Quantum-mechanical perturbations giving rise to a statistical transport equation. (English) Zbl 0065.19505

van Hove, Léon

Physica 21, 517-530 (1955).

The paper gives a quantum mechanical derivation of the statistical equations \( 13^{*} \) which govern the return to equilibrium: \( (*) d \varrho_{\alpha} / d t=\sum_{j}\left(W_{\alpha j} P_{j}-W_{\alpha j} P_{\alpha}\right) \) where \( P_{\alpha} \) is the probability of finding the system in groups of states labelled by \( \alpha \), and \( W_{\alpha j} \) are transition probabilities per unit time. It is claimed for this new derivation that (a) For two classes of initial states (*) has been derived without a priori statistical hypotheses; (b) For arbitrary initial states \( (*) \) has been derived using a random phase assumption only for the initial state. The usual derivations appeal to a random phase assumption repeatedly. - Dissipative effects in the time evolution of a system are traced to a characteristic property of perturbation operators in a very interesting manner.

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Keywords:

classical thermodynamics, heat transfer