Bosons in a double well: two-mode approximation and fluctuations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-16 DOI:10.2140/apde.2023.16.1885

Alessandro Olgiati, Nicolas Rougerie, Dominique Spehner

引用次数: 2

Abstract

We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well) are macroscopically occupied, and we are concerned with deriving the corresponding effective Bose-Hubbard Hamiltonian. We prove (i) an energy expansion, including the two-modes Bose-Hubbard energy and two independent Bogoliubov corrections (one for each potential well), (ii) a variance bound for the number of particles falling inside each potential well. The latter is a signature of a correlated ground state in that it violates the central limit theorem.

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双阱中的玻色子:双模近似和涨落

我们研究了双阱势中许多相互作用玻色子的基态，其中粒子数和势阱之间的距离都趋于无穷。两个单粒子轨道(每个阱一个)被宏观占据，我们关心的是推导相应的有效玻色-哈伯德哈密顿量。我们证明了(i)一个能量扩展，包括两模玻色-哈伯德能量和两个独立的Bogoliubov修正(每个势阱一个)，(ii)落在每个势阱内的粒子数量的方差界。后者是一个相关基态的标志，因为它违反了中心极限定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.