哈密顿动力学中局域化观测量与能量变化的关系式
A formula relating localisation observables to the variation of energy in Hamiltonian dynamics
摘要：
本文考虑在具有Poisson括号{，}的辛流形M上，具有完全流的Hamilton算子H和族Phi=（Phi_1，...，φ_d）.在这些假设下，我们证明了一个新的公式，该公式将用φ定义的定域观测量的时间演化与沿经典轨道的能量变化联系起来.证明了该公式与最近在量子力学框架内建立的一个公式之间的对应关系。在其他例子中，我们的理论适用于斯塔克哈密顿，齐次哈密顿，纯动力学哈密顿，排斥谐波势，单摆，中心力系统，庞加莱球模型，覆盖流形，波动方程，非线性薛定谔方程，Korteweg-de Vries方程和量子哈密顿定义通过期望值。
英文摘要：
We consider on a symplectic manifold M with Poisson bracket {,} an Hamiltonian H with complete flow and a family Phi=(Phi_1,...,Phi_d) of observables satisfying the condition {{Phi_j,H},H}=0 for each j. Under these assumptions, we prove a new formula relating the time evolution of localisation observables defined in terms of Phi to the variation of energy along classical orbits. The correspondence between this formula and a formula established recently in the framework of quantum mechanics is put into evidence. Among other examples, our theory applies to Stark Hamiltonians, homogeneous Hamiltonians, purely kinetic Hamiltonians, the repulsive harmonic potential, the simple pendulum, central force systems, the Poincare ball model, covering manifolds, the wave equation, the nonlinear Schroedinger equation, the Korteweg-de Vries equation and quantum Hamiltonians defined via expectation values.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
