Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional

Fournais, Søren; Napiórkowski, Marcin; Reuvers, Robin; Solovej, Jan Philip

doi:10.1063/1.5096987

Cited by 15 publications

(13 citation statements)

References 40 publications

(68 reference statements)

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“…Our method can be generalized to the strongly interacting case a i j ≳ a z , as long as a Fano-Feshbach resonance allows one to stay close to the SU(2) point. One could then address the LHY-type corrections at zero temperature 48 , 49 , the contributions of the weakly-bound dimer state and of three-body contact 13 , 14 , or the breaking of scale invariance expected at non-zero temperature.…”

Section: Discussionmentioning

confidence: 99%

Tan’s two-body contact across the superfluid transition of a planar Bose gas

et al. 2021

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Tan’s contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric method to realize experimentally the thermodynamic definition of the two-body contact, i.e., the change of the internal energy in a small modification of the scattering length. Our measurements are performed on a uniform two-dimensional Bose gas of 87Rb atoms across the Berezinskii–Kosterlitz–Thouless superfluid transition. They connect well to the theoretical predictions in the limiting cases of a strongly degenerate fluid and of a normal gas. They also provide the variation of this key quantity in the critical region, where further theoretical efforts are needed to account for our findings.

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Section: Discussionmentioning

confidence: 99%

Tan’s two-body contact across the superfluid transition of a planar Bose gas

et al. 2021

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“…To date, there is no rigorous proof of (9). Some partial result, based on the restriction to quasi-free states, has been recently obtained in [9,Theorem 1]. Extrapolating from (9), in the Gross-Pitaevskii regime we expect |E N −2π N | ≤ C. While our estimate (6) captures the correct lower bound, the upper bound is off by a logarithmic correction.…”

Section: Remarkmentioning

confidence: 59%

“…The leading order term on the r.h.s. of (9) has been first derived in [21] and then rigorously established in [15], with an error rate b −1/5 . The corrections up to order b have been predicted in [1,18,20].…”

Section: Remarkmentioning

confidence: 99%

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Bose–Einstein Condensation for Two Dimensional Bosons in the Gross–Pitaevskii Regime

2021

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“…Corresponding formulas for the ground state energy and the free energy of the two-and the three-dimensional dilute Fermi gas have been proven in [25] and [44]. We also mention the series of works [37,35,36,13], where the ground state energy and the free energy of the dilute Bose gas in two and three spatial dimensions were investigated by restricting attention to quasi-free states. These articles contain formulas for the energy and critical temperature that are conjecturally valid in a combined dilute and weak-coupling limit.…”

Section: Introduction and Main Results 1introductionmentioning

confidence: 97%

The Free Energy of the Two-Dimensional Dilute Bose Gas. I. lower Bound

Deuchert

Mayer

Seiringer

2020

Forum of Mathematics, Sigma

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We prove a lower bound for the free energy (per unit volume) of the twodimensional Bose gas in the thermodynamic limit. We show that the free energy at density ρ and inverse temperature β differs from the one of the non-interacting system by the correction term 4πρ 2 | ln a 2 ρ| −1 (2−[1−β c /β] 2 + ). Here a is the scattering length of the interaction potential, [·] + = max{0, ·} and β c is the inverse Berezinskii-Kosterlitz-Thouless critical temperature for superfluidity. The result is valid in the dilute limit a 2 ρ 1 and if βρ 1.2. The lower bound on the o(1) error term given here is uniform in βρ as long as βρ 1. The proof will show that the actual error rate is much better for βρ some distance away from β c ρ (either above or below), see (2.16.13). For very low temperatures, we utilize the proof method of [30]; this way, we recover the ground state energy error rate | ln a 2 ρ| −1/5 for very low temperatures, which was proved for T = 0 in [30].6

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Ground state energy of a dilute two-dimensional Bose gas from the Bogoliubov free energy functional

Abstract: We extend the analysis of the Bogoliubov free energy functional to two dimensions at very low temperatures. For sufficiently weak interactions, we prove two term asymptotics for the ground state energy.

Cited by 15 publications

References 40 publications

Tan’s two-body contact across the superfluid transition of a planar Bose gas

Tan’s two-body contact across the superfluid transition of a planar Bose gas

Bose–Einstein Condensation for Two Dimensional Bosons in the Gross–Pitaevskii Regime

The Free Energy of the Two-Dimensional Dilute Bose Gas. I. lower Bound

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