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A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation

Dhruba Banerjee·Bidhan Chandra Bag·Suman Kumar Banik·Deb Shankar Ray
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Abstract

Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E {\bf 65}, 021109 (2002); {\it ibid.} 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of {\it true} probability distribution functions in $c$-number phase space. We extend the treatment to develop a numerical method for generation of $c$-number noise with arbitrary correlation and strength at any temperature, along with the solution of the associated generalized quantum Langevin equation. The method is illustrated with the help of a calculation of quantum mean first passage time in a cubic potential to demonstrate quantum Kramers turnover and quantum Arrhenius plot.

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Dhruba Banerjee, Bidhan Chandra Bag, Suman Kumar Banik, Deb Shankar Ray. 2003-03-04. A numerical method for generation of quantum noise and solution of generalized c-number quantum Langevin equation. https://arxiv.org/abs/cond-mat/0303059

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