Approach to quantum Kramers' equation and barrier crossing dynamics

Banerjee, Dhruba ; Bag, Bidhan Chandra ; Banik, Suman Kumar ; Ray, Deb Shankar (2002) Approach to quantum Kramers' equation and barrier crossing dynamics Physical Review E - Statistical, Nonlinear and Soft Matter Physics, 65 (2). 021109_1-021109_13. ISSN 1539-3755

PDF - Author Version

Official URL:

Related URL:


We have presented a simple approach to quantum theory of Brownian motion and barrier crossing dynamics. Based on an initial coherent state representation of bath oscillators and an equilibrium canonical distribution of quantum-mechanical mean values of their co-ordinates and momenta we have derived a c number generalized quantum Langevin equation. The approach allows us to implement the method of classical non-Markovian Brownian motion to realize an exact generalized non-Markovian quantum Kramers' equation. The equation is valid for arbitrary temperature and friction. We have solved this equation in the spatial diffusion-limited regime to derive quantum Kramers' rate of barrier crossing and analyze its variation as a function of the temperature and friction. While almost all the earlier theories rest on quasiprobability distribution functions (e.g., Wigner function) and path integral methods, the present work is based on true probability distribution functions and is independent of path integral techniques. The theory is a natural extension of the classical theory to quantum domain and provides a unified description of thermally activated processes and tunneling.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:59108
Deposited On:03 Sep 2011 11:59
Last Modified:18 May 2016 09:47

Repository Staff Only: item control page