2010/05/07 by Hans Christian Öttinger · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Applied mathematics #Covariance #Hilbert space #Markov process #Master equation #Mathematical analysis #Mathematics #Nonlinear system #Normalization (sociology) #Physics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Statistics #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physreva.86.032101
published as Phys. Rev. A 86, 032101 (2012) · 4 pages
arxiv created 2010/05/07 · openalex publication_date 2012/09/04 · openalex created_date 2016/06/24 · arxiv updated 2018/03/09 · openalex updated_date 2026/08/05
We propose a piecewise deterministic Markovian jump process in Hilbert space such that the covariance matrix of this stochastic process solves the thermodynamic quantum master equation. The proposed stochastic process is particularly simple because the normalization of the vectors in Hilbert space is preserved only on average. As a consequence of the nonlinearity of the thermodynamic master equation, the construction of stochastic trajectories involves the density matrix as a running ensemble average. We identify a principle of detailed balance and a fluctuation-dissipation relation for our Markovian jump process.