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Register a new userIntegral equation theory based dielectric scheme for strongly coupled electron liquids
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In a recent paper, Lucco Castello et al. [arXiv:2107.03537] provided an accurate parametrization of classical one-component plasma bridge functions that was embedded in a novel dielectric scheme for strongly coupled electron liquids. Here, this approach is rigorously formulated, its set of equations is formally derived and its numerical algorithm is scrutinized. Systematic comparison with available and new path integral Monte Carlo simulations reveals a rather unprecedented agreement especially in terms of the interaction energy and the long wavelength limit of the static local field correction.
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We study the quantum quench in two coupled Tomonaga-Luttinger Liquids (TLLs), from the off-critical to the critical regime, relying on the conformal field theory approach and the known solutions for single TLLs. We consider a squeezed form of the initial state, whose low energy limit is fixed in a way to describe a massive and a massless mode, and we encode the non-equilibrium dynamics in a proper rescaling of the time. In this way, we compute several correlation functions, which at leading order factorize into multipoint functions evaluated at different times for the two modes. Depending on the observable, the contribution from the massive or from the massless mode can be the dominant one, giving rise to exponential or power-law decay in time, respectively. Our results find a direct application in all the quench problems where, in the scaling limit, there are two independent massless fields: these include the Hubbard model, the Gaudin-Yang gas, and tunnel-coupled tubes in cold atoms experiments.
We develop a microscopic approach to the consistent construction of the kinetic theory of dilute weakly ionized gases of hydrogen-like atoms. The approach is based on the framework of the second quantization method in the presence of bound states of particles and the method of reduced description of relaxation processes. Within the approach we developed the first-order perturbation theory over the weak interaction for a system of kinetic equations for the Wigner distribution functions of free fermions of both kinds and their bound states, the hydrogen-like atoms. It is shown that the conditions of low-temperature approximation, of the gas non-degeneracy and the approximation of weak interaction are realistic and can be met in a wide range of temperatures and the densities of the studied system. We obtain dispersion equations for determining the frequency and wave attenuation coefficients in dilute weakly ionized gas of hydrogen-like atoms near the described equilibrium state. In the two-level atom approximation it is shown that in the system there are longitudinal waves of matter polarization and transverse waves with the behavior characteristic of plasmon polaritons. The expressions for the dependence of the frequency and the Landau damping coefficients on the wave vector for all branches of the oscillations detected, are obtained. Quantitative estimations of the characteristics of the elementary perturbations in the system on an example of a weakly ionized dilute gas of Na-23 atoms are presented. The possibility of using the results of the theory developed to describe the properties of a Bose condensate of photons in dilute weakly ionized gas of hydrogen-like atoms is noted and the directions of its generalizations are discussed.
In this work we consider the hydrodynamic behavior of a coupled electron-phonon fluid, focusing on electronic transport under the conditions of strong phonon drag. This regime occurs when the rate of phonon equilibration due to e.g. umklapp scattering is much slower than the rate of normal electron-phonon collisions. Then phonons and electrons form a coupled out-of-equilibrium state where the total quasi-momentum of the electron-phonon fluid is conserved. A joint flow-velocity emerges as a collective hydrodynamic variable. We derive the equation of motion for this fluid from the underlying microscopic kinetic theory and elucidate its effective viscosity and thermal conductivity. In particular, we derive decay times of arbitrary harmonics of the distribution function and reveal its corresponding super-diffusive relaxation on the Fermi surface. We further consider several applications of this theory to magneto-transport properties in the Hall-bar and Corbino-disk geometries, relevant to experiments. In our analysis we allow for general boundary conditions that cover the crossover from no-slip to no-stress flows. Our approach also covers a crossover from the Stokes to the Ohmic regime under the conditions of the Gurzhi effect. In addition, we consider the frequency dependence of the surface impedance and non-equilibrium noise. For the latter, we notice that in the diffusive regime, a Fokker-Planck approximation, applied to the electron-phonon collision integral in the Eliashberg form, reduces it to a differential operator with Burgers nonlinearity. As a result, the non-equilibrium distribution function has a shock-wave structure in the energy domain. The consequence of this behavior for the Fano factor of the noise is investigated. In conclusion we discuss connections and limitations of our results in the context of recent electron-phonon drag measurements in Dirac and Weyl semimetals.
We develop a general framework to compute the scaling of entanglement entropy in inhomogeneous one-dimensional quantum systems belonging to the Luttinger liquid universality class. While much insight has been gained in homogeneous systems by making use of conformal field theory techniques, our focus is on systems for which the Luttinger parameter $K$ depends on position, and conformal invariance is broken. An important point of our analysis is that contributions stemming from the UV cutoff have to be treated very carefully, since they now depend on position. We show that such terms can be removed either by considering regularized entropies specifically designed to do so, or by tabulating numerically the cutoff, and reconstructing its contribution to the entropy through the local density approximation. We check our method numerically in the spin-1/2 XXZ spin chain in a spatially varying magnetic field, and find excellent agreement.
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