In this paper we discuss the solutions of the cubic nonlinear Schrödinger equation with variable coefficients that model a trapped, quasi-one-dimensional Bose–Einstein condensate with time-varying potential and time-varying atomic scattering length. By applying the theory of Jacobian elliptic functions, we propose a new ansatz to find two new families of solutions. We also obtained regions in the parameters space in which the found families of solutions exist.

International Journal of Modern Physics BMar 20, 20074 citations

THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND

Andreas Deuchert, SIMON MAYER, Robert Seiringer

arXiv:1910.03372Forum of Mathematics SigmaJan 1, 20208 citations

Laser Spectroscopy

EXPERIMENTAL STUDY OF A BOSE GAS IN ONE DIMENSION

William D. Phillips, J. H. Huckans, B. Laburthe-Tolra, Kenneth M. O’Hara, J. V. Porto, S. L. Rolston, Marco Anderlini

Published Feb 1, 2004• 0 citations

Publisher

DOI: 10.1142/9789812703002_0019

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THE FREE ENERGY OF THE TWO-DIMENSIONAL DILUTE BOSE GAS. I. LOWER BOUND

Andreas Deuchert, SIMON MAYER, Robert Seiringer

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\unicode[STIX]{x1D70C}$ and inverse temperature $\unicode[STIX]{x1D6FD}$ differs from the one of the noninteracting system by the correction term $4\unicode[STIX]{x1D70B}\unicode[STIX]{x1D70C}^{2}|\ln \,a^{2}\unicode[STIX]{x1D70C}|^{-1}(2-[1-\unicode[STIX]{x1D6FD}_{\text{c}}/\unicode[STIX]{x1D6FD}]_{+}^{2})$ . Here, $a$ is the scattering length of the interaction potential, $[\cdot ]_{+}=\max \{0,\cdot \}$ and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$ .We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\unicode[STIX]{x1D70C}$ and inverse temperature $\unicode[STIX]{x1D6FD}$ differs from the one of the noninteracting system by the correction term $4\unicode[STIX]{x1D70B}\unicode[STIX]{x1D70C}^{2}|\ln \,a^{2}\unicode[STIX]{x1D70C}|^{-1}(2-[1-\unicode[STIX]{x1D6FD}_{\text{c}}/\unicode[STIX]{x1D6FD}]_{+}^{2})$ . Here, $a$ is the scattering length of the interaction potential, $[\cdot ]_{+}=\max \{0,\cdot \}$ and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$ .

arXiv:1910.03372Forum of Mathematics SigmaJan 1, 20208 citations

a

is the scattering length of the interaction potential,

[\cdot ]_{+}=\max \{0,\cdot \}

and $\unicode[STIX]{x1D6FD}_{\text{c}}$ is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit $a^{2}\unicode[STIX]{x1D70C}\ll 1$ and if $\unicode[STIX]{x1D6FD}\unicode[STIX]{x1D70C}\gtrsim 1$ .