arXiv:2301.00430 · Annales Henri Poincaré

Large Deviations for the Ground State of Weakly Interacting Bose Gases

Simone Rademacher

Published Jul 2, 2024• 4 citations

Abstract

Abstract We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit $$N \rightarrow \infty $$ N → ∞ bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

DOI: 10.1007/s00023-024-01463-w

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arXiv:2301.00430 · Annales Henri Poincaré

Large Deviations for the Ground State of Weakly Interacting Bose Gases

Simone Rademacher

Published Jul 2, 2024• 4 citations

arXiv HTML PDF

Abstract

N \rightarrow \infty

N → ∞ bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

DOI: 10.1007/s00023-024-01463-w

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N \rightarrow \infty

Abstract We prove an upper bound for the ground state energy of a Bose gas consisting of N hard spheres with radius

\mathfrak {a}/N

a / N , moving in the three-dimensional unit torus

\Lambda

Λ . Our estimate captures the correct asymptotics of the ground state energy, up to errors that vanish in the limit

N \rightarrow \infty

N → ∞ . The proof is based on the construction of an appropriate trial state, given by the product of a Jastrow factor (describing two-particle correlations on short scales) and of a wave function constructed through a (generalized) Bogoliubov transformation, generating orthogonal excitations of the Bose–Einstein condensate and describing correlations on large scales.