Long time quantum-classical correspondence for open systems in trace norm

2024/08/30 by Zhenhao Li, Li, Zhenhao · 2 citations
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum Mechanics and Applications

paper · pdf · doi:10.48550/arxiv.2408.16953

Abstract

We consider a frictionless system coupled to an external Markovian environment. The quantum and classical evolution of such systems are described by the Lindblad and the Fokker-Planck equation respectively. We show that when such a system is given by an at most quadratically growing Hamiltonian and at most linearly growing real jump functions, the quantum and classical evolutions remain close on time scales much longer than Ehrenfest time. In particular, we show that the evolution of a density matrix by the Lindblad equation is close in trace norm to the quantization of the corresponding evolution by the Fokker-Planck equation. Such agreement improves upon recent results [arXiv:2403.09345, arXiv:2306.13717, arXiv:2307.05326], which proved long time agreement in weaker norms.

Cited by

• The threshold for quantum-classical correspondence is D ∼ ℏ^\frac43
• Frozen Gaussian sampling algorithms for simulating Markovian open quantum systems in the semiclassical regime

Related

• Classical-Quantum correspondence in Lindblad evolution
• Classical correspondence beyond the Ehrenfest time for open quantum systems with general Lindbladians
• The threshold for quantum-classical correspondence is D ∼ ℏ^\frac43
• Ehrenfest's theorem beyond the Ehrenfest time
• Quantum Fokker-Planck models: the Lindblad and Wigner approaches