2009/05/30 by Ion Nechita, Clément Pellegrini · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #math-ph #math.MP #math.PR #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1142/s1793744209000109
published as Confluentes Mathematici 1, 2 (2009) 249-289
openalex publication_date 2009/05/30 · arxiv created 2009/08/19 · arxiv updated 2010/06/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we derive the stochastic master equations corresponding to the statistical model of a heat bath. These stochastic differential equations are obtained as continuous time limits of discrete models of quantum repeated measurements. Physically, they describe the evolution of a small system in contact with a heat bath undergoing continuous measurement. The equations obtained in the present work are qualitatively different from the ones derived in [6], where the Gibbs model of heat bath has been studied. It is shown that the statistical model of a heat bath has a clear physical interpretation in terms of emissions and absorptions of photons. Our approach yields models of random environment and unravelings of stochastic master equations. The equations are rigorously obtained as solutions of martingale problems using the convergence of Markov generators.