Topics in Statistic Mechanics
Topics in Statistic Mechanics
Topics in Statistic Mechanics
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Adv. Sta. Phy. Homework 4 Quantum Is<strong>in</strong>g model Li,Zimeng PB06203182<br />
The propaganda operator is the Green function<br />
use (3.1) to rewrite it as<br />
and we<br />
(3.2)<br />
We can prove that<br />
The correspondence between (3.2) and (3.3) is just one example of Suzuki-Trotter<br />
Formula.We are not go<strong>in</strong>g to derive (3.3) from (3.2) here, as we have learned it <strong>in</strong> the<br />
Advanced Quantum <strong>Mechanics</strong> Course.However I would like to give the def<strong>in</strong>ition of<br />
general Suzuki-Trotter Formula below:<br />
THEOREM: (Suzuki-Trotter Formula) Let A and be l<strong>in</strong>ear operators on a Banach space X<br />
such that , and A+B are the <strong>in</strong>f<strong>in</strong>itesimal<br />
generators of the contraction semigroups , , and respectively. Then for all<br />
we have<br />
Reference<br />
1.Françoise J., Naber G., Tsun T.S."Encyclopedia of Mathematical Physics; Elsevier; 2006"<br />
(3246)<br />
2.Henkel M. Conformal <strong>in</strong>variance and critical phenomena (Spr<strong>in</strong>ger, 1999)(ISBN<br />
354065321X)(K)(T)(434s)<br />
3.Techniques and applications of path <strong>in</strong>tegration (Wiley, 1981 Schulman L.S. 375s)
Change language