Random non-Hermitian Hamiltonian framework for symmetry breaking dynamics

TL;DR

This paper introduces a framework using random non-Hermitian Hamiltonians to model stochastic quantum dynamics and symmetry-breaking processes, providing a linear, statistically symmetric approach to study state evolution.

Contribution

It presents a novel quantum modeling approach that incorporates stochasticity and symmetry-breaking dynamics using random non-Hermitian Hamiltonians.

Findings

Successfully models real-time symmetry-breaking dynamics

Demonstrates transition from symmetric to disordered states

Provides a linear, statistically symmetric quantum framework

Abstract

We propose random non-Hermitian Hamiltonians to model the generic stochastic nonlinear dynamics of a quantum state in Hilbert space. Our approach features an underlying linearity in the dynamical equations, ensuring the applicability of techniques used for solving linear systems. Additionally, it offers the advantage of easily incorporating statistical symmetry, a generalization of explicit symmetry to stochastic processes. To demonstrate the utility of our approach, we apply it to describe real-time dynamics, starting from an initial symmetry-preserving state and evolving into a randomly distributed, symmetry-breaking final state. Our model serves as a quantum framework for the transition process, from disordered states to ordered ones, where symmetry is spontaneously broken.