Spontaneous Symmetry Breaking: Variations on a Theme

Abstract

Spontaneous symmetry breaking (SSB) is a widespread phenomenon in several areas of physics. In this paper I wish to illustrate some situations where spontaneous symmetry breaking presents non obvious aspects. The first example is taken from molecular physics and is related to the paradox of existence of chiral molecules. The second case refers to a Dirac field in presence of a magnetic field. Gusynin, Miransky and Shovkovy have shown that Nambu-Jona-Lasinio (NJL) models, where SSB of chiral symmetry takes place for the nonlinear coupling over a certain threshold, in presence of a magnetic field exhibit SSB for any value of the coupling. They called this phenomenon magnetic catalysis. I will discuss this problem in 2 + 1 dimensions from an operatorial point of view and show that the basic phenomenon is a double pairing induced by the magnetic field in the vacuum for any value of the mass. This pairing provides the environment responsible for chiral symmetry breaking in NJL models with very weak nonlinearities. The third case illustrates briefly SSB in stationary nonequilibrium states and its possible relevance in natural phenomena.

Spontaneous Symmetry Breaking at the Fluctuating Level

“…This phenomenon, captured by hydrodynamic fluctuation theory, is most surprising as it happens in an equilibrium system in the absence of external fields, spontaneously breaking a symmetry in 1D. This illustrates the idea that critical phenomena not allowed in equilibrium steady states may however arise in their fluctuating behavior or under nonequilibrium conditions [15]. Remarkably, similar instabilities have been described in quantum systems [22].…”

“…This phenomenon, predicted by HFT [10,14], is most striking for this model as it happens in an isolated equilibrium system in the absence of any external field, spontaneously breaking a symmetry in 1D. This is an example of the general observation that symmetry-breaking instabilities forbidden in equilibrium steady states can, however, happen at the fluctuating level or in nonequilibrium settings [15]. Such instabilities may help explain puzzling asymmetries in nature [15], from the dominance of left-handed chiral molecules in biology to the matter-antimatter asymmetry in cosmology.…”

“…This is an example of the general observation that symmetry-breaking instabilities forbidden in equilibrium steady states can, however, happen at the fluctuating level or in nonequilibrium settings [15]. Such instabilities may help explain puzzling asymmetries in nature [15], from the dominance of left-handed chiral molecules in biology to the matter-antimatter asymmetry in cosmology.…”

Open two-species exclusion processes with integrable boundaries

“…Some particularly interesting cases are the following: the 2-TASEP model with unequal hopping rates [11] (the bulk dynamics is known to be integrable [19]), the homogeneous N-species ASEP (for generic N a brute force resolution of the reflection equation seems difficult but partial results were obtained using a baxterisation of a boundary Hecke algebra [20]) and the bridge model which is variant of the 2-TASEP. The bridge model, which for some choices of boundary rates displays a fascinating spontaneous symmetrybreaking [39,47], has eluded an exact solution. We hope that the formalism developed here will lead to some progress in solving this problem.…”

Current fluctuations in the weakly asymmetric exclusion process with open boundaries

“…This transition was observed in a weakly asymmetric exclusion process on a ring [9] and more recently in the KMP model [10], also on a ring. This type of dynamical transitions can occur in situations that are not allowed in equilibrium and have been conjectured to be of relevance to such issues as breaking of chiral or CP symmetry [11].…”