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

TL;DR

This paper introduces an exactly solvable quantum model that mimics autocatalytic reactions and optical cavity modes, demonstrating irreversibility and classical-like decay behavior after a quantum quench.

Contribution

It presents a novel fully solvable Hamiltonian capturing autocatalytic dynamics and relaxation phenomena in quantum many-body systems.

Findings

Wavefunction exhibits irreversibility post-quench

Model shows total B-to-A conversion under certain initial conditions

Behavior resembles classical decay processes

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.