Correlation functions of the one-dimensional attractive Bose gas

Abstract

The zero-temperature correlation functions of the one-dimensional attractive Bose gas with delta-function interaction are calculated analytically for any value of the interaction parameter and number of particles, directly from the integrability of the model. We point out a number of interesting features, including zero recoil energy for large number of particles, analogous to a Mössbauer effect.

4 pages, 2 figures

References in corpus (13)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Formation and Propagation of Matter Wave Soliton Trains
• Formation of a Matter-Wave Bright Soliton
• Observation of a Strongly-Interacting Degenerate Fermi Gas of Atoms
• Realization of Bose-Einstein condensates in lower dimensions
• Quantum Inverse Scattering Method and Correlation Functions
• Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
• Exciting Collective Oscillations in a Trapped 1D Gas
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases
• Dynamical density-density correlations in the one-dimensional Bose gas
• One-particle dynamical correlations in the one-dimensional Bose gas
• Determinant representation for dynamical correlation functions of the Quantum nonlinear Schrödinger equation

Cited by in corpus (88)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Free-energy distribution of the directed polymer at high temperature
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• An introduction to integrable techniques for one-dimensional quantum systems
• What is an integrable quench?
• Roadmap on Atomtronics: State of the art and perspective
• Exact local correlations and full counting statistics for arbitrary states of the one-dimensional interacting Bose gas
• Multi-particle bound state formation following a quantum quench to the one-dimensional Bose gas with attractive interactions
• Quench dynamics of a Tonks-Girardeau gas released from a harmonic trap
• Correlation functions of one-dimensional anyonic fluids
• Directed polymer near a hard wall and KPZ equation in the half-space
• Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
• Ramsey interference in one dimensional systems: The full distribution function of fringe contrast as a probe of many-body dynamics
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Exact methods in analysis of nonequilibrium dynamics of integrable models: application to the study of correlation functions in nonequilibrium 1D Bose gas
• Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers
• Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
• The One-dimensional KPZ Equation and the Airy Process
• From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
• Dynamics of the attractive 1D Bose gas: analytical treatment from integrability
• Exact dynamics following an interaction quench in a one-dimensional anyonic gas
• Interaction quench in a Lieb-Liniger model and the KPZ equation with flat initial conditions
• Quasi-local conserved charges and spin transport in spin-$1$ integrable chains
• Quantum transport of strongly interacting photons in a one-dimensional nonlinear waveguide
• One-particle density matrix and momentum distribution function of one-dimensional anyon gases
• Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• The quench action approach in finite integrable spin chains
• Memory and universality in interface growth
• Metastable criticality and the super Tonks-Girardeau gas
• Two-point free energy distribution function in (1+1) directed polymers
• Strongly interacting trapped one-dimensional quantum gases: an exact solution
• Excitation spectrum of bosons in a finite one-dimensional circular waveguide via the Bethe ansatz
• Generalized Hydrodynamics of the attractive Non-Linear Schroedinger Equation
• Short time growth of a KPZ interface with flat initial conditions
• Exact formulas for the form factors of local operators in the Lieb-Liniger model
• Dissociation of one-dimensional matter-wave breathers due to quantum many-body effects
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Two-time free energy distribution function in (1+1) directed polymers
• Attempted Bethe ansatz solution for one-dimensional directed polymers in random media
• Internal structure of a quantum soliton and classical excitations due to trap opening
• Bragg spectroscopy of clean and disordered lattice bosons in one dimension: a spectral fingerprint of the Bose glass
• Bound states of Dipolar Bosons in One-dimensional Systems
• Photonic quantum transport in a nonlinear optical fiber
• Raise and fall of a bright soliton in an optical lattice
• One-particle density matrix of a trapped Lieb-Liniger anyonic gas
• From the sine-Gordon field theory to the Kardar-Parisi-Zhang growth equation
• Adiabatic formation of bound states in the 1d Bose gas
• Correlation lengths of the repulsive one-dimensional Bose gas
• On integrable directed polymer models on the square lattice
• The quantum solitons atomtronic interference device
• Crossover from droplet to flat initial conditions in the KPZ equation from the replica Bethe ansatz
• Second quantization of Leinaas-Myrheim anyons in one dimension and their relation to the Lieb-Liniger model
• One-Dimensional Bose Gases with N-Body Attractive Interactions
• Tail of the two-time height distribution for KPZ growth in one dimension
• The propagator of the attractive delta-Bose gas in one dimension
• Delta-Bose gas on a half-line and the KPZ equation: boundary bound states and unbinding transitions
• Large-N ground state of the Lieb-Liniger model and Yang-Mills theory on a two-sphere
• Continuous Matrix Product Ansatz for the One-Dimensional Bose Gas with Point Interaction
• The crossing probability for directed polymers in random media
• Log-Gamma directed polymer with fixed endpoints via the replica Bethe Ansatz
• Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz
• Replica Bethe ansatz derivation of the GOE Tracy-Widom distribution in one-dimensional directed polymers with free boundary conditions
• Gapped solitons and periodic excitations in strongly coupled BEC
• Dynamically emergent correlations in bosons via quantum resetting
• Elastic scattering of a quantum matter-wave bright soliton on a barrier
• $N$-point free energy distribution function in one dimensional random directed polymers
• Two-time height distribution for 1D KPZ growth: the recent exact result and its tail via replica
• On two-time distribution functions in (1+1) random directed polymers
• Exact solution for $SU(2)$-symmetry breaking bosonic mixtures at strong interactions
• A liquid-gas transition for bosons with attractive interaction in one dimension
• Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas
• Crossover between various initial conditions in KPZ growth: flat to stationary
• Distribution function of the endpoint fluctuations of one-dimensional directed polymers in a random potential
• Mutually avoiding paths in random media and largests eigenvalues of random matrices
• High-momentum oscillating tails of strongly interacting 1D gases in a box
• Log-gamma directed polymer with one free end via coordinate Bethe Ansatz
• Determinant formula for the field form factor in the anyonic Lieb-Liniger model
• Equation of state for the one-dimensional attractive δ-potential Bose gas in the weak-coupling regime
• Measurement of one-dimensional matter-wave quantum breather
• A generalized Lieb-Liniger model
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective
• Clusters of bound particles in a quantum integrable many-body system and number theory
• Clusters of bound particles in the derivative delta-function Bose gas
• Necklace Ansatz for strongly repulsive spin mixtures on a ring
• Crossover in the log-gamma polymer from the replica coordinate Bethe Ansatz