Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

Beau, Mathieu; del Campo, Adolfo

doi:10.3390/e22050515

Title: Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

Journal Article · Thu Apr 30 00:00:00 EDT 2020 · Entropy

DOI:https://doi.org/10.3390/e22050515· OSTI ID:1648102

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Univ. of Massachusetts, Boston, MA (United States)
Univ. of Massachusetts, Boston, MA (United States); Donostia International Physics Center, San Sebastian (Spain); Basque Foundation for Science (IKERBASQUE), Bilbao (Spain); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1648102

Report Number(s):: LA-UR-20-22743; TRN: US2203013

Journal Information:: Entropy, Vol. 22, Issue 5; ISSN 1099-4300

Publisher:: MDPICopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 3 works

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Title: Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

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