THE DENSITY-MATRIX NEAR THE TOP OF A POTENTIAL BARRIER - A PROBLEM OF CAUSTICS IN PATH INTEGRATION

被引:19
作者
ANKERHOLD, J
GRABERT, H
机构
[1] Fachbereich Physik der Universität-GH
关键词
D O I
10.1016/0378-4371(92)90332-K
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Employing the path integral approach, the real space representation of the equilibrium density matrix of a particle moving in a nonlinear potential field is calculated for coordinates near the top of a potential barrier. As the temperature is decreased below a critical temperature T(c), the harmonic approximation for the potential fails even in the close vicinity of the barrier top and a caustic arises. The divergent semiclassical approximation of the path integral is regularized by taking into account anharmonic terms. This regularization is carried out explicitly for the case of a symmetric barrier. Apart from the behavior of the density matrix near T(c), the crossover to the semiclassical approximations of the path integral for high and low temperatures is discussed.
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页码:568 / 596
页数:29
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