Gross-Pitaevskii体系中捕获玻色子的最优速率玻色-爱因斯坦凝聚

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-04-12 DOI:10.1007/s11040-022-09424-7

Christian Brennecke, Benjamin Schlein, Severin Schraven

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引用次数: 22

摘要

我们考虑了一种在\({\mathbb {R}}^3\)中由N个粒子组成的玻色气体，它们被外场捕获，并通过散射长度为\(N^{-1}\)阶的两体势相互作用。我们证明了低能态表现出最优速率的完全玻色-爱因斯坦凝聚，推广了Boccato等人的先前工作(普通数学物理359(3):975 - 1026,2018;[376:1311-1395, 2020]，仅限于平移不变系统。这扩展了Nam等人最近的结果(预印本，2001年)。arXiv:2001.04364)，去掉了对散射长度大小的小假设。

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Bose–Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross–Pitaevskii Regime

We consider a Bose gas consisting of N particles in \({\mathbb {R}}^3\), trapped by an external field and interacting through a two-body potential with scattering length of order \(N^{-1}\). We prove that low energy states exhibit complete Bose–Einstein condensation with optimal rate, generalizing previous work in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018; 376:1311–1395, 2020), restricted to translation invariant systems. This extends recent results in Nam et al. (Preprint, 2001. arXiv:2001.04364), removing the smallness assumption on the size of the scattering length.

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.