Positive Hamiltonians cannot give exponential decay of positive observables

TL;DR

This paper proves that quantum systems with positive Hamiltonians cannot exhibit exponential decay of observables at large times, highlighting fundamental limits on decay behaviors in quantum dynamics.

Contribution

It demonstrates that positive Hamiltonians inherently prevent exponential decay of observable averages, revealing a fundamental constraint on quantum decay processes.

Findings

Exponential decay of observables is impossible under positive Hamiltonians.

Large-time deviations from exponential decay are a general quantum feature.

Open quantum systems with positive Hamiltonians cannot have exponential population decay.

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.