Solution of quantum Langevin equation: approximations, theoretical and numerical aspects.
Based on a coherent state representation of noise operator and an ensemble averaging procedure using Wigner canonical thermal distribution for harmonic oscillators, a generalized quantum Langevin equation has been recently developed [Phys. Rev. E 65, 021109 (2002); 66, 051106 (2002)] to derive the equations of motion for probability distribution functions in c-number phase-space. We extend the treatment to explore several systematic approximation schemes for the solutions of the Langevin equation for nonlinear potentials for a wide range of noise correlation, strength and temperature down to the vacuum limit. The method is exemplified by an analytic application to harmonic oscillator for arbitrary memory kernel and with the help of a numerical calculation of barrier crossing, in a cubic potential to demonstrate the quantum Kramers' turnover and the quantum Arrhenius plot.
Banerjee
Dhruba
D
Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India.
Bag
Bidhan Chandra
BC
Banik
Suman Kumar
SK
Ray
Deb Shankar
DS