2013/09/30 by Chaitanya Joshi, Patrik Öhberg, Patrik Ohberg +2 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Coupling (piping) #Dissipation #Harmonic #Harmonic oscillator #Lindblad equation #Markov process #Master equation #Mathematics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum #Quantum Information and Cryptography #Quantum entanglement #Quantum mechanics #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.90.063815
published as Phys. Rev. A 90, 063815 (2014) · 11 pages, 4 figures, significantly revised and close to the published version
openalex publication_date 2014/12/11 · arxiv created 2014/12/16 · arxiv updated 2014/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We investigate how to model Markovian evolution of coupled harmonic oscillators, each of them interacting with a local environment. When the coupling between the oscillators is weak, dissipation may be modeled using local Lindblad terms for each of the oscillators in the master equation, as is commonly done. When the coupling between oscillators is strong, this model may become invalid. We derive a master equation for two coupled harmonic oscillators that are subject to individual heat baths modeled by a collection of harmonic oscillators and show that this master equation in general contains nonlocal Lindblad terms. We compare the resulting time evolution with that obtained for dissipation through local Lindblad terms for each individual oscillator and show that the evolution is different in the two cases. In particular, the two descriptions give different predictions for the steady state and for the entanglement between strongly coupled oscillators. This shows that when describing strongly coupled harmonic oscillators, one must take great care in how dissipation is modeled and that a description using local Lindblad terms may fail. This may be particularly relevant when attempting to generate entangled states of strongly coupled quantum systems.