Self-adjoint Lyapunov variables, temporal ordering, and irreversible representations of Schroedinger evolution
- Einstein Institute of Mathematics, Hebrew University of Jerusalem, Jerusalem, 91904 (Israel)
In nonrelativistic 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 admits 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 proven 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.
- OSTI ID:
- 21335901
- Journal Information:
- Journal of Mathematical Physics, Vol. 51, Issue 2; Other Information: DOI: 10.1063/1.3276419; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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