Spontaneous symmetry emergence in a Hermitian system of coupled oscillators without symmetry

TL;DR

This paper predicts a novel phenomenon where a system without inherent symmetry spontaneously develops symmetry in its dynamics, representing a phase transition in a Hermitian coupled oscillator system.

Contribution

It introduces the concept of spontaneous symmetry emergence in a Hermitian system lacking initial symmetry, demonstrated through a model of coupled oscillators.

Findings

System state can acquire symmetry not present in the Hamiltonian

Symmetry emergence manifests as a change in system dynamics

Represents a phase transition in a non-symmetric Hermitian system

Abstract

Spontaneous symmetry breaking in systems with symmetry is a cornerstone phenomenon accompanying second-order phase transitions. Here, we predict the opposite phenomenon, namely, spontaneous symmetry emergence in a system that lacks symmetry. In the example of two coupled oscillators interacting non-symmetrically with a set of oscillators whose frequencies uniformly fill a finite frequency range, we demonstrate that the system state can acquire symmetry that is not inherent in the system Hamiltonian. The emergence of symmetry is manifested as a change in the system dynamics, which can be interpreted as a phase transition in a Hermitian system that lacks symmetry.