2019/10/31 by Shane P. Kelly, Eddy Timmermans, Shan-Wen Tsai +1
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Eigenvalues and eigenvectors #Hamiltonian (control theory) #Integrable system #Mathematical physics #Mathematics #Nonlinear system #Observable #Physics #Quantum #Quantum Information and Cryptography #Quantum many-body systems #Quantum mechanics #Semiclassical physics #Spectroscopy and Quantum Chemical Studies #Statistical physics #Thermalisation #Time evolution #cond-mat.quant-gas #quant-ph
paper · pdf · doi:10.1103/physreva.102.052210
published as Phys. Rev. A 102, 052210 (2020) · 10 pages
arxiv created 2020/09/08 · openalex publication_date 2020/11/06 · arxiv updated 2020/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
By developing a semiclassical analysis based on the eigenstate thermalization hypothesis, we determine the long time behavior of a large spin evolving with a nonlinear Hamiltonian. Despite integrable classical dynamics, we find the eigenstate thermalization hypothesis for the diagonal matrix elements of observables is satisfied in the majority of eigenstates, and thermalization of long time averaged observables is generic. The exception is an unusual mechanism for the breakdown of thermalization based on an unstable fixed point in the classical dynamics. Using the semiclassical analysis, we derive how the equilibrium values of observables encode properties of the initial state. This analysis shows an unusual memory effect in which the remembered initial state property is not conserved in the integrable classical dynamics. We conclude with a discussion of relevant experiments and the potential generality of this mechanism for long time memory and the breakdown of thermalization.