Dynamical typicality of isolated many-body quantum systems

Abstract

Dynamical typicality refers to the property that two pure states, which initially exhibit (almost) the same expectation value for some given observable $A$, are very likely to exhibit also very similar expectation values when evolving in time according to the pertinent Schrödinger equation. We unify and generalize a variety of previous findings of this type for sufficiently high dimensional quantum mechanical model systems. Particular emphasize is put on the necessary and sufficient conditions, which the initial expectation value and the spectrum of $A$ have to fulfill.

References in corpus (4)

• Typicality for Generalized Microcanonical Ensembles
• Generalization of von Neumann's Approach to Thermalization
• Quantum parallelism as a tool for ensemble spin dynamics calculations
• Concentration of measure for quantum states with a fixed expectation value

Cited by in corpus (45)

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• Sudden removal of a static force in a disordered system: Induced dynamics, thermalization, and transport
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• Decoherence of a singlet-triplet superposition state under dipolar interactions of an uncorrelated environment
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
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• Canonical Typicality For Other Ensembles Than Micro-Canonical
• Modification of quantum many-body relaxation by perturbations exhibiting a banded matrix structure
• Comparative Microscopic Study of Entropies and their Production
• Full expectation value statistics for randomly sampled pure states in high-dimensional quantum systems
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Nontrivial damping of quantum many-body dynamics
• Typical Macroscopic Long-Time Behavior for Random Hamiltonians
• Hilbert space average of transition probabilities
• Anomalous Diffusion, Prethermalization, and Particle Binding in an Interacting Flat Band System
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• Compelling Bounds on Equilibration Times -- the Issue with Fermi's Golden Rule
• A Complexity-Based Approach to Quantum Observable Equilibration
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• On the difference between thermalization in open and isolated quantum systems: a case study
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