Quantum Correlations in Metals that Grow in Time and Space

TL;DR

This paper reveals that electron correlations in metals exhibit anomalous growth over time and space due to soft modes and incomplete screening, with distinct behaviors in 2D and 3D systems, and suggests experimental measurement methods.

Contribution

It identifies and characterizes anomalous time and space dependence of electron correlations in metals, highlighting effects of soft modes and screening in Fermi liquids.

Findings

Correlations in 2D grow as t^2 over time.

Spatial correlations in disordered 2D systems grow as the square of distance.

We propose experimental methods to measure these correlations.

Abstract

We show that the correlations of electrons with a fixed energy in metals have very anomalous time and space dependences. Due to soft modes that exist in any Fermi liquid, combined with the incomplete screening of the Coulomb interaction at finite frequencies, the correlations in 2-d systems grow with time as $t^2$. In the presence of disorder, the spatial correlations grow as the distance squared. Similar, but in general weaker, effects are present in 3-d systems and in the absence of quenched disorder. We propose ways to experimentally measure these anomalous correlations.