Quantum fields in disequilibrium: neutral scalar bosons with long-range, inhomogeneous perturbations

TL;DR

This paper develops a quantum field theory framework for neutral scalar bosons with inhomogeneous sources, revealing complex phenomena like chaos, phase transitions, and non-equilibrium dynamics through a novel representation involving generalized chemical potentials.

Contribution

It introduces a method using dispersion relations and Gaussian approximation to analyze inhomogeneous, non-equilibrium scalar fields, connecting dissipation with a pseudo-gauge theory analogy.

Findings

Inhomogeneity induces a discrete spectrum in the field.

Rapid transport causes second order phase transitions and anomalous dispersion.

Non-equilibrium dynamics can be represented via generalized chemical potentials.

Abstract

Using Schwinger's quantum action principle, dispersion relations are obtained for neutral scalar mesons interacting with bi-local sources. These relations are used as the basis of a method for representing the effect of interactions in the Gaussian approximation to field theory, and it is argued that a marked inhomogeneity, in space-time dependence of the sources, forces a discrete spectrum on the field. The development of such a system is characterized by features commonly associated with chaos and self-organization (localization by domain or cell formation). The Green functions play the role of an iterative map in phase space. Stable systems reside at the fixed points of the map. The present work can be applied to self-interacting theories by choosing suitable properties for the sources. Rapid transport leads to a second order phase transition and anomalous dispersion. Finally, it is shown that there is a compact representation of the non-equilibrium dynamics in terms of generalized chemical potentials, or equivalently as a pseudo-gauge theory, with an imaginary charge. This analogy shows, more clearly, how dissipation and entropy production are related to the source picture and transform a flip-flop like behaviour between two reservoirs into the Landau problem in a constant `magnetic field'. A summary of conventions and formalism is provided as a basis for future work.