This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks—Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose—Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson—fermion interaction, the system exhibits composite-fermionization crossover.This paper investigates the ground-state properties of the mixture composed of the strongly interacting Tonks—Girardeau gas and spin polarized Fermi gas confined in one-dimensional harmonic traps, where the interaction between the Bose atoms and Fermi atoms is tunable. With a generalized Bose—Fermi transformation the mixture is mapped into a two-component Fermi gas. The homogeneous Fermi gas is exactly solvable by the Bethe-ansatz method and the ground state energy density can be obtained. Combining the ground-state energy function of the homogeneous system with local density approximation it obtains the ground-state density distributions of inhomogeneous mixture. It is shown that with the increase in boson—fermion interaction, the system exhibits composite-fermionization crossover.

Chinese Physics BJun 1, 20115 citations

Dilute Bose gas in two dimensions: Density expansions and the Gross-Pitaevskii equation

Alexander Yu. Cherny, Arkady A Shanenko

A dilute homogeneous two-dimensional (2D) Bose gas at zero temperature is studied with the method developed earlier by the authors. This method allows for considering renormalization of an arbitrary pairwise potential in a self-consistent manner, without the pseudopotential delta-function representation. Low-density expansions are derived for the chemical potential, ground-state energy, pair distribution function, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+ln u=-ln(na(2)pi)-2gamma, where na(2) and gamma are the gas parameter and the Euler constant, respectively. It is shown that the ground-state energy is mostly kinetic in the low-density limit. This result does not depend on a specific form of the pairwise interaction potential, contrary to the 3D case. A new form of the 2D Gross-Pitaevskii equation is proposed within our scheme.A dilute homogeneous two-dimensional (2D) Bose gas at zero temperature is studied with the method developed earlier by the authors. This method allows for considering renormalization of an arbitrary pairwise potential in a self-consistent manner, without the pseudopotential delta-function representation. Low-density expansions are derived for the chemical potential, ground-state energy, pair distribution function, kinetic and interaction energies. The expansion parameter is found to be a dimensionless in-medium scattering amplitude u obeying the equation 1/u+ln u=-ln(na(2)pi)-2gamma, where na(2) and gamma are the gas parameter and the Euler constant, respectively. It is shown that the ground-state energy is mostly kinetic in the low-density limit. This result does not depend on a specific form of the pairwise interaction potential, contrary to the 3D case. A new form of the 2D Gross-Pitaevskii equation is proposed within our scheme.

arXiv:cond-mat/0103632Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsJul 27, 200145 citations

The Ground State Energy of a Dilute Two-Dimensional Bose Gas

Élliott H. Lieb, Jakob Yngvason

arXiv:math-ph/0002014Journal of Statistical PhysicsMay 1, 2001106 citations

Ground-state properties of a dilute homogeneous Bose gas of hard disks in two dimensions

Ferran Mazzanti, A. Polls, Adelchi Fabrocini

The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\ensuremath{\sim}0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same $x$ .The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\ensuremath{\sim}0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same $x$.

arXiv:cond-mat/0410690Physical Review AMar 10, 200511 citations

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