We derive a kinetic equation for a polarized paramagnetic gas that is exact in the Boltzmann (binary) approximation. The equation is written in a compact form and applies to both Fermi and Bose gases in a wide temperature range as long as the Boltzmann approximation remains applicable. The derived equation is used to analyze the conditions for the propagation of spin waves in polarized Fermi and Bose gases. We deduce a universal criterion for the propagation of weakly damped spin waves in a wide temperature range. The criterion is reduced to the condition that the real parts of the particle zero-angle scattering amplitudes (or T matrices) be much larger than their imaginary parts. We derive dispersion equations for spin waves at high and low gas temperatures and show that spin waves can propagate in both these limiting cases.We derive a kinetic equation for a polarized paramagnetic gas that is exact in the Boltzmann (binary) approximation. The equation is written in a compact form and applies to both Fermi and Bose gases in a wide temperature range as long as the Boltzmann approximation remains applicable. The derived equation is used to analyze the conditions for the propagation of spin waves in polarized Fermi and Bose gases. We deduce a universal criterion for the propagation of weakly damped spin waves in a wide temperature range. The criterion is reduced to the condition that the real parts of the particle zero-angle scattering amplitudes (or T matrices) be much larger than their imaginary parts. We derive dispersion equations for spin waves at high and low gas temperatures and show that spin waves can propagate in both these limiting cases.

Journal of Experimental and Theoretical PhysicsMay 1, 20062 citations

Generalized Boltzmann equation for a quantum gas

Shigeji Fujita

Physics LettersOct 1, 19643 citations

On the generalized Boltzmann equation of a quantum gas

Shigeji Fujita

PhysicaOct 1, 196110 citations

Applicability of the Boltzmann equation for a two-dimensional Fermi gas

Lei Wu, Yonghao Zhang

We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than $0.47{T}_{F}$ , up to the strong coupling regime, where ${T}_{F}$ is the Fermi temperature.We study the validity range of the semiclassical Boltzmann equation in describing the dynamics of two-dimensional Fermi gas. Here we numerically solve the Boltzmann equation based on the relaxation-time approximation. By comparing the numerically extracted damping of the quadrupole mode with the experimental data reported in Vogt et al. [Phys. Rev. Lett. 108, 070404 (2012)], we demonstrate that the Boltzmann equation is applicable at least when the temperature is larger than $0.47{T}_{F}$, up to the strong coupling regime, where ${T}_{F}$ is the Fermi temperature.

Physical Review AApr 12, 201213 citations

Generalized Boltzmann equation describing the dynamics of bosons and fermions

G. Kaniadakis

Physics Letters AJul 1, 199530 citations

Quantum Boltzmann equation for a mobile impurity in a degenerate Tonks-Girardeau gas

Oleksandr Gamayun

We investigate the large-time asymptotical behavior of a mobile impurity immersed in a degenerate Tonks-Girardeau gas. We derive a correct weak-coupling kinetic equation valid for N arbitrary ratio of masses of gas and impurity particles. When gas particles are either lighter or heavier than the impurity we find that our theory is equivalent to the Boltzmann theory with the collision integral calculated via the Fermi Golden Rule. On the contrary, in the equal-mass case, Fermi Golden Rule treatment gives false results due to not accounting for multiple coherent scattering events. The latter are treated by the resummation of ladder diagrams, which leads to a new kinetic equation. The asymptotic momentum of the impurity produced from this equation coincides with the result obtained by means of the Bethe ansatz.We investigate the large-time asymptotical behavior of a mobile impurity immersed in a degenerate Tonks-Girardeau gas. We derive a correct weak-coupling kinetic equation valid for N arbitrary ratio of masses of gas and impurity particles. When gas particles are either lighter or heavier than the impurity we find that our theory is equivalent to the Boltzmann theory with the collision integral calculated via the Fermi Golden Rule. On the contrary, in the equal-mass case, Fermi Golden Rule treatment gives false results due to not accounting for multiple coherent scattering events. The latter are treated by the resummation of ladder diagrams, which leads to a new kinetic equation. The asymptotic momentum of the impurity produced from this equation coincides with the result obtained by means of the Bethe ansatz.

arXiv:1402.7064Physical Review AJun 30, 201429 citations

0.47{T}_{F}

, up to the strong coupling regime, where

{T}_{F}

is the Fermi temperature.