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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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“…(11) with boundary conditions (12). Finding the value of the temperature jump ε T is especially interesting.…”

Section: Consequently the Distribution Function Is The Chapman-enskomentioning

confidence: 99%

“…The temperature jump problem for a quantum Fermi gas was considered in [12]. An analytic solution for an arbitrary degree of gas degeneracy was obtained.…”

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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“…For neutral Fermi gases, an equation similar to (1) was studied in [8]. In the case of finite temperatures, we must take into account that the relaxation time τ can depend on the electron velocity.…”

Section: The Kinetic Equationmentioning

confidence: 99%

“…The problem is to determine a solution of system (8) such that boundary conditions (9)-(11) are satisfied. We stress that the functions ϕ as and e as constitute the solution of system of equations (8).…”

Section: The Boundary Conditions and Problem Statementmentioning

confidence: 99%

Smoluchowski problem for metals with mirror-diffusive boundary conditions

Латышев

Yushkanov

2009

Theor Math Phys

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“…Gases of this type were already studied [6][7][8]. The temperature jump problem has been solved for Fermi gases [6] and for degenerate Bose gases for which the presence of a Bose-Einstein condensate was taken into consideration [7]. The Kramers problem has also been analytically solved for the condition of pure diffuse reflection of molecules from the wall [8].…”

Section: Introductionmentioning

confidence: 99%

Isothermal slip of a Fermi gas with specular-diffuse reflection from the boundary

2009

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A solution of the Kramers problem on isothermal slip of a quantum Fermi gas along a plane solid surface has been obtained. The reflection of molecules from the wall was supposed to be specular-diffuse. A model kinetic equation with the τ-model collision integral and with the collision frequency proportional to the molecular velocity was used. The slip velocity has been analyzed in relation to a parameter representing the ratio of the chemical potential to the product of Boltzmann's constant by the absolute temperature.

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Cited by 12 publications

References 7 publications

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

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

Smoluchowski problem for metals with mirror-diffusive boundary conditions

Isothermal slip of a Fermi gas with specular-diffuse reflection from the boundary

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