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Register a new userGround state properties of hard-core anyons in a harmonic potential
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Yajiang Hao
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Using anyon-fermion mapping method, we investigate the ground state properties of hard-core anyons confined in a one-dimensional harmonic trap. The concise analytical formula of the reduced one-body density matrix are obtained. Basing on the formula, we evaluated the momentum distribution, the natural orbitals and their occupation distributions for different statistical parameters. The occupation and occupation fraction of the lowest natural orbital versus anyon number are also displayed. It is shown that the ground state properties of anyons interplay between Bosons and Fermions continuously. We can expect that the hard-core anyons of larger statistical parameter exhibit the similar properties to the hard-core Bosons although anyon system satisfy specific fractional statistics.
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We investigate the strongly interacting hard-core anyon gases in a one dimensional harmonic potential at finite temperature by extending thermal Bose-Fermi mapping method to thermal anyon-ferimon mapping method. With thermal anyon-fermion mapping method we obtain the reduced one-body density matrix and therefore the momentum distribution for different statistical parameters and temperatures. At low temperature hard-core anyon gases exhibit the similar properties as those of ground state, which interpolate between Bose-like and Fermi-like continuously with the evolution of statistical properties. At high temperature hard-core anyon gases of different statistical properties display the same reduced one-body density matrix and momentum distribution as those of spin-polarized fermions. The Tans contact of hard-core anyon gas at finite temperature is also evaluated, which take the simple relation with that of Tonks-Girardeau gas $C_b$ as $C=frac12(1-coschipi)C_b$.
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