A stochastic golden rule and quantum Langevin equation for the low density limit

Abstract

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups.

References in corpus (8)

• Scaling corrections: site-percolation and Ising model in three dimensions
• Dynamics of Dissipative Two-Level Systems in the Stochastic Approximation
• Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium properties
• Quantum stochastic equation for the low density limit
• Subdynamics of relevant observables: a field theoretical approach
• Bifurcation Phenomenon in a Spin Relaxation
• Non-Exponential Decay for Polaron Model
• On the Long Time Behavior of the Quantum Fokker-Planck equation

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