正则化Nelson模型的Bogoliubov动力学和高阶修正

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Reviews in Mathematical Physics Pub Date : 2021-10-01 DOI:10.1142/s0129055x2350006x

M. Falconi, Nikolai Leopold, D. Mitrouskas, S. Petrat

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引用次数: 5

摘要

我们研究了Nelson模型在平均场极限下的时间演化，其中N个非相对论玻色子弱耦合（w.r.t.粒子数）到正或零质量量化标量场。我们的主要结果是Bogoliubov动力学的推导和高阶校正。更准确地说，我们证明了近似波函数在范数下对多体波函数的收敛性，收敛速度与近似中考虑的校正次数成正比。我们证明了酉传播子的一个类似结果。作为一个应用，我们导出了一个简单的偏微分方程系统，该系统分别描述了粒子和量子场的单粒子约化密度矩阵的一阶和二阶近似的时间演化。MSC等级：35Q40、35Q55、81Q05、81T10、81V73、82C10

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Bogoliubov Dynamics and Higher-order Corrections for the Regularized Nelson Model

We study the time evolution of the Nelson model in a mean-field limit in which N nonrelativistic bosons weakly couple (w.r.t. the particle number) to a positive or zero mass quantized scalar field. Our main result is the derivation of the Bogoliubov dynamics and higher-order corrections. More precisely, we prove the convergence of the approximate wave function to the many-body wave function in norm, with a convergence rate proportional to the number of corrections taken into account in the approximation. We prove an analogous result for the unitary propagator. As an application, we derive a simple system of PDEs describing the time evolution of the firstand second-order approximation to the one-particle reduced density matrices of the particles and the quantum field, respectively. MSC class: 35Q40, 35Q55, 81Q05, 81T10, 81V73, 82C10

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来源期刊

Reviews in Mathematical Physics 物理-物理：数学物理

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.