非对易空间中势阱下堵塞颗粒介质动力学有效质量的广义 Lewis-Riesenfeld 不变性
Generalized Lewis-Riesenfeld invariance for dynamical effective mass in jammed granullar media under a potential well in non-commutative space
AI总结：
本文将 Kuiper 带建模为非对易空间势阱中的堵塞颗粒介质，采用 Lewis-Riesenfeld 不变量方法构造含时不变算符，从而为测定非对易时空形变参数提供理论与实验基础。
摘要：
将小行星带（Kuiper 带）视为堵塞颗粒介质，在凝聚态物理与天体物理之间建立了一座桥梁。这为测定非对易时空的形变参数开辟了一种实验可能性。Kuiper 带的动力学可以简化为引力势阱下堵塞颗粒介质的动力学有效质量的动力学。此外，如果将时空视为非对易的，那么就可以建立一个用于测定非对易时空形变参数的实验模型。该模型本征函数与不变性的构造通常是一个棘手的问题。我们利用 Lewis-Riesenfeld 不变量方法来确定这一时间依赖量子系统的不变性。在本文中，我们证明了，对于非对易空间中势阱下堵塞颗粒介质内具有动力学有效质量的系统，存在一类广义的时间依赖 Lewis-Riesenfeld 不变量算符。为使讨论具有相当的一般性，我们同时考虑了位置—位置非对易性和动量—动量非对易性。由于在相差一个时间依赖相位因子的意义下，不变量算符的本征函数将满足该系统时间依赖哈密顿量的时间依赖 Schrödinger 方程，因此不变量算符的构造在数学上相当好地解决了该问题，其结果可用于演示一项实验。
英文摘要：
Consideration of the asteroid belt (Kuiper belt) as a jammed-granular media establishes a bridge between condensed matter physics and astrophysics. It opens up an experimental possibility to determine the deformation parameters for noncommutative space-time. Dynamics of the Kuiper belt can be simplified as dynamics of a dynamical effective mass for a jammed granular media under a gravitational well. Alongside, if one considers the space-time to be noncommutative, then an experimental model for the determination of the deformation parameters for noncommutative space-time can be done. The construction of eigenfunctions and invariance for this model is in general a tricky problem. We have utilized the Lewis-Riesenfeld invariant method to determine the invariance for this time-dependent quantum system. In this article, we have shown that a class of generalized time-dependent Lewis-Riesenfeld invariant operators exist for the system with dynamical effective mass in jammed granular media under a potential well in noncommutative space. To keep the discussion fairly general, we have considered both position-position and momentum-momentum noncommutativity. Since, up to a time-dependent phase-factor, the eigenfunctions of the invariant operator will satisfy the time-dependent Schrödinger equation for the time-dependent Hamiltonian of the system, the construction of the invariant operator fairly solve the problem mathematically, the results of which can be utilized to demonstrate an experiment.
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