Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

Cheng, Run; Wang, Qianyi; Wang, Yong-Long; Zong, Hong-Shi

doi:10.3390/sym13020300

Cited by 7 publications

(15 citation statements)

References 69 publications

(103 reference statements)

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“…A big open question here is at which length scale along the confined direction the BEC starts to appear. While the Mermin-Wagner theory states that no BEC would occur at exactly d = 2 for extended free-particle systems, calculations coming from the 3D limit of finite films like the one reported here or in [20] for the cubic-box geometry, suggest a divergence of T c as the thickness goes to zero, asymptotically. The emerging picture, to be tested in future work, is that a maximum in T c could occur for some very small but fi-nite length scale along the confining direction, before T c drops to zero according to the Mermin-Wagner theory, as the exactly 2D limit is reached.…”

Section: Introductionmentioning

confidence: 59%

“…Unfortunately, to date there are no experimental studies that explore the effect of confinement along a single spatial direction on the equilibrium properties of Bose-Einstein condensates, or the relationship between the condensation temperature and the thickness of the film, apart from studies focusing on the 2D limit of superfluids with just a couple atomic layers thickness where the physics is much more complicated [10]. However, various theoretical and especially numerical studies have been performed to describe finite size effects on BEC [7,20,36,37].…”

Section: Comparison With Similar Systemsmentioning

confidence: 99%

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Analytical theory of enhanced Bose-Einstein condensation in thin films

Travaglino,

Zaccone

2022

Preprint

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We present an analytically solvable theory of Bose-Einstein condensation in thin film geometries. Analytical closed-form expressions for the critical temperature are obtained in both the low-tomoderate confinement regime (where the film thickness L is in the order of microns) as well as in the strong confinement regime where the thickness is in the order of few nanometers or lower. The possibility of high-temperature BEC is predicted in the strong confinement limit, with a square-root divergence of the critical temperature Tc ∼ L −1/2 . For cold Bose gases, this implies an enhancement up to two orders of magnitude in Tc for films on the nanometer scale. Analytical predictions are also obtained for the heat capacity and the condensate fraction. A new law for the heat capacity of the condensate, i.e. C ∼ T 2 , is predicted for nano-scale films, which implies a different λ-point behavior with respect to bulk systems, while the condensate fraction is predicted to follow a [1 − (T /Tc) 2 ] law.

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Section: Introductionmentioning

confidence: 59%

Section: Comparison With Similar Systemsmentioning

confidence: 99%

Analytical theory of enhanced Bose-Einstein condensation in thin films

Travaglino,

Zaccone

2022

Preprint

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“…Analogously, substituting ξ = 1 into (28) and (30) it follows directly that ∂ξ ∂β N,κ = 0. Therefore, (27) becomes (18) for β ≥ β c and from the direct differentiation of (18) one obtains (21) for β ≥ β c , completing the calculation.…”

Section: B Calculations In the Thermodynamic Limitmentioning

confidence: 65%

“…1. Similarly the specific heat is calculated in (27) and the numerical results are presented in Fig. 2.…”

Section: Discussionmentioning

confidence: 99%

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Bose-Einstein statistics for a finite number of particles

Pessoa

2021

Preprint

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This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -namely, the fraction of particles in the ground state and the specific heat -are calculated here exactly in terms of temperature and fugacity. These calculations are complemented by a numerical calculation of fugacity in terms of the number of particles, without taking the thermodynamic limit. The main advantage of this approach is that it does not rely on approximations made in the vicinity of the usually defined critical temperature, rather it makes calculations with arbitrary precision possible, irrespective of temperature. Graphs for the calculated thermodynamical quantities are presented in comparison to the results previously obtained in the thermodynamic limit. In particular, it is observed that for the gas trapped in a 3-dimensional box the derivative of specific heat reaches smaller values than what was expected in the thermodynamic limit -here, this result is also verified with analytical calculations. This is an important result for understanding the role of the thermodynamic limit in phase transitions and makes possible to further study BE statistics without relying neither on the thermodynamic limit nor on approximations near critical temperature.

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Finite-size effect of a weakly interacting Bose gas at zero-temperature

Song

2022

Physics Letters A

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Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

Cited by 7 publications

References 69 publications

Analytical theory of enhanced Bose-Einstein condensation in thin films

Analytical theory of enhanced Bose-Einstein condensation in thin films

Bose-Einstein statistics for a finite number of particles

Finite-size effect of a weakly interacting Bose gas at zero-temperature

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