arXiv subjects

M. Pustilnik

Publications and source records attributed to M. Pustilnik.

At least 19 recordsLinked to original sources

arXiv2025

Dynamic correlations in Calogero-Sutherland model

The Calogero-Sutherland model represents a paradigmatic example of an integrable quantum system with applications ranging from cold atoms to random matrix theory. Combining sum rules with the Monte Carlo technique, we introduce a stochastic method that allows one to compute the dynamic structure factor and obtain an exact description of excitations beyond the conventional Luttinger liquid regime. We explore a broad range of interaction regimes, including weak interactions, where a Bogoliubov-type spectrum emerges, the Tonks-Girardeau regime, where excitations resemble those of an ideal Fermi gas, and strong interactions, where umklapp scattering leads to a Brillouin zone structure, typical of a crystal. Additionally, we discuss the connection between the hydrodynamic description of one-dimensional quantum gases, liquids, and solids with the Calogero-Sutherland wave function. The model's universality extends beyond atoms in waveguides, with implications for disordered systems and random matrix theory.

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↗

arXiv2017

Quantum Criticality in Resonant Andreev Conduction

Motivated by recent experiments with proximitized nanowires, we study a mesoscopic s-wave superconductor connected via point contacts to normal-state leads. We demonstrate that at energies below the charging energy the system is described by the two-channel Kondo model, which can be brought to the quantum critical regime by varying the gate potential and conductances of the contacts.

cond-mat.mes-hall↗

arXiv2016

Effective mass of elementary excitations in Galilean-invariant integrable models

We study low-energy excitations of one-dimensional Galilean-invariant models integrable by Bethe ansatz and characterized by nonsingular two-particle scattering phase shifts. We prove that the curvature of the excitation spectra is described by the recently proposed phenomenological expression for the effective mass. Our results apply to such models as the repulsive Lieb-Liniger model and the hyperbolic Calogero-Sutherland model.

cond-mat.str-el↗

arXiv2015

Fate of classical solitons in one-dimensional quantum systems

We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic particles and holes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model. We argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.

cond-mat.str-el↗

arXiv2014

Solitons in a one-dimensional Wigner crystal

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. We demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. We compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. We discuss implications of our results for the behavior of the dynamic structure factor.

cond-mat.str-el↗

arXiv2014

Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion

We study elementary excitations of a system of one-dimensional bosons with weak contact repulsion. We show that the Gross-Pitaevskii regime, in which the excitations are the well-known Bogoliubov quasiparticles and dark solitons, does not extend to the low energy limit. Instead, the spectra of both excitations have finite curvatures at zero momentum, in agreement with the phenomenological picture of fermionic quasiparticles. We describe analytically the crossover between the Gross-Pitaevskii and the low-energy regimes, and discuss implications of our results for the behavior of the dynamic structure factor.

cond-mat.quant-gas↗

arXiv2012

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature.

cond-mat.str-el↗

arXiv2011

Rate of equilibration of a one-dimensional Wigner crystal

We consider a system of one-dimensional spinless particles interacting via long-range repulsion. In the limit of strong interactions the system is a Wigner crystal, with excitations analogous to phonons in solids. In a harmonic crystal the phonons do not interact, and the system never reaches thermal equilibrium. We account for the anharmonism of the Wigner crystal and find the rate at which it approaches equilibrium. The full equilibration of the system requires umklapp scattering of phonons, resulting in exponential suppression of the equilibration rate at low temperatures.

cond-mat.str-el↗

arXiv2010

Equilibration of a one-dimensional Wigner crystal

Equilibration of a one-dimensional system of interacting electrons requires processes that change the numbers of left- and right-moving particles. At low temperatures such processes are strongly suppressed, resulting in slow relaxation towards equilibrium. We study this phenomenon in the case of spinless electrons with strong long-range repulsion, when the electrons form a one-dimensional Wigner crystal. We find the relaxation rate by accounting for the Umklapp scattering of phonons in the crystal. For the integrable model of particles with inverse-square repulsion, the relaxation rate vanishes.

