2021/11/19 by Sabine Bögli, Bögli, Sabine, Pierre-A. Vuillermot +1
Mathematics · Physics and Astronomy · #47.A.75 47.B.93 47.D.06 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #FOS: Physical sciences #Mathematical Biology Tumor Growth #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2111.10123
openalex publication_date 2021/11/19 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this article we investigate the long time behavior of solutions to a class\nof infinitely many master equations defined from transition rates that are\nsuitable for the description of a quantum system approaching thermodynamical\nequilibrium with a heat bath at fixed temperature and a reservoir consisting of\none species of particles characterized by a fixed chemical potential. We do so\nby proving a result which pertains to the spectral resolution of the semigroup\ngenerated by the equations, whose infinitesimal generator is realized as a\ntrace-class self-adjoint operator defined in a suitable weighted sequence\nspace. This allows us to prove the existence of global solutions which all\nstabilize toward the grand canonical equilibrium probability distribution as\nthe time variable becomes large, some of them doing so exponentially rapidly.\nWhen we set the chemical potential equal to zero, the stability statements\ncontinue to hold in the sense that all solutions converge toward the Gibbs\nprobability distribution of the canonical ensemble which characterizes the\nequilibrium of the given system with a heat bath at fixed temperature.\n