Classical equations for quantum systems
- Theoretical Astrophysics Group (T-6), Los Alamos National Laboratory, Los Alamos, New Mexico 87545; United States; Santa Fe Institute, 1660 Old Pecos Trail, Santa Fe, New Mexico 87501
- Department of Physics, University of California enSanta Barbara, Santa Barbara, (California) 93106
The origin of the phenomenological deterministic laws that approximately govern the quasiclassical domain of familiar experience is considered in the context of the quantum mechanics of closed systems such as the universe as a whole. A formulation of quantum mechanics is used that predicts probabilities for the individual members of a set of alternative coarse-grained histories that [ital decohere], which means that there is negligible quantum interference between the individual histories in the set. We investigate the requirements for coarse grainings to yield decoherent sets of histories that are quasiclassical, i.e., such that the individual histories obey, with high probability, effective classical equations of motion interrupted continually by small fluctuations and occasionally by large ones. We discuss these requirements generally but study them specifically for coarse grainings of the type that follows a distinguished subset of a complete set of variables while ignoring the rest. More coarse graining is needed to achieve decoherence than would be suggested by naive arguments based on the uncertainty principle. Even coarser graining is required in the distinguished variables for them to have the necessary inertia to approach classical predictability in the presence of the noise consisting of the fluctuations that typical mechanisms of decoherence produce. We describe the derivation of phenomenological equations of motion explicitly for a particular class of models.
- DOE Contract Number:
- AC03-81ER40050
- OSTI ID:
- 6943334
- Journal Information:
- Physical Review, D (Particles Fields); (United States), Vol. 47:8; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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