Order parameter in electron systems: its fluctuations and oscillations

TL;DR

This paper explores the extension of the order parameter concept to fluctuating and oscillating cases, unifying diverse phenomena such as superconductivity, localization, and quantum crystals.

Contribution

It introduces a unified framework for describing fluctuating and oscillating order parameters across various complex physical systems.

Findings

Unified description of coexisting phases in low-dimensional systems

Insights into mesoscopic effects and localization phenomena

Framework applicable to thermodynamic quantum time-space crystals

Abstract

The concept of the order parameter is extremely useful in physics. Here, I discuss extensions of this concept to cases when the order parameter is no longer a constant but fluctuates or oscillates in space and time. This allows one to describe in an unified manner diverse physical phenomena including coexisting superconductivity and insulators in (quasi)one-dimensional systems, superconductivity and Coulomb blockade in granular superconductors and Josephson networks, Anderson localization and mesoscopic effects in disordered and chaotic systems, and thermodynamic quantum time-space crystals.