We study heat transport in a gas of one-dimensional fermions in the presence of a small temperature gradient. At temperatures well below the Fermi energy there are two types of relaxation processes in this system, with dramatically different relaxation rates. As a result, in addition to the usual thermal conductivity, one can introduce the thermal conductivity of the gas of elementary excitations, which quantifies the dissipation in the system in the broad range of frequencies between the two relaxation rates. We develop a microscopic theory of these transport coefficients in the limit of weak interactions between the fermions.
We study the viscous properties of a system of weakly interacting spin-1/2 fermions in one dimension. Accounting for the effect of interactions on the quasiparticle energy spectrum, we obtain the bulk viscosity of this system at low temperatures. Our result is valid for frequencies that are small compared with the rate of fermion backscattering. For frequencies larger than this exponentially small rate, the excitations of the system become decoupled from the center of mass motion, and the fluid is described by two-fluid hydrodynamics. We calculate the three transport coefficients required to describe viscous dissipation in this regime.
The longitudinal relaxation time T
sb1 is calculated for a dilute Fermi gas. We include the possibility of arbitrary degrees of polarization P, and uniform external magnetic fields. At low temperatures T
sb1 is proportional to T
sp−2 for the unpolarized gas in agreement with earlier calculations. For a polarized system in zero applied field the separation between up and down Fermi spheres provides an open channel in phase space for spin flipping processes. As temperature is reduced to zero T
sb1 levels off and approaches a constant value which depends sensitively on P, leading to much smaller values of T
sb1 than in the unpolarized case. For relaxation in a uniform external field H, Zeeman energy conservation during spin flipping interactions essentially shifts the location of the T
sp−2 behavior from zero polarization to the polarization P(H) which would be produced in equilibrium with the external field H. When the initial polarization of the system is different from P(H), T
sb1 again approaches a constant value which is equally sensitive to the initial polarization as temperature is reduced to zero. We apply our calculations to the case of dilute
sp3He-HeII solutions. We also consider the calculation of density dependent corrections to T
sb1 for unpolarized, or weakly polarized
sp3He-HeII using the long wavelength limit of the Bardeen-Baym-Pines interaction as a form for the spin independent part of the
sp3He-
sp3He interaction. Owing to the positive sign of the antisymmetric Landau parameter
rmFsbspoa in dilute
sp3He-HeII Fermi Liquid interactions act to screen the magnetic dipole interactions which cause relaxation. To lowest order in density we find that the relaxation rate 1/T
sb1 is reduced by factor
rm(1−3Fsbspoa) which compares favorably with recent calculations of T
sb1 for pure
sp3He.
In this work, we study the dynamics of an atomic harmonically trapped large-spin Fermi gas in one dimension (1D). We investigate the interplay of different collision processes. Coherent spin oscillations, driven by spin-changing forward scattering are captured by a mean-field description and scale linearly with density regardless of the dimension of the system. Conversely, "incoherent" collision processes which e.g. lead to the damping of spin oscillations, behave differently. In the usual three-dimensional (3D) case, the rate of incoherent processes increases faster with density than mean-field effects, but in 1D it increases slower. This means, that in the 1D case, incoherent collisions become more important at lower densities. We study these effects by deriving and integrating a quantum Boltzmann equation. We demonstrate that the well known fact that in one dimension, interaction-induced correlations become more dominant at low densities can be observed in far-from-equilibrium spin dynamics.
We consider a system of charged one-dimensional spin-1/2 fermions at low temperature. We study how the energy of a highly excited quasiparticle (or hole) relaxes toward the chemical potential in the regime of weak interactions. The dominant relaxation processes involve collisions with two other fermions. We find a dramatic enhancement of the relaxation rate at low energies, with the rate scaling as the inverse sixth power of the excitation energy. This behavior is caused by the long-range nature of the Coulomb interaction.
Spin propagation in systems of one-dimensional interacting fermions at finite temperature is intrinsically diffusive. The spreading rate of a spin packet is controlled by a transport coefficient termed ``spin drag'' relaxation time ${\ensuremath{\tau}}_{\mathrm{sd}}$. In this paper we present both numerical and analytical calculations of ${\ensuremath{\tau}}_{\mathrm{sd}}$ for a two-component spin-polarized cold Fermi gas trapped inside a tight atomic waveguide. At low temperatures we find an activation law for ${\ensuremath{\tau}}_{\mathrm{sd}}$, in agreement with earlier calculations of Coulomb drag between slightly asymmetric quantum wires, but with a different and much stronger temperature dependence of the prefactor. Our results provide a fundamental input for microscopic time-dependent spin-density functional theory calculations of spin transport in one-dimensional inhomogeneous systems of interacting fermions.