Hilbert space average of transition probabilities

Hahn, Nico; Guhr, Thomas; Waltner, Daniel

doi:10.1103/physreve.101.062135

Cited by 3 publications

(2 citation statements)

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“…Thus, instead of conjecturing the applicability of typicality arguments at each time step as in Refs. [31][32][33][34], we argue that it is justified to apply them for a generic slow and coarse observable.…”

Section: A Microscopic Derivationmentioning

confidence: 96%

“…Quite naturally, research on pure state statistical mechanics has started to focus on nonequilibrium phenomena. For instance, it has been shown that typicality arguments remain useful even out of equilibrium ("dynamical typicality" [28][29][30]) and can be used to derive master equations [31][32][33][34]. Moreover, random matrix theory has been used to predict the time evolution of expectation values of observables [35][36][37][38] and general results on the time-scales of thermalization have been found [39][40][41][42][43][44][45].…”

Section: A Related Literaturementioning

confidence: 99%

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Classicality, Markovianity and local detailed balance from pure state dynamics

Strasberg¹,

Winter²,

Gemmer³

et al. 2022

Preprint

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When describing the effective dynamics of an observable in a many-body system, the repeated randomness assumption, which states that the system returns in a short time to a maximum entropy state, is a crucial hypothesis to guarantee that the effective dynamics is classical, Markovian and obeys local detailed balance. While the latter behaviour is frequently observed in naturally occurring processes, the repeated randomness assumption is in blatant contradiction to the microscopic reversibility of the system. Here, we show that the use of the repeated randomness assumption can be justified in the description of the effective dynamics of an observable that is both slow and coarse, two properties we will define rigorously. Then, our derivation will invoke essentially only the eigenstate thermalization hypothesis and typicality arguments. While the assumption of a slow observable is subtle, as it provides only a necessary but not sufficient condition, it also offers a unifying perspective applicable to, e.g., open systems as well as collective observables of many-body systems. All our ideas are numerically verified by studying density waves in spin chains.

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Section: A Microscopic Derivationmentioning

confidence: 96%