arXiv subjects

K. A. Matveev

Publications and source records attributed to K. A. Matveev.

At least 19 recordsLinked to original sources

arXiv2023

Tunneling between two systems of interacting chiral fermions

We develop a theory of tunneling between two systems of spinless chiral fermions. This setup can be realized at the edge of a quantum Hall bilayer structure. We find that the differential conductance of such a device in the absence of interactions has an infinitely sharp peak as a function of applied voltage. Interaction between fermions results in broadening of the conductance peak. We focus on the regime of strong interactions, in which the shape of the peak manifests well defined features associated with the elementary excitations of the system.

cond-mat.mes-hall↗

arXiv2023

Physics of the Majorana-superconducting qubit hybrids

Manipulation of decoupled Majorana zero modes (MZMs) could enable topologically-protected quantum computing. However, the practical realization of a large number of perfectly decoupled MZMs needed to perform nontrivial quantum computation has proven to be challenging so far. Fortunately, even a small number of imperfect MZMs can be used to qualitatively extend the behavior of standard superconducting qubits, allowing for new approaches for noise suppression, qubit manipulation and read-out. Such hybrid devices take advantage of interplay of Cooper pair tunneling, coherent single electron tunneling, and Majorana hybridization. Here we provide a qualitative understanding of this system, give analytical results for its ground state energy spanning full parameter range, and describe potential sensing applications enabled by the interplay between Majorana and Cooper pair tunneling.

cond-mat.mes-hall↗

arXiv2023

Viscous dissipation in a gas of one-dimensional fermions with generic dispersion

A well-known feature of the classical monoatomic gas is that its bulk viscosity is strongly suppressed because the single-particle dispersion is quadratic. On the other hand, in condensed matter systems the effective single-particle dispersion is altered by lattice effects and interactions. In this work, we study the bulk viscosity of one-dimensional Fermi gases with generic energy-momentum dispersion relations. As an application, viscous dissipation arising from lattice effects is analyzed for the tight-binding model. In addition, we investigate how weak interactions affect the bulk viscosity. Finally, we discuss viscous dissipation in the regime in which the Fermi gas is not fully equilibrated, as can occur when the system is driven at frequencies that exceed the rate of fermion backscattering. In this case, the Fermi gas is described by three bulk viscosities, which we obtain for a generic single-particle dispersion.

cond-mat.quant-gas↗

arXiv2023

Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions

We study general features of the excitation spectrum of a system of one-dimensional chiral spinless fermions with short-range interactions. We show that the nature of the elementary excitations of such a system depends strongly on the nonlinearity of the underlying dispersion of the fermions. In the case of quadratic nonlinearity, the low-momentum excitations are essentially fermionic quasiparticles and quasiholes, whereas the high-momentum ones are classical harmonic waves and solitons. In the case of cubic nonlinearity, the nature of the elementary excitations does not depend on momentum and is determined by the strength of the interactions. At a certain critical value of the interaction strength the excitation spectrum changes qualitatively, pointing to a dynamic phase transition in the system.

cond-mat.mes-hall↗

arXiv2022

Spectral function of chiral one-dimensional Fermi liquid in the regime of strong interactions

We study momentum-resolved tunneling into a system of spinless chiral one-dimensional fermions, such as electrons at the edge of an integer quantum Hall system. Interactions between particles give rise to broadening of the spectral function of the system. We develop an approach that enables one to obtain the shape of the peak in the spectral function in the regime of strong interaction. We apply our technique to the special cases of short-range and Coulomb interactions.

cond-mat.str-el↗

arXiv2022

Scar states in a system of interacting chiral fermions

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 the strong interaction limit, persist at intermediate and weak couplings, enabling persistent density oscillations in the system, despite it being far from integrability.

cond-mat.str-el↗

arXiv2021

Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction

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.

cond-mat.str-el↗

arXiv2020

Sound in a system of chiral one-dimensional fermions

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.

cond-mat.mes-hall↗

arXiv2020

Viscous Properties of a Degenerate One-Dimensional Fermi Gas

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 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.

cond-mat.quant-gas↗

arXiv2020

Relaxation of the degenerate one-dimensional Fermi gas

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 the 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.

cond-mat.mes-hall↗

arXiv2019

Two-fluid dynamics of one-dimensional quantum liquids in the absence of Galilean invariance

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 applies 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.

cond-mat.mes-hall↗

arXiv2019

Thermal conductivity of the degenerate one-dimensional Fermi gas

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.

cond-mat.mes-hall↗

arXiv2019

Equilibration of Quasi-One-Dimensional Fermi Gases

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 temperatures. 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.

cond-mat.mes-hall↗

arXiv2018

Propagation and attenuation of sound in one-dimensional quantum liquids

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.

cond-mat.mes-hall↗

arXiv2018

Hybrid sound modes in one-dimensional quantum liquids

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 the 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.

cond-mat.mes-hall↗

arXiv2017

Second sound in systems of one-dimensional fermions

We study sound in Galilean invariant systems of one-dimensional fermions. At low temperatures, we find a broad range of frequencies in which in addition to the waves of density there is a second sound corresponding to ballistic propagation of heat in the system. The damping of the second sound mode is weak, provided the frequency is large compared to a relaxation rate that is exponentially small at low temperatures. At lower frequencies the second sound mode is damped, and the propagation of heat is diffusive.

cond-mat.mes-hall↗

arXiv2017

Viscosity of a Multi-channel One-Dimensional Fermi Gas

Many one-dimensional systems of experimental interest possess multiple bands arising from shallow confining potentials. In this work, we study a gas of weakly interacting fermions and show that the bulk viscosity is dramatically altered by the occupation of more than one band. The reasons for this are two-fold: a multichannel system is more easily displaced from equilibrium and the associated relaxation processes lead to more rapid equilibration than in the single channel case. We estimate the bulk viscosity in terms of the underlying microscopic interactions. The experimental relevance of this physics is discussed in the context of quantum wires and trapped cold atomic gases.

cond-mat.quant-gas↗

arXiv2017

Viscous Dissipation in One-Dimensional Quantum Liquids

We develop a theory of viscous dissipation in one-dimensional single-component quantum liquids at low temperatures. Such liquids are characterized by a single viscosity coefficient, the bulk viscosity. We show that for a generic interaction between the constituent particles this viscosity diverges in the zero-temperature limit. In the special case of integrable models, the viscosity is infinite at any temperature, which can be interpreted as a breakdown of the hydrodynamic description. Our consideration is applicable to all single-component Galilean-invariant one-dimensional quantum liquids, regardless of the statistics of the constituent particles and the interaction strength.

cond-mat.str-el↗