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arXiv · 1806.08897

Probabilistic bound on extreme fluctuations in isolated quantum systems

Joshua M. Deutsch·Dominik Šafránek·Anthony Aguirre
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Abstract

We ask to what extent an isolated quantum system can eventually "contract" to be contained within a given Hilbert subspace. We do this by starting with an initial random state, considering the probability that all the particles will be measured in a fixed subspace, and maximizing this probability over all time. This is relevant, for example, in a cosmological context, which may have access to indefinite timescales. We find that when the subspace is much smaller than the entire space, this maximal probability goes to $1/2$ for real initial wave functions, and to $\pi^2/16$ when the initial wave function has been drawn from a complex ensemble. For example when starting in a real generic state, the chances of collapsing all particles into a small box will be less than but come arbitrarily close to $50\%$. This contraction corresponds to an entropy reduction by a factor of approximately two, thus bounding large downward fluctuations in entropy from generic initial states.

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Joshua M. Deutsch, Dominik Šafránek, Anthony Aguirre. 2018-06-23. Probabilistic bound on extreme fluctuations in isolated quantum systems. https://doi.org/10.1103/physreve.101.032112

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