Year: 2020
Type: article
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 π^{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 2, thus bounding large downward fluctuations in entropy from generic initial states.
Source: Physical review. E
Institution: University of California, Santa Cruz
Language: English
Topic: Quantum many-body systems
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Funder: Foundational Questions Institute
OpenAlex ID: W3012208543