adjust: auto; text-transform: none; orphans: 2; white-space: normal; widows: 2; word-spacing: 0px; "><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">---</SPAN></SPAN></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">Stefano Baroni - SISSA</SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; "> </SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">&</SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; "> </SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">DEMOCRITOS National Simulation Center - Trieste</SPAN></SPAN></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)</SPAN></SPAN></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; font: normal normal normal 12px/normal Helvetica; min-height: 14px; ; font-size: 12px; "><BR style="; font-size: 12px; "></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">Please, if possible, don't</SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; "> </SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">send me MS Word or PowerPoint attachments</SPAN></SPAN></SPAN></FONT></DIV><DIV style="margin-top: 0px; margin-right: 0px; margin-bottom: 0px; margin-left: 0px; "><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; ">Why? See:</SPAN></SPAN></SPAN></FONT><FONT class="Apple-style-span" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;"><SPAN class="Apple-style-span" style="font-size: 12px; "><SPAN class="Apple-style-span" style="font-size: 12px; "> </SPAN></SPAN></SPAN></FONT><A href="http://www.gnu.org/philosophy/no-word-attachments.html"><FONT class="Apple-style-span" color="#0023E9" size="3"><SPAN class="Apple-style-span" style="font-size: 12px;; color: rgb(0, 35, 233); -khtml-text-decorations-in-effect: underline; "><SPAN class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; "><SPAN class="Apple-style-span" style="color: rgb(0, 35, 233); font-size: 12px; -khtml-text-decorations-in-effect: underline; ">http://www.gnu.org/philosophy/no-word-attachments.html</SPAN></SPAN></SPAN></FONT></A></DIV><DIV><BR class="khtml-block-placeholder"></DIV><BR class="Apple-interchange-newline"></SPAN></SPAN></SPAN> </DIV><BR></DIV></DIV></DIV></BODY></HTML>