536. Stationary and nonstationary quantum problems soluble by the contour integral technique. (USSR)

Yu. N. Demkov, Vladimir I. Osherov

Yu. N. Demkov, Valentin N. Ostrovsky

Yu. N. Demkov, Vladimir I. Osherov

David W. McLaughlin

By developing an analogy between the Feynman path integral and contour integral representations of the special functions, we obtain WKB formulas for barrier penetration from a path integral. We first show that there exists for the path integral a notion of contour independence in the time parameter. We then select an appropriate contour to describe the physical situation of barrier penetration and obtain asymptotic formulas from the function space integral. The method is interpreted as a path integral derivation of the complex ray description of barrier penetration. In the last three sections we investigate several canonical problems of the theory of complex rays with these path integral techniques.

Chi H. Mak, David Chandler

A method of solving the sign problem in the Monte Carlo path-integral simulations of quantum dynamics is presented. Our method is based on the distortion of integration contours in conjunction with a stationary-phase-filtering method. Using this importance sampling, correlation functions for the spin-boson model have been computed for real times much longer than \ensuremath{\beta}\ensuremath{\Elzxh}.

Nickola Stefanov Todorov