We study the nature of many-body eigenstates of a system of interacting chiral spinless fermions on a ring. We find a coexistence of fermionic and bosonic types of eigenstates in parts of the many-body spectrum. Some bosonic eigenstates, native to th
e strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability.
We consider a system of charged one-dimensional spin-$frac{1}{2}$ 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.
We consider a system of one-dimensional fermions moving in one direction, such as electrons at the edge of a quantum Hall system. At sufficiently long time scales the system is brought to equilibrium by weak interactions between the particles, which
conserve their total number, energy, and momentum. Time evolution of the system near equilibrium is described by hydrodynamics based on the three conservation laws. We find that the system supports three sound modes. In the low temperature limit one mode is a pure oscillation of particle density, analogous to the ordinary sound. The other two modes involve oscillations of both particle and entropy densities. In the presence of disorder, the first sound mode is strongly damped at frequencies below the momentum relaxation rate, whereas the other two modes remain weakly damped.
We study the viscous properties of a system of weakly interacting spin-$frac{1}{2}$ 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 temperat
ures. 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.
We study how a system of one-dimensional spin-1/2 fermions at temperatures well below the Fermi energy approaches thermal equilibrium. The interactions between fermions are assumed to be weak and are accounted for within the perturbation theory. In t
he absence of an external magnetic field, spin degeneracy strongly affects relaxation of the Fermi gas. For sufficiently short-range interactions, the rate of relaxation scales linearly with temperature. Focusing on the case of the system near equilibrium, we linearize the collision integral and find exact solution of the resulting relaxation problem. We discuss the application of our results to the evaluation of the transport coefficients of the one-dimensional Fermi gas.
Luttinger liquid theory of one-dimensional quantum systems ignores exponentially weak backscattering of particles. This endows Luttinger liquids with superfluid properties. The corresponding two-fluid hydrodynamic description available at present app
lies only to Galilean-invariant systems, whereas most experimental realizations of one-dimensional quantum liquids lack Galilean invariance. Here we develop the two-fluid theory of such quantum liquids. In the low-frequency limit the theory reduces to single-fluid hydrodynamics. However, the absence of Galilean invariance brings about three new transport coefficients. We obtain expressions for these coefficients in terms of the backscattering rate.
One-dimensional systems often possess multiple channels or bands arising from the excitation of transverse degrees of freedom. In the present work, we study the specific processes that dominate the equilibration of multi-channel Fermi gases at low te
mperatures. Focusing on the case of two channels, we perform an analysis of the relaxation properties of these systems by studying the spectrum and eigenmodes of the linearized collision integral. As an application of this analysis, a detailed calculation of the bulk viscosity is presented. The dominant scattering processes obey an unexpected conservation law which is likely to affect the hydrodynamic behavior of these systems.
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 relaxati
on 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.
At low temperatures, elementary excitations of a one-dimensional quantum liquid form a gas that can move as a whole with respect to the center of mass of the system. This internal motion attenuates at exponentially long time scales. As a result, in a
broad range of frequencies the liquid is described by two-fluid hydrodynamics, and the system supports two sound modes. The physical nature of the two sounds depends on whether the particles forming the quantum liquid have a spin degree of freedom. For particles with spin, the modes are analogous to the first and second sound modes in superfluid $^4$He, which are the waves of density and entropy, respectively. When dissipative processes are taken into account, we find that at low frequencies the second sound is transformed into heat diffusion, while the first sound mode remains weakly damped and becomes the ordinary sound. In a spinless liquid the entropy and density oscillations are strongly coupled, and the resulting sound modes are hybrids of the first and second sound. As the frequency is lowered and dissipation processes become important, the crossover to single-fluid regime occurs in two steps. First the hybrid modes transform into predominantly density and entropy waves, similar to the first and second sound, and then the density wave transforms to the ordinary sound and the entropy wave becomes a heat diffusion mode. Finally, we account for the dissipation due to viscosity and intrinsic thermal conductivity of the gas of excitations, which controls attenuation of the sound modes at high frequencies.
We study sound in a single-channel one-dimensional quantum liquid. In contrast to classical fluids, instead of a single sound mode we find two modes of density oscillations. The speeds at which these two sound modes propagate are nearly equal, with t
he difference that scales linearly with the small temperature of the system. The two sound modes emerge as hybrids of the first and second sounds, and combine oscillations of both density and entropy of the liquid.
