On One-Dimensional Bose Gases with Two-Body and (Critical) Attractive Three-Body Interactions

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-05-03 DOI:10.1137/22m1535139

Dinh-Thi Nguyen, Julien Ricaud

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引用次数: 0

Abstract

SIAM Journal on Mathematical Analysis, Volume 56, Issue 3, Page 3203-3251, June 2024.
Abstract. We consider a one-dimensional, trapped, focusing Bose gas where [math] bosons interact with each other via both a two-body interaction potential of the form [math] and an attractive three-body interaction potential of the form [math], where [math], [math], [math], [math], and [math]. The system is stable either for any [math] as long as [math] —the critical strength of the one-dimensional focusing quintic nonlinear Schrödinger (NLS) equation— or for [math] when [math]. In the former case, fixing [math], we prove that in the mean-field limit the many-body system exhibits the Bose–Einstein condensation on the cubic-quintic NLS ground states. When assuming [math] and [math] as [math], with the former convergence being slow enough and “not faster” than the latter, we prove that the ground state of the system is fully condensed on the (unique) solution to the quintic NLS equation. In the latter case, [math] fixed, we obtain the convergence of many-body energy for small [math] when [math] is fixed. Finally, we analyze the behavior of the many-body ground states when the convergence [math] is “faster” than the slow enough convergence [math].

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关于具有两体相互作用和（临界）吸引三体相互作用的一维玻色气体

SIAM 数学分析期刊》，第 56 卷，第 3 期，第 3203-3251 页，2024 年 6 月。摘要。我们考虑了一个一维的、被困的、聚焦玻色气体，其中[math]玻色子通过[math]形式的两体相互作用势和[math]形式的三体相互作用势相互作用，其中[math]，[math]，[math]，[math]，[math]和[math]。只要[math]--一维聚焦五元非线性薛定谔（NLS）方程的临界强度--为任何[math]，系统都是稳定的；或者当[math]为[math]时，系统也是稳定的。在前一种情况下，固定[math]，我们证明在均场极限中，多体系统在立方-五次NLS基态上表现出玻色-爱因斯坦凝聚。当把[math]和[math]假设为[math]，前者的收敛速度足够慢，且 "不比后者快 "时，我们证明系统的基态完全凝聚在五元 NLS 方程的（唯一）解上。在[math]固定的后一种情况下，当[math]固定时，我们得到了小[math]的多体能量收敛。最后，我们分析了当收敛[math]比足够慢的收敛[math]"更快 "时多体基态的行为。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.