✦ LIBER ✦

Semiclassical density matrix near the top of a potential barrier

✍ Scribed by Franz Josef Weiper; Joachim Ankerhold; Hermann Grabert

Book ID: 103896080
Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 920 KB
Volume: 223
Category: Article
ISSN: 0378-4371
DOI: 10.1016/0378-4371(95)00297-9

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✦ Synopsis

Employing the path integral approach, we calculate the semiclassicai equilibrium density matrix of a particle moving in a nonlinear potential field for coordinates near the top of a potential barrier. As the temperature is decreased, near a critical temperature Tc the harmonic approximation for the fluctuation path integral fails. This is due to a caustic arising at a bifurcation point of the classical paths. We provide a selfconsistent scheme to treat the large quantum fluctuations leading to a nonlinear fluctuation potential. The procedure differs from methods used near caustics of the real time propagator. The semiclassical density matrix is determined explicitly for the case of asymmetric barriers from high temperatures down to temperatures somewhat below To.

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