cond-mat.mes-hall↗

arXiv2008

Correlations in an expanding gas of hard-core bosons

We consider a longitudinal expansion of a one-dimensional gas of hard-core bosons suddenly released from a trap. We show that the broken translational invariance in the initial state of the system is encoded in correlations between the bosonic occupation numbers in the momentum space. The correlations are protected by the integrability and exhibit no relaxation during the expansion.

cond-mat.stat-mech↗

arXiv2008

Threshold singularities in the dynamic response of gapless integrable models

We develop a method of an asymptotically exact treatment of threshold singularities in dynamic response functions of gapless integrable models. The method utilizes the integrability to recast the original problem in terms of the low-energy properties of a certain deformed Hamiltonian. The deformed Hamiltonian is local, hence it can be analysed using the conventional field theory methods. We apply the technique to spinless fermions on a lattice with nearest-neighbors repulsion, and evaluate the exponent characterizing the threshold singularity in the dynamic structure factor.

cond-mat.str-el↗

arXiv2007

Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions

We evaluate the spectral function of interacting fermions in one dimension. Contrary to the Tomonaga-Luttinger model, our treatment accounts for the nonlinearity of the free fermion spectrum. In a striking departure from the Luttinger liquid theory, the spectrum nonlinearity restores the main feature of the Fermi liquid: a Lorentzian peak in the spectral function on the particle mass-shell. At the same time, the spectral function displays a power-law singularity on the hole mass-shell, similar to that in the Luttinger liquid.

cond-mat.mes-hall↗

arXiv2007

Dynamics of excitations in a one-dimensional Bose liquid

We show that the dynamic structure factor of a one-dimensional Bose liquid has a power-law singularity defining the main mode of collective excitations. Using the Lieb-Liniger model, we evaluate the corresponding exponent as a function of the wave vector and the interaction strength.

cond-mat.stat-mech↗

arXiv2007

Permanent polarization of small metallic particles

Electric charge density in a metallic nanoparticle fluctuates due to inhomogeneities of various kinds. While in the bulk these fluctuations are compensated via Thomas--Fermi screening, residual surface charges give rise to a permanent electric dipole moment. We show that this dipole moment increases linearly with particle size, and fluctuates strongly from particle to particle

cond-mat.mes-hall↗

arXiv2006

Generation of spin current by Coulomb drag

Coulomb drag between two quantum wires is exponentially sensitive to the mismatch of their electronic densities. The application of a magnetic field can compensate this mismatch for electrons of opposite spin directions in different wires. The resulting enhanced momentum transfer leads to the conversion of the charge current in the active wire to the spin current in the passive wire.

cond-mat.mes-hall↗

arXiv2006

Dynamic structure factor of the Calogero-Sutherland model

We evaluate the dynamic structure factor $S(q,ω)$ of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small $q$, the structure factor differs from zero in a finite interval of frequencies of the width $δω\propto q^2/m$. At the borders of this interval $S(q,ω)$ exhibits power-law singularities with exponents depending only on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the X-ray absorption spectra of metals.

cond-mat.mes-hall↗

arXiv2006

Dynamic response of one-dimensional interacting fermions

We evaluate the dynamic structure factor $S(q,ω)$ of interacting one-dimensional spinless fermions with a nonlinear dispersion relation. The combined effect of the nonlinear dispersion and of the interactions leads to new universal features of $S(q,ω)$. The sharp peak $S\propto qδ(ω-uq)$, characteristic for the Tomonaga-Luttinger model, broadens up; $S(q,ω)$ for a fixed $q$ becomes finite at arbitrarily large $ω$. The main spectral weight, however, is confined to a narrow frequency interval of the width $δω\sim q^2/m$. At the boundaries of this interval the structure factor exhibits power-law singularities with exponents depending on the interaction strength and on the wave number $q$.

cond-mat.mes-hall↗