Delay-Time and Thermopower Distributions at the Spectrum Edges of a Chaotic Scatterer

TL;DR

This paper investigates how delay-time and thermopower distributions behave near the spectrum edges of a chaotic scatterer, revealing universal forms that differ from bulk behavior and are consistent across different system sizes.

Contribution

It derives the asymptotic universal distributions of delay-time and thermopower at the spectrum edges of a chaotic scatterer, extending known bulk results to the edge regime.

Findings

Delay-time and thermopower distributions differ near spectrum edges from bulk universal forms.

Universal edge distributions are obtained for arbitrary M, matching those for M=2.

Edge distributions are characterized by a specific energy scaling proportional to M^{-1/3}.

Abstract

We study chaotic scattering outside the wide band limit, as the Fermi energy $E_F$ approaches the band edges $E_B$ of a one-dimensional lattice embedding a scattering region of M sites. We show that the delay-time and thermopower distributions differ near the edges from the universal expressions valid in the bulk. To obtain the asymptotic universal forms of these edge distributions, one must keep constant the energy distance $E_F-E_B$ measured in units of the same energy scale proportional to $\propto M^{-1/3}$ which is used for rescaling the energy level spacings at the spectrum edges of large Gaussian matrices. In particular the delay-time and the thermopower have the same universal edge distributions for arbitrary M as those for an M=2 scatterer, which we obtain analytically.