We study the statistics of large deviations of the intensive work done in an interaction quench of a one-dimensional Bose gas with a large number N of particles, system size L, and fixed density. We consider the case in which the system is initially prepared in the noninteracting ground state and a repulsive interaction is suddenly turned on. For large deviations of the work below its mean value, we show that the large-deviation principle holds by means of the quench action approach. Using the latter, we compute exactly the so-called rate function and study its properties analytically. In particular, we find that fluctuations close to the mean value of the work exhibit a marked non-Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases. Deviations larger than the mean value exhibit an algebraic decay whose exponent cannot be determined directly by large-deviation theory. Exploiting the exact Bethe ansatz representation of the eigenstates of the Hamiltonian, we calculate this exponent for vanishing particle density. Our approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.

Quench action and large deviations: Work statistics in the one-dimensional Bose gas / Perfetto, G.; Piroli, L.; Gambassi, A.. - In: PHYSICAL REVIEW. E. - ISSN 2470-0045. - 100:3(2019), pp. 1-20. [10.1103/PhysRevE.100.032114]

Quench action and large deviations: Work statistics in the one-dimensional Bose gas

Perfetto G.
;
Piroli L.;Gambassi A.
2019

Abstract

We study the statistics of large deviations of the intensive work done in an interaction quench of a one-dimensional Bose gas with a large number N of particles, system size L, and fixed density. We consider the case in which the system is initially prepared in the noninteracting ground state and a repulsive interaction is suddenly turned on. For large deviations of the work below its mean value, we show that the large-deviation principle holds by means of the quench action approach. Using the latter, we compute exactly the so-called rate function and study its properties analytically. In particular, we find that fluctuations close to the mean value of the work exhibit a marked non-Gaussian behavior, even though their probability is always exponentially suppressed below it as L increases. Deviations larger than the mean value exhibit an algebraic decay whose exponent cannot be determined directly by large-deviation theory. Exploiting the exact Bethe ansatz representation of the eigenstates of the Hamiltonian, we calculate this exponent for vanishing particle density. Our approach can be straightforwardly generalized to quantum quenches in other interacting integrable systems.
100
3
1
20
032114
https://arxiv.org/abs/1904.06259
Perfetto, G.; Piroli, L.; Gambassi, A.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/103482
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