Equilibration in a chiral Luttinger liquid

Abstract

We explore the weak-strong-coupling Bose-Fermi duality in a model of a single-channel integer or fractional quantum Hall edge state with a finite-range interaction. The system is described by a chiral Luttinger liquid with non-linear dispersion of bosonic and fermonic excitations. We use the bosonization, a unitary transformation, and a refermionization to map the system onto that of weakly interacting fermions at low temperature $T$ or weakly interacting bosons at high $T$. We calculate the equilibration rate which is found to scale with temperature as $T^5$ and $T^{14}$ in the high-temperature ("bosonic") and the low-temperature ("fermonic") regimes, respectively. The relaxation rate of a hot particle with the momentum $k$ in the fermonic regime scales as $k^7{T}^7$.

arXiv comment9 pages, 2 figures

References in corpus (49)

• Many-Body Physics with Ultracold Gases
• Artificial gauge potentials for neutral atoms
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• An Electronic Mach-Zehnder Interferometer
• Rapidly Rotating Atomic Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Fractional quantum Hall states of atoms in optical Lattices
• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Universal theory of nonlinear Luttinger liquids
• Direct measurement of the coherence length of edge states in the Integer Quantum Hall Regime
• Non-Equilibrium Edge Channel Spectroscopy in the Integer Quantum Hall Regime
• Realizing Fractional Chern Insulators with Dipolar Spins
• Energy Relaxation in the Integer Quantum Hall Regime
• Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet
• Reaching Fractional Quantum Hall States with Optical Flux Lattices
• Finite bias visibility of the electronic Mach-Zehnder interferometer
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Reconstruction of Fractional Quantum Hall Edges
• Decoherence and single electron charging in an electronic Mach-Zehnder interferometer
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Entanglement, Dephasing, and Phase Recovery via Cross-Correlation Measurements of Electrons
• Tuning Energy Relaxation along Quantum Hall Channels
• Controlled Dephasing of Electrons by Non-Gaussian Shot Noise
• Edge Channel Interference Controlled by Landau Level Filling
• Unexpected finite-bias visibility dependence in an electronic Mach Zehnder interferometer
• Non-equilibrium Tunneling Spectroscopy in Carbon Nanotubes
• Three-particle collisions in quantum wires: Corrections to thermopower and conductance
• Noise dephasing in the edge states of the Integer Quantum Hall regime
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Tuning decoherence with a voltage probe
• Quantum coherence engineering in the integer quantum Hall regime
• Dynamics of waves in 1D electron systems: Density oscillations driven by population inversion
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Decay of fermionic quasiparticles in one-dimensional quantum liquids
• Thermalization of nonequilibrium electrons in quantum wires
• Tunable non-equilibrium Luttinger liquid based on counter-propagating edge channels
• Class of exactly soluble models of one-dimensional spinless fermions and its application to the Tomonaga-Luttinger Hamiltonian with nonlinear dispersion
• Coulomb drag between ballistic quantum wires
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
• Dissipationless kinetics of one dimensional interacting fermions
• Density-density propagator for one-dimensional interacting spinless fermions with non-linear dispersion and calculation of the Coulomb drag resistivity
• Relaxation of weakly interacting electrons in one dimension
• Measurement of the Transmission Phase through a Quantum Dot Embedded in One Arm of an Electronic Mach-Zehnder Interferometer
• Energy transport by neutral collective excitations at the quantum Hall edge
• Decay of Bogoliubov quasiparticles in a nonideal one-dimensional Bose gas
• Relaxation and edge reconstruction in integer quantum Hall systems
• Thermal transport and quench relaxation in nonlinear Luttinger liquids
• Impact of electron heating on the equilibration between quantum Hall edge channels

Cited by in corpus (10)

• Exact Quantum Scars in the Chiral Non-Linear Luttinger Liquid
• Determination of topological edge quantum numbers of fractional quantum Hall phases
• Decay of Bogoliubov excitations in one-dimensional Bose gases
• Viscous Dissipation in One-Dimensional Quantum Liquids
• Time evolution during and after finite-time quantum quenches in Luttinger liquids
• Quasiparticle decay in a one-dimensional Bose-Fermi mixture
• Spin correlation functions and quasiparticle decay
• Sound in a system of chiral one-dimensional fermions
• Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction
• From Luttinger liquids to Luttinger droplets via higher-order bosonization identities