2025/09/29 by Xiao Wang, Wang, Xiao, Wen-ge Wang +1 · 2 citations
Computer Science · Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural Networks and Applications #Phase-change materials and chalcogenides #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2509.24490
openalex publication_date 2025/09/29 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28
In this letter, by an approach that employs Weyl symbols for operators, a semiclassical theory is developed for the off-diagonal function in the eigenstate thermalization hypothesis, which is for off-diagonal elements 〈Ei|O|Ej〉 of an observable O on the energy basis. It is shown analytically that the matrix of O has a banded structure, possessing a bandwidth wb that scales linearly with ℏ, a phase-space gradient of the classical Hamiltonian 〈|∇Hcl|〉 and an O-dependent property. This predicts that the thermalization timescale of a quantum system may be inversely proportional to the phase-space gradient of the Hamiltonian, aligning with intuitions in classical thermalization. This approach also elucidates the origin of a ρdos-1/2 scaling of the off-diagonal function. The analytical predictions are checked numerically in the Lipkin-Meshkov-Glick model.