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

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Based on a coherent state representation of noise operator and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002); ibid. 051106 (2002)] a scheme for quantum Brownian motion to derive the equations for time evolution of 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.