Related papers: Quantum Langevin equation

Quantum Langevin equation

URL: http://arxiv.org/abs/1912.12063v1
Date: Fri, 27 Dec 2019 11:49:39 GMT
Title: Quantum Langevin equation
Authors: M\'ario J. de Oliveira
Abstract summary: We propose a Langevin equation to describe the quantum Brownian motion of bounded particles. The fluctuation force is similar to that employed in the classical case. The dissipation force is not restrict to be proportional to the velocity.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We propose a Langevin equation to describe the quantum Brownian motion of bounded particles based on a distinctive formulation concerning both the fluctuation and dissipation forces. The fluctuation force is similar to that employed in the classical case. It is a white noise with a variance proportional to the temperature. The dissipation force is not restrict to be proportional to the velocity and is determined in a way as to guarantee that the stationary state is given by a density operator of the Gibbs canonical type. To this end we derived an equation that gives the time evolution of the density operator, which turns out to be a quantum Fokker-Planck-Kramers equation. The approach is applied to the harmonic oscillator in which case the dissipation force is found to be non Hermitian and proportional to the velocity and position.

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