论文标题
振荡器的常规和无序谐波网络的最佳光谱差距
The optimal spectral gap for regular and disordered harmonic networks of oscillators
论文作者
论文摘要
我们考虑在不同温度下与两个Langevin热源库相连的谐波振荡器的一维链和多维网络。每个粒子通过谐波电位与最近的邻居相互作用，所有单个粒子也都受谐波电位的限制。在本文中，我们首次提供了在各种物理假设和不同空间维度下相关发生器光谱间隙的急剧n依赖性。我们的证明方法依赖于一种新方法来分析非自我伴侣特征值问题，该问题涉及辅助离散schrödinger运算符的低级别非热扰动。
We consider one-dimensional chains and multi-dimensional networks of harmonic oscillators coupled to two Langevin heat reservoirs at different temperatures. Each particle interacts with its nearest neighbors by harmonic potentials and all individual particles are confined by harmonic potentials, too. In this article, we provide, for the first time, the sharp N dependence of the spectral gap of the associated generator under various physical assumptions and for different spatial dimensions. Our method of proof relies on a new approach to analyze a non self-adjoint eigenvalue problem involving low-rank non-hermitian perturbations of auxiliary discrete Schrödinger operators.
