Kinetics and Boltzmann kinetic equation for fluctuation Cooper pairs above T_c

The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid $^3$ He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid $^3$ He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid $^3$He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid $^3$He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.

arXiv:2110.14073Oct 26, 20210 citations

Density dependence of the energy of N Cooper pairs

Monique Combescot, Tristan Cren, Michel Crouzeix +1 more

The European Physical Journal BMar 1, 20119 citations

Phonon-assisted Boltzmann kinetics of a Bose gas: Generic solution for T⩽ Tc

A. L. Ivanov, Claudia Ell, H. Haug

The relaxation kinetics of an ideal Bose gas coupled to a phonon bath at temperatures below or equal to the critical temperature ${\mathrm{T}}_{\mathrm{c}}$ is given within a unique scenario. During the first transient stage, which lasts a few characteristic scattering times, the initial distribution disappears. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein condensate is a slow adiabatic process. For this second kinetic stage we find an analytic generic solution of the Boltzmann equation. The generic solution is independent of the initial distribution and completely defined by the ratio ${\mathrm{T}}_{\mathrm{c}}$ / ${\mathrm{T}}_{\mathrm{b}}$ of the critical and bath temperatures.The relaxation kinetics of an ideal Bose gas coupled to a phonon bath at temperatures below or equal to the critical temperature ${\mathrm{T}}_{\mathrm{c}}$ is given within a unique scenario. During the first transient stage, which lasts a few characteristic scattering times, the initial distribution disappears. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein condensate is a slow adiabatic process. For this second kinetic stage we find an analytic generic solution of the Boltzmann equation. The generic solution is independent of the initial distribution and completely defined by the ratio ${\mathrm{T}}_{\mathrm{c}}$/${\mathrm{T}}_{\mathrm{b}}$ of the critical and bath temperatures.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJun 1, 199729 citations

^3

He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid

^3

He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.

The relaxation kinetics of an ideal Bose gas coupled to a phonon bath at temperatures below or equal to the critical temperature

{\mathrm{T}}_{\mathrm{c}}

is given within a unique scenario. During the first transient stage, which lasts a few characteristic scattering times, the initial distribution disappears. The following nonexponential relaxation towards a quantum degenerate equilibrium state with a Bose-Einstein condensate is a slow adiabatic process. For this second kinetic stage we find an analytic generic solution of the Boltzmann equation. The generic solution is independent of the initial distribution and completely defined by the ratio

{\mathrm{T}}_{\mathrm{c}}

{\mathrm{T}}_{\mathrm{b}}

of the critical and bath temperatures.