One-dimensional anyons with competing $\delta$-function and derivative $\delta$-function potentials

Abstract

We propose an exactly solvable model of one-dimensional anyons with competing $\delta$-function and derivative $\delta$-function interaction potentials. The Bethe ansatz equations are derived in terms of the $N$-particle sector for the quantum anyonic field model of the generalized derivative nonlinear Schrödinger equation. This more general anyon model exhibits richer physics than that of the recently studied one-dimensional model of $\delta$-function interacting anyons. We show that the anyonic signature is inextricably related to the velocities of the colliding particles and the pairwise dynamical interaction between particles.

9 pages, 2 figures, minor changes, references updated

References in corpus (26)

• Topologically-Protected Qubits from a Possible Non-Abelian Fractional Quantum Hall State
• Detecting Non-Abelian Statistics in the nu=5/2 Fractional Quantum Hall State
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Braid Topologies for Quantum Computation
• Exact Dynamical Correlation Functions of Calogero-Sutherland Model and One-Dimensional Fractional Statistics
• Exact solution of double-delta function Bose gas through interacting anyon gas
• A Class of Exactly Solvable Pairing Models
• The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
• Signatures of fractional statistics in noise experiments in quantum Hall fluids
• Correlation functions of one-dimensional anyonic fluids
• Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
• Correlation Functions of One-Dimensional Lieb-Liniger Anyons
• Anyons in a weakly interacting system
• Generalized exclusion statistics and degenerate signature of strongly interacting anyons
• Bethe Ansatz for 1D interacting anyons
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Entanglement properties and moment distributions of a system of hard-core anyons on a ring
• One-Dimensional XXZ Model for Particles Obeying Fractional Statistics
• Bosonization at Finite Temperature and Anyon Condensation
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
• Coulomb blockade of anyons
• Ground state of one-dimensional bosons with delta interaction: link to the BCS model
• Ground and excited states of spinor Fermi gases in tight waveguides and the Lieb-Liniger-Heisenberg model
• Fermionic long range correlations realized by particles obeying deformed statistics
• Multi-band structure of the quantum bound states for a generalized nonlinear Schrodinger model

Cited by in corpus (22)

• Fermionization and bosonization of expanding 1D anyonic fluids
• Nonequilibrium dynamics of one-dimensional hard-core anyons following a quench: Complete relaxation of one-body observables
• Junctions of anyonic Luttinger wires
• Off-diagonal correlations in one-dimensional anyonic models: A replica approach
• Correlation functions of one-dimensional strongly interacting two-component gases
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. III. Large distance asymptotics of the space correlations
• One-Dimensional Impenetrable Anyons in Thermal Equilibrium. IV. Large Time and Distance Asymptotic Behavior of the Correlation Functions
• Quantum Inverse Scattering Method with anyonic grading
• Quantum holonomy in Lieb-Liniger model
• Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
• Center-of-mass-momentum-dependent interaction between ultracold atoms
• Center of Mass Momentum Dependent Interaction Between Ultracold Atoms
• The asymptotic Bethe ansatz solution for one-dimensional SU(2) spinor bosons with finite range Gaussian interactions
• Anyonic Liquids in Nearly Saturated Spin Chains
• Tailoring Dynamical Fermionization: Delta kick cooling of a Tonks-Girardeau gas
• Equation of state for the one-dimensional attractive δ-potential Bose gas in the weak-coupling regime
• Dualities for anyons
• Thermodynamics of Statistical Anyons
• Construction and exact solution of a nonlinear quantum field model in quasi-higher dimension
• Singularity-free treatment of delta-function point scatterers in two dimensions and its conceptual implications
• Universal properties and dynamical bosonization of strongly interacting one-dimensional anyons
• Introducing a general method for solving electromagnetic radiation problem in an arbitrary linear medium