薛定谔演化的自伴李雅普诺夫变量、时间序和不可逆表示
Self-adjoint Lyapunov variables, temporal ordering and irreversible representations of Schroedinger evolution
摘要：
在非相对论性的量子力学中，时间是薛定谔方程中的一个参数。然而，在各种情况下，需要将时间视为动态变量。在本文中，我们考虑通过构造一个李雅普诺夫变量的时间的动态作用-即，期望值随时间单调变化的自伴量子可观测值。它示出，在一个建设性的方式，某一类模型承认一个李雅普诺夫变量和李雅普诺夫变量的存在意味着存在的变换映射到一个等价的不可逆表示的原始量子力学问题。此外，证明了在不可逆表示中存在一个自然的时间序观测量，它在每个t>0处将Hilbert空间分裂为过去和未来子空间。
英文摘要：
In non relativistic quantum mechanics time enters as a parameter in the Schroedinger equation. However, there are various situations where the need arises to view time as a dynamical variable. In this paper we consider the dynamical role of time through the construction of a Lyapunov variable - i.e., a self-adjoint quantum observable whose expectation value varies monotonically as time increases. It is shown, in a constructive way, that a certain class of models admit a Lyapunov variable and that the existence of a Lyapunov variable implies the existence of a transformation mapping the original quantum mechanical problem to an equivalent irreversible representation. In addition, it is proved that in the irreversible representation there exists a natural time ordering observable splitting the Hilbert space at each t>0 into past and future subspaces.
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