论文标题
非线性汉密尔顿系统和类似哈珀的动力学的广义相空间描述
Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
论文作者
论文摘要
Wigner流的相空间特征，用于带有哈密顿量的通用一维系统，$ h^{w}（q，q，\，p）$，受$ \ \ partial^2 H^{w} / \ partial q \ partial q \ partial q \ partial q \ partial q \ partial p = 0 $的条件，以Wignerer功能和Wignigner函数分析。针对热力学（TD）和高斯量子合奏确定了liouvillian和固定曲线，以考虑由于经典相位空间模式上的量子修改而导致的精确校正。然后，一般结果专门针对哈珀·汉密尔顿系统（Harper Hamiltonian System），除了作为此处引入的框架的可行测试平台外，还接受了TD和Gaussian合奏的统计描述，其中Wigner Flow属性都是通过分析工具获得的。因此，每当提供经典的汉密尔顿背景时，通过概率和信息通量来量化经典制度的量子波动。除了允许广泛的理论应用外，我们的结果还表明，这种广义的Wigner方法可以作为对Harper样系统的量子性和经典性的探测，该框架可以扩展到汉密尔顿人以$ H^}的形式描述的任何量子系统，以$ h^}（w}（q，q，\，\，p）= k（p）= k（p）= k（p）= k（p） + v（q） + v（q（q）$。
Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian, $H^{W}(q,\,p)$, constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition are analytically obtained in terms of Wigner functions and Wigner currents. Liouvillian and stationary profiles are identified for thermodynamic (TD) and Gaussian quantum ensembles to account for exact corrections due to quantum modifications over a classical phase-space pattern. General results are then specialized to the Harper Hamiltonian system which, besides working as a feasible test platform for the framework here introduced, admits a statistical description in terms of TD and Gaussian ensembles, where the Wigner flow properties are all obtained through analytical tools. Quantum fluctuations over the classical regime are therefore quantified through probability and information fluxes whenever the classical Hamiltonian background is provided. Besides allowing for a broad range of theoretical applications, our results suggest that such a generalized Wigner approach works as a probe for quantumness and classicality of Harper-like systems, in a framework which can be extended to any quantum system described by Hamiltonians in the form of $H^{W}(q,\,p) = K(p) + V(q)$.
