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Semiclassical density matrix near the top of a potential barrier

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  • Weiper, Franz Josef
  • Ankerhold, Joachim
  • Grabert, Hermann

Abstract

Employing the path integral approach, we calculate the semiclassical 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 Tc.

Suggested Citation

  • Weiper, Franz Josef & Ankerhold, Joachim & Grabert, Hermann, 1996. "Semiclassical density matrix near the top of a potential barrier," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 223(1), pages 193-213.
    • Handle: RePEc:eee:phsmap:v:223:y:1996:i:1:p:193-213
    DOI: 10.1016/0378-4371(95)00297-9
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