2012/08/08 by Didier Robert, Robert, Didier
Computer Science · Mathematics · Physics and Astronomy · #35Q40 #82C23 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.DS #math.MP #msc:35Q40 #msc:82C23 #quant-ph
paper · pdf · doi:10.48550/arxiv.1208.1598
openalex publication_date 2012/08/08 · arxiv created 2012/11/16 · arxiv updated 2012/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Our main goal in this paper is to extend to any system of coupled quadratic Hamiltonians some properties known for systems of quantum harmonic oscillators related with the Brownian Quantum Motion model. In a first part we get a rather general formula for the purity (or the linear entropy) in a short time approximation. In a second part we establish a master equation (or a Fokker-Planck type equation) for the time evolution of the reduced matrix density for bilinearly coupled quadratic Hamiltonians. The Hamiltonians and the bilinear coupling can be time dependent. Moreover we give an explicit formula for the solution of this master equation so that the time evolution of the reduced density at time t is connected with the reduced density at initial time t0 for t0 ≤ t <t0 +tc where tc∈ ]0, ∞] is a critical time but reversibility is lost for t ≥ t0 +tc.