Modeling the Impact of Hamiltonian Perturbations on Expectation Value Dynamics

Abstract

Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their impact on expectation value dynamics. These theories suggest that a majority of the very numerous, possible Hamiltonian perturbations entail more or less the same type of alteration of the decay dynamics. Thus, in this paper, we study how the approach towards equilibrium in closed quantum systems is altered due to weak perturbations. To this end, we perform numerical experiments on a particular, exemplary spin system. We compare our numerical data to predictions from three particular theories. We find satisfying agreement in the weak perturbation regime for one of these approaches.

arXiv comment6 pages, 8 figures

References in corpus (9)

• Chaos and Quantum Thermalization
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Canonical Typicality
• Typicality for Generalized Microcanonical Ensembles
• Occurrence of exponential relaxation in closed quantum systems
• Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum
• Stability of Quantum Dynamics under Constant Hamiltonian Perturbations
• Burnett coefficients in quantum many-body systems
• Decoherence Entails Exponential Forgetting in Systems Complying with the Eigenstate Thermalization Hypothesis

Cited by in corpus (2)

• Stability of Exponentially Damped Oscillations under Perturbations of the Mori-Chain
• Typical perturbation theory: conditions, accuracy and comparison with a mesoscopic case