Undecidability of the fate of relaxation in one-dimensional quantum systems
arXiv:2012.13890 · doi:10.1038/s41467-021-25053-0
Abstract
We investigate the relaxation dynamics in an isolated quantum many-body system. The stationary value of an observable after relaxation is a topic of researches in the field of quantum thermalization, since thermalization is a relaxation phenomena where this stationary value coincides with the equilibrium value. Therefore, computing the stationary value in quantum many-body systems is regarded as an important problem. We, however, prove that the stationary value in quantum many-body systems is incomputable. More precisely, we show that whether the stationary value is in the vicinity of a given value or not is an undecidable problem. Our undecidable result is still satisfied when we restrict our system to a one-dimensional shift-invariant system with nearest-neighbor interaction, our initial state to a product state of a state on a single site, and our observable to a shift-sum of a one-body observable. This result clearly shows that there is no general theorem or procedure to decide the presence or absence of thermalization in a given quantum many-body system.
arXiv comment41 pages, 8 figures. See our shorter companion paper arXiv:2012.13889
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