Positive Hamiltonians cannot give exponential decay of positive observables

• URL: http://arxiv.org/abs/2309.03625v1
• Date: Thu, 7 Sep 2023 10:41:08 GMT
• Title: Positive Hamiltonians cannot give exponential decay of positive observables
• Authors: Paolo Facchi, Davide Lonigro
• Abstract summary: We show that the average value of any quantum observable, whenever well-defined, cannot converge exponentially to an extremal value of the spectrum of the observable. As a simple application of these results, we show that, when considering an open quantum system whose dynamics is generated by a Hamiltonian with a finite ground energy, a large-time exponential decay of populations is forbidden.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The survival probability of a quantum system with a finite ground energy is known to decay subexponentially at large times. Here we show that, under the same assumption, the average value of any quantum observable, whenever well-defined, cannot converge exponentially to an extremal value of the spectrum of the observable. Large-time deviations from the exponential decay are therefore a general feature of quantum systems. As a simple application of these results, we show that, when considering an open quantum system whose dynamics is generated by a Hamiltonian with a finite ground energy, a large-time exponential decay of populations is forbidden, whereas coherences may still decay exponentially.

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