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      One-particle density matrix of trapped one-dimensional impenetrable bosons from conformal invariance

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          Abstract

          The one-particle density matrix of the one-dimensional Tonks-Girardeau gas with inhomogeneous density profile is calculated, thanks to a recent observation that relates this system to a two-dimensional conformal field theory in curved space. The result is asymptotically exact in the limit of large particle density and small density variation, and holds for arbitrary trapping potentials. In the particular case of a harmonic trap, we recover a formula obtained by Forrester et al. [Phys. Rev. A 67, 043607 (2003)] from a different method.

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          Most cited references 42

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          Infinite conformal symmetry in two-dimensional quantum field theory

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            Conformal invariance and surface critical behavior

             John Cardy (1984)
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              One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases

              We review the physics of one-dimensional interacting bosonic systems. Beginning with results from exactly solvable models and computational approaches, we introduce the concept of bosonic Tomonaga-Luttinger Liquids relevant for one-dimension, and compare it with Bose-Einstein condensates existing in dimensions higher than one. We discuss the effects of various perturbations on the Tomonaga-Luttinger liquid state as well as extensions to multicomponent and out of equilibrium situations. Finally, we review the experimental systems that can be described in terms of models of interacting bosons in one dimension.
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                Author and article information

                Journal
                2017-01-09
                Article
                1701.02248

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                19 pages, 2 figures, 2 tables
                cond-mat.stat-mech cond-mat.quant-gas math-ph math.MP

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