Abstract
We study the equilibration properties of isolated ergodic quantum systems initially prepared in a cat state, i.e a macroscopic quantum superposition of states. Our main result consists in showing that, even though decoherence is at work in the mean, there exists a remnant of the initial quantum coherences visible in the strength of the fluctuations of the steady state. We back-up our analysis with numerical results obtained on the XXX spin chain with a random field along the z-axis in the ergodic regime and find good qualitative and quantitative agreement with the theory. We also present and discuss a framework where equilibrium quantities can be computed from general statistical ensembles without relying on microscopic details about the initial state, akin to the eigenstate thermalization hypothesis.
Highlights
Upon encountering the quantum statistical ensembles for the first time, one is often struck by the strong similitude they share with their classical counterpart
The previous years have seen the development of a general framework known as the eigenstate thermalization hypothesis (ETH) which explains the emergence of statistical ensembles from a given set of assumptions on the spectral properties of the observables of the system [3,4,5,6]
We show that these results are in qualitative and quantitative agreement with numerical results obtained in a quantum ergodic spin chain
Summary
Upon encountering the quantum statistical ensembles for the first time, one is often struck by the strong similitude they share with their classical counterpart. We intend to prove that, even if on average information about the quantum coherence of the initial state is lost at equilibrium, there is a remnant of the latter visible in the fluctuations around the stationary state This phenomenon was already seen in a model of stochastic fermionic chain on a discrete lattice [11,12] and we provide here the generalization of these results to any ergodic quantum system. In the context of ETH, one important assumption is that the initial states considered must have an energy comprised in a narrow energy shell This assumption is tightly bound with having initial states which fulfill a cluster decomposition [13] constraint, i.e that the typical coherence length is small compared to the size of the system.
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