Wigner–Kirkwood expansion for semi-infinite quantum fluids

Šamaj, L.; Jancovici, B.

doi:10.1088/1742-5468/2007/02/p02002

Cited by 7 publications

(14 citation statements)

References 23 publications

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“…This can be done using a formal expansion in powers of [36]. For simplicity we will perform the computation directly for m = 1, starting from (15).…”

Section: First Order Quantum Correctionmentioning

confidence: 99%

A Tentative Replica Theory of Glassy Helium 4

Biroli¹,

Zamponi²

2012

J Low Temp Phys

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We develop a quantum replica method for interacting particle systems and use it to estimate the location of the glass transition line in Helium 4. Although we do not fully succeed in taking into account all quantum effects, we make a thorough semiclassical analysis. We confirm previous suggestions that quantum fluctuations promote the formation of the glass and give a quantitative estimate of this effect at high density. Finally, we discuss the difficulties that are met when one tries to extend the calculation to the region of low densities and low temperatures, where quantum effects are strong and the semiclassical expansion breaks down.

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“…This can be done using a formal expansion in powers of [36]. For simplicity we will perform the computation directly for m = 1, starting from (15).…”

Section: First Order Quantum Correctionmentioning

confidence: 99%

A Tentative Replica Theory of Glassy Helium 4

Biroli¹,

Zamponi²

2012

J Low Temp Phys

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“…For infinite (bulk) quantum fluids of particles interacting via pairwise sufficiently smooth interactions with neglected fermion/boson exchange effects, Wigner [4] and Kirkwood [5] constructed a semiclassical expansion of the Boltzmann density in configuration space (at inverse temperature β), B β ( r) = r|e −βH | r , in even powers of the thermal de Broglie wavelength λ =h(β/m) 1/2 . Recently [6], we have generalized the Wigner-Kirkwood method to quantum fluids constrained to the above defined halfspace Λ. The final result for the Boltzmann density in configuration space was obtained as a series…”

Section: Boltzmann Density For the Half-space Geometrymentioning

confidence: 99%

Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma

Jancovici¹,

Šamaj²

2007

J. Stat. Mech.

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This paper is the continuation of a previous one [L. Šamaj and B. Jancovici, 2007 J. Stat. Mech. P02002]; for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had generalized the Wigner-Kirkwood expansion of the equilibrium statistical quantities in powers of Planck's constanth. As a model system for a more detailed study, we consider the quantum two-dimensional one-component plasma: a system of charged particles of one species, interacting through the logarithmic Coulomb potential in two dimensions, in a uniformly charged background of opposite sign, such that the total charge vanishes. The corresponding classical system is exactly solvable in a variety of geometries, including the present one of a half-plane, when βe 2 = 2, where β is the inverse temperature and e is the charge of a particle: all the classical n-body densities are known. In the present paper, we have calculated the expansions of the quantum density profile and truncated two-body density up to orderh 2 (instead of only to order h in the previous paper). These expansions involve the classical n-body densities up to n = 4, thus we obtain exact expressions for these quantum expansions in this special case.For the quantum one-component plasma, two sum rules involving the truncated two-body density (and, for one of them, the density profile) have been derived, a long time ago, by heuristic macroscopic arguments: one sum rule is about the asymptotic form along the wall of the truncated two-body density, the other one is about the dipole moment of the structure factor. In the two-dimensional case at βe 2 = 2, we have now explicit expressions up to orderh 2 of these two quantum densities, thus we can microscopically check the sum rules at this order. The checks are positive, reinforcing the idea that the sum rules are correct.Correlations and sum rules in a half-space quantum plasma

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“…At the same time, it is obviously important to take boundary effects into account when studying the properties of such systems. We mention a paper where the thermodynamically equilibrium properties of quantum gases in a half-space were considered [10].…”

Section: Introductionmentioning

confidence: 99%

Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose-Einstein condensate

Латышев

Yushkanov

2010

Theor Math Phys

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We construct a linearized kinetic equation modeling the behavior of degenerate quantum Bose gases with the collision rate dependent on the momentum of elementary excitations. We consider the general case where the energy of elementary excitations depends on the momentum according to the Bogoliubov formula. We analytically solve the half-space boundary value problem of the temperature jump at the boundary of the degenerate Bose gas in the presence of the Bose-Einstein condensate. We obtain an expression for the Kapitza resistance.

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Wigner–Kirkwood expansion for semi-infinite quantum fluids

Cited by 7 publications

References 23 publications

A Tentative Replica Theory of Glassy Helium 4

A Tentative Replica Theory of Glassy Helium 4

Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma

Temperature jump in degenerate quantum gases with the Bogoliubov excitation energy and in the presence of the Bose-Einstein condensate

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