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.
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- 1 2 Tony Jin
- Association Sorbonne Université (through Organization: Sorbonne Universités / Sorbonne University)
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung / Swiss National Science Foundation [SNF]