Dynamic and static density-density correlations in the one-dimensional Bose gas: exact results and approximations

Abstract

We discuss approximate formulas for the dynamic structure factor of the one-dimensional Bose gas in the Lieb-Liniger model that appear to be applicable over a wide range of the relevant parameters such as the interaction strength, frequency, and wavenumber. The suggested approximations are consistent with the exact results known in limiting cases. In particular, we encompass exact edge exponents as well as Luttinger liquid and perturbation theoretic results. We further discuss derived approximations for the static structure factor and the pair distribution function g(x). The approximate expressions show excellent agreement with numerical results based on the algebraic Bethe ansatz.

8 pages, 6 figures

References in corpus (13)

• Many-Body Physics with Ultracold Gases
• Bosonizing one-dimensional cold atomic gases
• Universal theory of nonlinear Luttinger liquids
• Dynamical density-density correlations in the one-dimensional Bose gas
• One-particle dynamical correlations in the one-dimensional Bose gas
• Exact exponents of edge singularities in dynamic correlation functions of 1D Bose gas
• Dynamics of excitations in a one-dimensional Bose liquid
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• Spatial nonlocal pair correlations in a repulsive 1D Bose gas
• Threshold singularities in the dynamic response of gapless integrable models
• The Dynamic Structure Factor of the 1D Bose Gas near the Tonks-Girardeau Limit
• Self-consistent calculation of the coupling constant in the Gross-Pitaevskii equation
• Approximate expression for the dynamic structure factor in the Lieb-Liniger model

Cited by in corpus (25)

• One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Robust Mesoscopic Superposition of Strongly Correlated Ultracold Atoms
• Theory of superfluidity and drag force in the one-dimensional Bose gas
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Dynamic structure factor and drag force in a one-dimensional strongly-interacting Bose gas at finite temperature
• Dynamic response of 1D bosons in a trap
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
• Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions
• Correlation lengths of the repulsive one-dimensional Bose gas
• Decay of superfluid currents in the interacting one-dimensional Bose gas
• Variational Bethe Ansatz approach for dipolar one-dimensional bosons
• Exact spectral function of a Tonks-Girardeau gas in a lattice
• Exact results for polaron and molecule in one-dimensional spin-1/2 Fermi gas
• Polarization angle dependence of the breathing modes in confined one-dimensional dipolar bosons
• The two particle-hole pairs contribution to the dynamic correlation functions of quantum integrable models
• Duality between weak and strong interactions in quantum gases
• Density ripples in expanding low-dimensional gases as a probe of correlations
• Time-resolved density correlations as probe of squeezing in toroidal Bose-Einstein condensates
• Effect of transverse confinement on a quasi-one dimensional dipolar Bose gas
• Probing the quantum state of a 1D Bose gas using off-resonant light scattering
• Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials
• Properties of bosons in a one-dimensional bichromatic optical lattice in the regime of the Sine-Gordon transition: a Worm Algorithm Monte Carlo study
• Structural Dynamics and Strong Correlations in Dynamical Quantum Optical Lattices