含杂质玻色气体在Gross-Pitaevskii体系中的激发谱

IF 2.4 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2025-07-03 DOI:10.1007/s00205-025-02112-0

Jonas Lampart, Arnaud Triay

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引用次数: 0

摘要

我们研究了一个由N个相互作用玻色子在Gross-Pitaevskii体系中通过对势耦合到杂质粒子的稀系统。我们导出了基态能量在玻色子数中向上一阶的展开式，并证明了激发态的本征值与基态的差值由极限\(N\rightarrow \infty \)中重整化的Bogoliubov-Fröhlich哈密顿量的本征值给出。

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The Excitation Spectrum of a Bose Gas with an Impurity in the Gross–Pitaevskii Regime

We study a dilute system of N interacting bosons coupled to an impurity particle via a pair potential in the Gross–Pitaevskii regime. We derive an expansion of the ground state energy up to order one in the boson number, and show that the difference of excited eigenvalues to the ground state is given by the eigenvalues of the renormalized Bogoliubov–Fröhlich Hamiltonian in the limit \(N\rightarrow \infty \).

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.