Long-range correlations and generic scale invariance in classical fluids and disordered electron systems

TL;DR

This paper discusses the origin and characteristics of long-range correlations in classical and quantum systems, highlighting how zero temperature introduces additional soft modes leading to extended correlation ranges.

Contribution

It provides a comparative analysis of correlation behaviors at different temperatures and explains the role of soft modes in long-range correlations.

Findings

Correlations are longer-ranged at zero temperature due to additional soft modes.

Classical and finite-temperature quantum systems exhibit power-law correlations.

Zero-temperature quantum systems show more extended correlations than their finite-temperature counterparts.

Abstract

Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero temperature. The origin of the long-ranged correlations is explained in terms of soft modes. In general, correlations at zero temperature are of longer range than their finite temperature or classical counterparts. This phenomenon is due to additional soft modes that exist at zero temperature.