Non-equilibrium dynamics of the open quantum $O(n)$-model with non-Markovian noise: exact results

TL;DR

This paper provides exact results on the non-equilibrium quantum dynamics of the $O(n)$-model after a quench, highlighting the role of non-Markovian noise and universal aging and coarsening behaviors.

Contribution

It derives exact solutions for the quantum Langevin dynamics of the $O(n)$-model, revealing the impact of non-Markovian noise on quantum aging and coarsening in the large-$n$ limit.

Findings

Quantum dynamics reach a non-equilibrium stationary state.

Universal exponents for quantum aging and coarsening are identified.

Non-Markovian noise significantly influences long-time quantum dynamics.

Abstract

The collective and purely relaxational dynamics of quantum many-body systems after a quench at temperature $T=0$, from a disordered state to various phases is studied through the exact solution of the quantum Langevin equation of the spherical and the $O(n)$-model in the limit $n\to\infty$. The stationary state of the quantum dynamics is shown to be a non-equilibrium state. The quantum spherical and the quantum $O(n)$-model for $n\to\infty$ are in the same dynamical universality class. The long-time behaviour of single-time and two-time correlation and response functions is analysed and the universal exponents which characterise quantum coarsening and quantum ageing are derived. The importance of the non-Markovian long-time memory of the quantum noise is elucidated by comparing it with an effective Markovian noise having the same scaling behaviour and with the case of non-equilibrium classical dynamics.