The internal energy and thermodynamic behaviour of a boson gas below the Bose–Einstein temperature

Deeney, F.A.; O'Leary, J P

doi:10.1016/j.physleta.2011.02.066

Cited by 4 publications

(6 citation statements)

References 4 publications

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“…An alternative equation of state was proposed in Ref. 37 considering that in the ground state the system holds the kinetic energy associated with the gas cloud right at the condensation temperature. The proposed equation of state below the condensation temperature reads 37 :…”

Section: Bose-einstein Condensationmentioning

confidence: 99%

“…It turns out that employing such expressions both below and above the Bose-Einstein condensation temperature GR=2/3, as in the case of the ideal gas. An alternative equation of state was proposed in [40] considering that in the ground state the system holds the kinetic energy associated with the gas cloud right at the condensation temperature. The proposed equation of state below the condensation temperature reads [40] […”

Section: Bose-einstein Condensationmentioning

confidence: 99%

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Grüneisen parameter for gases and superfluid helium

et al. 2016

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The Grüneisen ratio (Γ), i.e. the ratio of the linear thermal expansivity to the specific heat at constant pressure, quantifies the degree of anharmonicity of the potential governing the physical properties of a system. While Γ has been intensively explored in solid state physics, very little is known about its behavior for gases. This is most likely due to the difficulties posed to carry out both thermal expansion and specific heat measurements in gases with high accuracy as a function of pressure and temperature. Furthermore, to the best of our knowledge a comprehensive discussion about the peculiarities of the Grüneisen ratio is still lacking in the literature. Here we report on a detailed and comprehensive overview of the Grüneisen ratio. Particular emphasis is placed on the analysis of Γ for gases. The main findings of this work are: i) for the Van der Waals gas Γ depends only on the co-volume b due to interaction effects, it is smaller than that for the ideal gas (Γ = 2/3) and diverges upon approaching the critical volume; ii) for the Bose-Einstein condensation of an ideal boson gas, assuming the transition as first-order Γ diverges upon approaching a critical volume, similarly to the Van der Waals gas; iii) for 4 He at the superfluid transition Γ shows a singular behavior. Our results reveal that Γ can be used as an appropriate experimental tool to explore pressure-induced critical points.

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Section: Bose-einstein Condensationmentioning

confidence: 99%

Section: Bose-einstein Condensationmentioning

confidence: 99%

Grüneisen parameter for gases and superfluid helium

et al. 2016

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“…where c = nkT −3/2 B (g 5/2 (1)/g 3/2 (1)). For temperatures below T B , we have shown elsewhere [13] that the previous expressions for the energy density and pressure must be modified to include the effects of the kinetic energy of the particles in the ground state. In London's paper [15], he assumed that when a boson drops into the ground state condensate, its kinetic energy disappears.…”

Section: Internal Energy and Pressurementioning

confidence: 99%

“…Recent experiments have sought such an equation in the case of Bose and Fermi atomic gases [11,12]. We have recently published the derivation of an equation for an ideal boson gas where we showed how, at temperatures below the Bose-Einstein temperature, the existing form needs to be modified to include the hitherto omitted energy of the particles in the ground state of a boson gas [13,14]. The omission arose due to the belief, first expressed by London [15], that such particles could not have kinetic energy.…”

Section: Introductionmentioning

confidence: 99%

A van der Waals equation of state for a dilute boson gas

Deeney¹,

O'Leary²

2012

Eur. J. Phys.

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“…We show here that this energy cannot be ignored, since the particles in the ground state are spatially confined in the condensate, and the Heisenberg uncertainty principle requires that such confinement must give rise to a ZPE. Elsewhere [14], we have already shown how its inclusion removes the problems associated with London's equations. In identifying the ZPE with the kinetic energy of the particles in the condensate, we obtain the added insight that this type of energy is 'ordered', with zero associated entropy, unlike the random thermal kinetic energy of the particles in the excited states.…”

Section: Introductionmentioning

confidence: 98%

A note on the zero point energy of an ideal boson gas

Deeney¹,

O'Leary²

2011

Eur. J. Phys.

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We have recently demonstrated that, when investigating the internal energy and pressure of an ideal boson gas at temperatures below the Bose–Einstein temperature, it is necessary to include the contribution from the kinetic energy of the particles in the condensate. Here we express the same requirement in terms of the constraints of the Heisenberg uncertainty principle applied to the particles confined in the condensate. The problem may be used by undergraduate students as an additional example of the connection between the ground state energy of a system and the Heisenberg uncertainty principle.

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The internal energy and thermodynamic behaviour of a boson gas below the Bose–Einstein temperature

Cited by 4 publications

References 4 publications

Grüneisen parameter for gases and superfluid helium

Grüneisen parameter for gases and superfluid helium

A van der Waals equation of state for a dilute boson gas

A note on the zero point energy of an ideal boson gas

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