Average quantum dynamics of closed systems over stochastic Hamiltonians

2011/11/29 by Yu Li, Daniel F. V. James, Yu, Li +1 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph)

paper · pdf · doi:10.48550/arxiv.1111.6686

openalex publication_date 2011/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a master equation formalism to describe the evolution of the average density matrix of a closed quantum system driven by a stochastic Hamiltonian. The average over random processes generally results in decoherence effects in closed system dynamics, in addition to the usual unitary evolution. We then show that, for an important class of problems in which the Hamiltonian is proportional to a Gaussian random process, the 2nd-order master equation yields exact dynamics. The general formalism is applied to study the examples of a two-level system, two atoms in a stochastic magnetic field and the heating of a trapped ion.

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• Classical non-equilibrium statistical mechanics and an "open system dynamics" perspective on quantum-classical analogy

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