Universal correlations of trapped one-dimensional impenetrable bosons

Abstract

We calculate the asymptotic behaviour of the one body density matrix of one-dimensional impenetrable bosons in finite size geometries. Our approach is based on a modification of the Replica Method from the theory of disordered systems. We obtain explicit expressions for oscillating terms, similar to fermionic Friedel oscillations. These terms are universal and originate from the strong short-range correlations between bosons in one dimension.

18 pages, 3 figures. Published version

References in corpus (26)

• Realization of Bose-Einstein condensates in lower dimensions
• A quasi-pure Bose-Einstein condensate immersed in a Fermi sea
• Regimes of quantum degeneracy in trapped 1D gases
• Exploring phase coherence in a 2D lattice of Bose-Einstein condensates
• Exciting Collective Oscillations in a Trapped 1D Gas
• Bosons in cigar-shape traps: Thomas-Fermi regime, Tonks-Girardeau regime, and between
• Collective oscillations of a 1D trapped Bose gas
• Stability and phase coherence of trapped 1D Bose gases
• Pair correlations in a finite-temperature 1D Bose gas
• Momentum spectroscopy of 1D phase fluctuations in Bose-Einstein condensates
• Application of the $\tau$-Function Theory of Painlevé Equations to Random Matrices: PIV, PII and the GUE
• Equation of State of an Anyon Gas in a Strong Magnetic Field
• Finite one dimensional impenetrable Bose systems: Occupation numbers
• Factorization of Correlation Functions and the Replica Limit of the Toda Lattice Equation
• Wigner-Dyson Statistics from the Replica Method
• Dynamical transition from a quasi-one dimensional Bose-Einstein condensate to a Tonks-Girardeau gas
• Replica Limit of the Toda Lattice Equation
• Replica field theories, Painleve transcendents, and exact correlation functions
• Autocorrelation of Random Matrix Polynomials
• Ground-state properties of hard core bosons in one-dimensional harmonic traps
• Level Correlations in Disordered Metals: the Replica sigma-Model
• Non-perturbative results for level correlations from the replica nonlinear sigma model
• Replica Treatment of the Calogero-Sutherland Model
• Random matrix averages and the impenetrable Bose gas in Dirichlet and Neumann boundary conditions
• Correlation functions of the BC Calogero-Sutherland model
• Logarithmic moments of characteristic polynomials of random matrices

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