2017/02/22 by B. A. Tay · 5 citations
Computer Science · Mathematics · Physics and Astronomy · #Bilinear interpolation #Master equation #Mathematical physics #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Quantum optics and atomic interactions #Stationary state #Statistics #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1016/j.physa.2017.02.020
published in Physica A Statistical Mechanics and its Applications 477, 42-64 (Elsevier BV) · Accepted by Physica A
openalex publication_date 2017/02/22 · arxiv created 2017/03/02 · arxiv updated 2017/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We obtain the solutions of the generic bilinear master equation for a quantum oscillator with constant coefficients in the Gaussian form. The well-behavedness and positive semidefiniteness of the stationary states could be characterized by a three-dimensional Minkowski vector. By requiring the stationary states to satisfy a factorized condition, we obtain a generic class of master equations that includes the well-known ones and their generalizations, some of which are completely positive. A further subset of the master equations with the Gibbs states as stationary states is also obtained. For master equations with not completely positive generators, an analysis on the stationary states suggests conditions on the coefficients of the master equations that generate positive evolution for a given initial state.