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Symplectic coarse-grained dynamics: Chalkboard motion in classical and quantum mechanics
Advances in Theoretical and Mathematical Physics ( IF 1.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/atmp.2020.v24.n4.a3
Maurice A. de Gosson 1
Affiliation  

In the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schrodinger). In the present work we reverse this paradigm and view the motions themselves as being the primary objects. This is made possible by studying arbitrary phase space motions, not of points, but of (small) ellipsoids with the requirement that the symplectic capacity of these ellipsoids is preserved. This allows us to guide and control these motions as we like. In the classical case these ellipsoids correspond to a symplectic coarse graining of phase space, and in the quantum case they correspond to the "quantum blobs" we defined in previous work, and which can be viewed as minimum uncertainty phase space cells which are in a one-to-one correspondence with Gaussian pure states.

中文翻译:

辛粗粒度动力学:经典力学和量子力学中的黑板运动

在通常的力学(经典或量子)方法中,感兴趣的主要对象是哈密顿量,人们试图从中推导出运动方程(汉密尔顿或薛定谔)的解。在目前的工作中,我们逆转了这种范式,并将运动本身视为主要对象。通过研究任意相空间运动,而不是点的,而是(小)椭球的,并要求保留这些椭球的辛容量,这使之成为可能。这使我们可以随心所欲地引导和控制这些运动。在经典情况下,这些椭球对应于相空间的辛粗粒度,而在量子情况下,它们对应于我们在之前工作中定义的“量子斑点”,
更新日期:2020-01-01
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