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Article Dans Une Revue Journal of Statistical Physics Année : 1996

Upper bounds for the energy expectation in time-dependent quantum mechanics

Alain Joye

Résumé

We consider quantum systems driven by Hamiltonians of the formH+W(t), where the spectrum ofH consists of an infinite set of bands andW(t) depends arbitrarily on time. Let 〈H〈φ (t) denote the expectation value ofH with respect to the evolution at timet of an initial state φ. We prove upper bounds of the type 〈H〉φ (t)=O(t δ), δ>0, under conditions on the strength ofW(t) with respect toH. Neither growth of the gaps between the bands nor smoothness ofW(t) is required. Similar estimates are shown for the expectation value of functions ofH. Sufficient conditions to have uniformly bounded expectation values are made explicit and the consequences on other approaches to quantum stability are discussed.

Dates et versions

hal-01232516 , version 1 (23-11-2015)

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Alain Joye. Upper bounds for the energy expectation in time-dependent quantum mechanics. Journal of Statistical Physics, 1996, 85 (5-6), pp.575-606. ⟨10.1007/BF02199357⟩. ⟨hal-01232516⟩
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