Analytic solutions of the 1D finite coupling delta function Bose gas

Abstract

An intensive study for both the weak coupling and strong coupling limits of the ground state properties of this classic system is presented. Detailed results for specific values of finite $N$ are given and from them results for general $N$ are determined. We focus on the density matrix and concomitantly its Fourier transform, the occupation numbers, along with the pair correlation function and concomitantly its Fourier transform, the structure factor. These are the signature quantities of the Bose gas. One specific result is that for weak coupling a rational polynomial structure holds despite the transcendental nature of the Bethe equations. All these new results are predicated on the Bethe ansatz and are built upon the seminal works of the past.

23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by Phys. Rev. A

References in corpus (12)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Transition from a strongly interacting 1D superfluid to a Mott insulator
• Quantum Inverse Scattering Method and Correlation Functions
• Strongly inhibited transport of a 1D Bose gas in a lattice
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• Exact ground state of finite Bose-Einstein condensates on a ring
• Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures
• The 1D interacting Bose gas in a hard wall box
• Painlevé transcendent evaluations of finite system density matrices for 1d impenetrable Bosons
• 1D Bose Gases in an Optical Lattice
• Solvable three boson model with attractive delta function interactions
• Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions

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• Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
• Free expansion of a Lieb-Liniger gas: Asymptotic form of the wave functions
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: A coordinate Bethe-ansatz analysis
• Local correlations in the attractive 1D Bose gas: from Bethe ansatz to the Gross-Pitaevskii equation
• Momentum distribution of a freely expanding Lieb-Liniger gas
• A coordinate Bethe ansatz approach to the calculation of equilibrium and nonequilibrium correlations of the one-dimensional Bose gas
• Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems
• Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz
• Single-particle density matrix for a time-dependent strongly interacting one-dimensional Bose gas
• Lieb-Liniger gas in a constant force potential
• From hardcore Bosons to free Fermions with Painlev{é} V
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
• Momentum distribution and non-local high order correlation functions of 1D strongly interacting Bose gas