Symmetry breaking in non conservative systems

TL;DR

This paper explores how Noether's theorem reveals symmetry breaking in nonconservative systems using Galley's variational formulation, showing that nonconservative potentials break initial symmetries, leading to conservation law violations and frequency differences in supersymmetric oscillators.

Contribution

It extends Galley's variational approach to analyze symmetry breaking in nonconservative, fermionic, and supersymmetric systems, revealing new insights into their dynamics.

Findings

Symmetry breaking occurs due to nonconservative potentials not being invariant under inverse transformations.

In supersymmetric oscillators, damping causes bosonic and fermionic frequencies to diverge.

The formulation generalizes Noether's theorem to nonconservative and supersymmetric contexts.

Abstract

We apply Noether's theorem to show how the invariances of conservative systems are broken for nonconservative systems, in the variational formulation of Galley. This formulation considers a conservative action, extended by the inclusion of a time reversed sector and a nonconservative generalized potential. We assume that this potential is invariant under the symmetries of the initial conservative system. The breaking occurs because the time reversed sector requires inverse symmetry transformations, under which the nonconservative potential is not invariant. The resulting violation of the conservation laws is consistent with the equations of motion. We generalize this formulation for fermionic and sypersymmetric systems. In the case of a supersymmetric oscillator, the effect of damping is that the bosonic and fermionic components become different frequencies. Considering that initially the nonconservative action is invariant under supersymmetry, and that the breaking is associated to an instability, this result is reminiscent of spontaneous symmetry breaking.