Fate of classical solitons in one-dimensional quantum systems

Abstract

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.

References in corpus (10)

• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Fermi-Luttinger liquid: Spectral function of interacting one-dimensional fermions
• Breakdown of integrability in a quasi-one-dimensional ultracold bosonic gas
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Fermionic Quasiparticle Representation of Tomonaga-Luttinger Hamiltonian
• Relaxation of a high-energy quasiparticle in a one-dimensional Bose gas
• Hydrodynamics of cold atomic gases in the limit of weak nonlinearity, dispersion and dissipation
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Low-energy excitations of a one-dimensional Bose gas with weak contact repulsion
• Solitons in a one-dimensional Wigner crystal

Cited by in corpus (11)

• Equilibration in one-dimensional quantum hydrodynamic systems
• Decay of Bogoliubov excitations in one-dimensional Bose gases
• Traveling Majorana solitons in a one-dimensional spin-orbit coupled Fermi superfluid
• Viscous Dissipation in One-Dimensional Quantum Liquids
• Effective mass of elementary excitations in Galilean-invariant integrable models
• Analytical results for the capacitance of a circular plate capacitor
• Hydrodynamics of local excitations after an interaction quench in 1D cold atomic gases
• Exotic Topological States with Raman-Induced Spin-Orbit Coupling
• Phase space holography with no strings attached
• Local Properties of the Rapidity Distribution in the Lieb-Liniger Model
• Elementary excitations of a system of one-dimensional chiral fermions with short-range interactions