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Related papers: Ground State Asymptotics of a Dilute, Rotating Gas

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Gross-Pitaevskii and nonlinear Hartree equations are equations of nonlinear Schroedinger type, which play an important role in the theory of Bose-Einstein condensation. Recent results of Aschenbacher et. al. [AFGST] demonstrate, for a class…

Pattern Formation and Solitons · Physics 2009-11-10 Russell K. Jackson , Michael I. Weinstein

We consider a system of $N$ bosons interacting in a three-dimensional box endowed with periodic boundary condition that is strongly confined in one direction such that the normalized thickness of the box $d\ll1$. We assume particles to…

Mathematical Physics · Physics 2025-07-01 Xuwen Chen , Jiahao Wu , Zhifei Zhang

A generalized particle system interacting with a massless Bose field is investigated. We assume regularity conditions for the commutation relations of the interaction and annihilation operators. It is proven that if the ground state exists,…

Mathematical Physics · Physics 2026-01-01 Toshimitsu Takaesu

We derive the Gross-Pitaevskii equation in two-dimension from the first principles of two-dimensional scattering theory. Numerical calculation of the condensate wave function shows that atoms in a two-dimensional harmonic trap can be…

Condensed Matter · Physics 2007-05-23 Sang-Hoon Kim , Changyeon Won , Sung Dahm Oh , Wonho Jhe

We consider the dynamics of $N$ boson systems interacting through a pair potential $N^{-1} V_a(x_i-x_j)$ where $V_a (x) = a^{-3} V (x/a)$. We denote the solution to the $N$-particle Schr\"odinger equation by $\psi_{N, t}$. Recall that the…

Mathematical Physics · Physics 2007-05-23 Alexander Elgart , Laszlo Erdos , Benjamin Schlein , Horng-Tzer Yau

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…

Statistical Mechanics · Physics 2009-11-10 F. Mazzanti , A. Polls , A. Fabrocini

We investigate the ground state properties of a two-dimensional electron gas in the lowest Landau level using the Density Matrix Renormalization Group. The electron gas is confined to a cylinder with a strong magnetic field perpendicular to…

Mesoscale and Nanoscale Physics · Physics 2007-05-23 Emil J. Bergholtz , Anders Karlhede

We determined perturbatively the low-energy universal thermodynamics of dilute one-dimensional bosons with the three-body repulsive forces. The final results are presented for the limit of vanishing potential range in terms of…

Quantum Gases · Physics 2019-03-27 Volodymyr Pastukhov

The ground state of Bose--Einstein condensates can be described as the minimizer of the Gross--Pitaevskii energy functional subject to a mass conservation constraint. In this paper, we study the corresponding discrete optimization problem…

Numerical Analysis · Mathematics 2026-05-25 Chen Zhang , Heyan Zhu , Wenbin Chen

The energy super-critical Gross--Pitaevskii equation with a harmonic potential is revisited in the particular case of cubic focusing nonlinearity and dimension d > 4. In order to prove the existence of a ground state (a positive, radially…

Mathematical Physics · Physics 2021-04-13 Piotr Bizon , Filip Ficek , Dmitry E. Pelinovsky , Szymon Sobieszek

We investigate the fragmented many-body ground states of a spin-2 Bose gas in zero magnetic field.\ We point out that the exact ground state is not simply an average over rotationally-invariant mean-field states, in contrast to the spin-1…

Quantum Gases · Physics 2015-06-19 H. H. Jen , S. -K. Yip

This paper is concerned with the properties of $L^2$-normalized minimizers of the Gross-Pitaevskii (GP) functional for a two-dimensional Bose-Einstein condensate with attractive interaction and ring-shaped potential. By establishing some…

Functional Analysis · Mathematics 2020-02-27 Yujin Guo , Xiaoyu Zeng , Huan-Song Zhou

The isotropic scattering phase shift is calculated for non-relativistic bosons interacting at low energies via an arbitrary finite-range potential in d spacetime dimensions. Scattering on a (d-1)-dimensional torus is then considered, and…

Quantum Gases · Physics 2011-04-14 Silas R. Beane

The standard calculations of the ground-state energy of a homogeneous Bose gas rely on approximations which are physically reasonable but difficult to control. Lieb and Yngvason [Phys. Rev. Lett. 80, 2504 (1998)] have proved rigorously that…

Statistical Mechanics · Physics 2007-05-23 Christoph Weiss , Andre Eckardt

We analyze the ground-state properties and the excitation spectrum of Bose-Einstein condensates of trapped dipolar particles. First, we consider the case of a single-component polarized dipolar gas. For this case we discuss the influence of…

Condensed Matter · Physics 2007-05-23 K. Goral , L. Santos

When calculating the ground-state energy of a weakly interacting Bose gas with the help of the customary contact pseudopotential, one meets an artifical ultraviolet divergence which is caused by the incorrect treatment of the true…

Statistical Mechanics · Physics 2007-05-23 Andre Eckardt , Christoph Weiss , Martin Holthaus

We investigate the ground-state phases and spin-scissors dynamics of binary Bose-Einstein condensates confined in a twisted two-dimensional harmonic trap. The ground state hosts three distinct phases-phase-separated, polarized, and…

Quantum Gases · Physics 2025-09-16 Huaxin He , Fengtao Pang , Xianchao Zhang , Yongping Zhang , Chunlei Qu

We consider ground states of three-dimensional dipolar Bose-Einstein condensate involving quantum fluctuations and three-body losses, which can be described equivalently by positive $L^2$-constraint critical point of the Gross-Pitaevskii…

Analysis of PDEs · Mathematics 2020-11-03 Xiao Luo , Tao Yang

We present a quantum Monte Carlo study of two-dimensional dipolar Bose gases in the limit of zero temperature. The analysis is mainly focused on the anisotropy effects induced in the homogeneous gas when the polarization angle with respect…

Quantum Gases · Physics 2015-06-11 A. Macia , F. Mazzanti , J. Boronat

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the…

Analysis of PDEs · Mathematics 2018-04-11 Mathieu Lewin , Phan Thành Nam , Nicolas Rougerie