The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

Napiórkowski, Marcin; Piasecki, J.

doi:10.1007/s10955-012-0522-x

Cited by 10 publications

(19 citation statements)

References 39 publications

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“…In Ref. [15] analogous results have been derived for the imperfect Bose gas [19,20] which belongs to a different universality class than the ideal Bose gas [17].…”

Section: Range Of Casimir Forces and Bulk Correlation Lengthmentioning

confidence: 87%

“…Although the above basic formula has been derived for the ideal Bose gas we expect a similar formula to hold for the imperfect Bose gas [13,15,17,19,20], where the interparticle repulsion is taken into account in the mean-field way. On the other hand, one should not expect such simple relation to hold between the Casimir force and the one-particle density matrix when fluctuations of the interacting Bose gas are taken into account.…”

Section: Relation Between Casimir Forces and The One-particle Densitymentioning

confidence: 99%

“…The Casimir forces acting on planar walls immersed in a perfect quantum gas (the slit geometry) have been the object of numerous studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, a microscopic explanation of the remarkable similarity in the behavior of the range of the Casimir forces and the bulk correlation length remained on open problem.…”

Section: Introductionmentioning

confidence: 99%

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On the Relation Between Casimir Forces and Bulk Correlations

Napiórkowski

Piasecki

2014

J Stat Phys

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Within a microscopic approach we show that in the case of an ideal quantum gas enclosed in a slit the Casimir force can be simply expressed in terms of the bulk one-particle density matrix. The corresponding formula, which holds both for bosons and fermions, allows to relate the range of the Casimir force to the bulk correlation length. The low-temperature behavior of the Casimir forces is derived.

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“…In Ref. [15] analogous results have been derived for the imperfect Bose gas [19,20] which belongs to a different universality class than the ideal Bose gas [17].…”

Section: Range Of Casimir Forces and Bulk Correlation Lengthmentioning

confidence: 87%

Section: Relation Between Casimir Forces and The One-particle Densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the Relation Between Casimir Forces and Bulk Correlations

Napiórkowski

Piasecki

2014

J Stat Phys

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“…This results in finite bulk correlation length ξ ∼ |s 0 | −1/2 (see Refs. 8,9) and the absence of the Bose-Einstein condensation at any µ and T > 0. On the other hand, for d > 2 the function g d 2 (e s0 ) is finite for s 0 = 0.…”

Section: The Bulk Systemmentioning

confidence: 93%

The imperfect Bose gas inddimensions: critical behavior and Casimir forces

Napiórkowski¹,

Jakubczyk²,

Nowak³

2013

J. Stat. Mech.

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We consider the d-dimensional imperfect (mean-field) Bose gas confined in a slit-like geometry and subject to periodic boundary conditions. Within an exact analytical treatment we first extract the bulk critical properties of the system at Bose-Einstein condensation and identify the bulk universality class to be the one of the classical d-dimensional spherical model. Subsequently we consider finite slit width D and analyze the excess surface free energy and the related Casimir force acting between the slit boundaries. Above the bulk condensation temperature (T > Tc) the Casimir force decays exponentially as a function of D with the bulk correlation length determining the relevant length scale. For T = Tc and for T < Tc its decay is algebraic. The magnitude of the Casimir forces at Tc and for T < Tc is governed by the universal Casimir amplitudes. We extract the relevant values for different d and compute the scaling functions describing the crossover between the critical and low-temperature asymptotics of the Casimir force. The scaling function is monotonous at any d ∈ (2, 4) and becomes constant for d > 4 and T ≤ Tc.

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“…After these seminal works, a great deal of effort has been devoted to the calculation of the Casimir force of the free and trapped Bose gas for different geometries and different boundary conditions. [ 7–29 ]…”

Section: Introductionmentioning

confidence: 99%

Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

Aydıner

2020

Annalen der Physik

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In this study, ideal free and harmonically trapped Bose gases confined by two plates in the x-y-plane in-between distance d are considered. The Casimir potential is obtained from the grand canonical potential of these quantum Bose gases for the Zaremba and the anti-periodic boundary conditions. The Casimir force is then obtained for the Bose-Einstein condensate phase T ≤ T c and for the non-condensate phase T > T c. It is shown that Casimir forces are repulsive for these boundary conditions. Additionally, it is shown that Casimir forces exponentially decay in the non-condensate phase T > T c with the decay lengths. These decay lengths were discussed and compared for different boundary conditions. As a result, new results are obtained for harmonically trapped Bose gas and the free gas results are compared with previous results.

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The Bulk Correlation Length and the Range of Thermodynamic Casimir Forces at Bose-Einstein Condensation

Cited by 10 publications

References 39 publications

On the Relation Between Casimir Forces and Bulk Correlations

On the Relation Between Casimir Forces and Bulk Correlations

The imperfect Bose gas inddimensions: critical behavior and Casimir forces

Repulsive Casimir Force of the Free and Harmonically Trapped Bose Gas in the Bose–Einstein Condensate Phase

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