论托马斯-费米体系中的玻色-爱因斯坦凝聚体

IF 0.9 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2022-10-14 DOI:10.1007/s11040-022-09439-0

Daniele Dimonte, Emanuela L. Giacomelli

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引用次数: 4

摘要

我们研究了在Thomas-Fermi体系中N个被困玻色子的系统，其相互作用对势的形式为\( g_N N^{3\beta -1} V(N^\beta x) \)，其中一些\( \beta \in (0,1/3) \)和\( g_N \)发散为\( N \rightarrow \infty \)。我们证明了在基态水平上存在完全的玻色-爱因斯坦凝聚，并且进一步证明，如果\( \beta \in (0,1/6) \)，凝聚被时间演化所保留。

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On Bose–Einstein condensates in the Thomas–Fermi regime

We study a system of N trapped bosons in the Thomas–Fermi regime with an interacting pair potential of the form \( g_N N^{3\beta -1} V(N^\beta x) \), for some \( \beta \in (0,1/3) \) and \( g_N \) diverging as \( N \rightarrow \infty \). We prove that there is complete Bose–Einstein condensation at the level of the ground state and, furthermore, that, if \( \beta \in (0,1/6) \), condensation is preserved by the time evolution.

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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.