Relaxation in Luttinger liquids: Bose-Fermi duality

Abstract

We explore the life time of excitations in a dispersive Luttinger liquid. We perform a bosonization supplemented by a sequence of unitary transformations that allows us to treat the problem in terms of weakly interacting quasiparticles. The relaxation described by the resulting Hamiltonian is analyzed by bosonic and (after a refermionization) by fermionic perturbation theory. We show that the the fermionic and bosonic formulations of the problem exhibit a remarkable strong-weak-coupling duality. Specifically, the fermionic theory is characterized by a dimensionless coupling constant $\lambda =m^{\ast }{l}^{2}T$ and the bosonic theory by ${\lambda }^{-1}$, where $1/m^{\ast }$ and $l$ characterize the curvature of the fermionic and bosonic spectra, respectively, and $T$ is the temperature.

15 page, 2 Figures; manuscript unchanged; misprint in metadata corrected

References in corpus (10)

• Universal theory of nonlinear Luttinger liquids
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit
• Three-particle collisions in quantum wires: Corrections to thermopower and conductance
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• 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
• 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

Cited by in corpus (14)

• Determination of topological edge quantum numbers of fractional quantum Hall phases
• Viscous Dissipation in One-Dimensional Quantum Liquids
• Thermal Transport in One Dimensional Electronic Fluid
• Thermal conductivity of the degenerate one-dimensional Fermi gas
• Equilibration in a chiral Luttinger liquid
• Second sound in systems of one-dimensional fermions
• Anomalous Hydrodynamics in One Dimensional Electronic Fluid
• Quantum kinetics of quenched two-dimensional Bose superfluids
• Quasiparticle decay in a one-dimensional Bose-Fermi mixture
• Equilibration of Quasi-One-Dimensional Fermi Gases
• Relaxation of the degenerate one-dimensional Fermi gas
• Plasmon decay and thermal transport from spin-charge coupling in generic Luttinger liquids
• Kinetic processes in Fermi-Luttinger liquids
• Quasiparticle energy relaxation in a gas of one-dimensional fermions with Coulomb interaction