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arXiv · 2208.04183

An Exactly Solvable Toy Model of Autocatalysis: Irreversible Relaxation after a Quantum Quench

Roberto Merlin
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Abstract

A fully resolvable quantum many-body Hamiltonian is introduced that mimics the behavior of the autocatalytic chemical reaction A+B <-> 2B involving two different molecular species, A and B. The model also describes two nonlinearly-coupled modes of an optical cavity. Consistent with the current understanding of the relaxation dynamics of integrable systems in isolation, the wavefunction following a quantum quench exhibits irreversibility with retention of the memory about its initial conditions. Salient features of the model include a marked similarity with conventional quantum decay and a total B-to-A conversion, with associated classical-like behavior of the wavefunction, when the initial state does not contain A-type molecules.

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Roberto Merlin. 2022-08-05. An Exactly Solvable Toy Model of Autocatalysis: Irreversible Relaxation after a Quantum Quench. https://doi.org/10.1103/physreve.108.014104

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