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

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.

References in corpus (5)

• Many body localization and thermalization in quantum statistical mechanics
• Many-body localization, thermalization, and entanglement
• Generalized Thermalization in an Integrable Lattice System
• Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance
• Quantum dynamics of the intramolecular vibrational energy redistribution in OCS: From localization to quasi-thermalization