发表机构
The University of Tokyo（东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将Husimi绝热参数推广至多体谐振子系统，通过简正模式分解和算术平均定义广义参数，证明循环操作下平均能量非递减，并用数值模拟验证。
AI 中文摘要
在一篇经典论文[K. Husimi, Prog. Theor. Phys. 9, 381 (1953)]中，Husimi证明，对于具有含时角频率且初始条件从平衡分布中采样的单个谐振子，在循环操作后其平均能量不能减少。这种不可逆性由基于绝热不变量构成的Husimi绝热参数来量化。在本工作中，我们将Husimi框架推广到一维谐振子耦合在任意连通网络上的多体系统，其中所有弹簧常数共享一个共同的含时依赖性。对于固定在墙上的系统，通过变换到质量加权坐标并对所得正定矩阵进行对角化，动力学可分解为独立的简正模式，每个模式由其自身的Husimi绝热参数表征。通过将广义Husimi绝热参数定义为其算术平均值，我们推导出平均能量的精确时间演化，并确立其在循环操作下的非递减性。数值模拟证实了这些结果，适用于均匀最近邻链和异质网络。
英文摘要
In a classical paper [K. Husimi, Prog. Theor. Phys. 9, 381 (1953)], Husimi showed that, for a single harmonic oscillator with a time-dependent angular frequency and initial conditions sampled from an equilibrium distribution, the averaged energy cannot decrease after a cyclic operation. This irreversibility is quantified by Husimi's adiabaticity parameter constituted with adiabatic invariants. In this work, we generalize Husimi's framework to a many-body system of one-dimensional harmonic oscillators coupled on an arbitrary connected network, with all spring constants sharing a common time dependence. For a system attached to a fixed wall, the dynamics can be decomposed into independent normal modes by transforming to mass-weighted coordinates and diagonalizing the resulting positive definite matrix, with each mode characterized by its own Husimi's adiabaticity parameter. By defining the generalized Husimi's adiabaticity parameter as their arithmetic mean, we derive the exact time evolution of the averaged energy and establish its non-decrease under cyclic operations. Numerical simulations confirm these results for both a uniform nearest-neighbor chain and a heterogeneous network.
Comments10 pages, 3 figures
