Non-Ergodic Mesoscopic Systems

TL;DR

This paper demonstrates that in non-ergodic mesoscopic systems, the density of states can be exactly determined from asymptotic wave-functions or scattering matrices, enabling experimental measurement without detailed internal knowledge.

Contribution

It introduces a method to determine the density of states in non-ergodic mesoscopic systems directly from asymptotic wave-functions or scattering matrices.

Findings

Density of states can be exactly obtained from asymptotic wave-functions.

Experimental determination of density of states is possible without internal system details.

Counterintuitive relations between wave-functions and density of states are derived.

Abstract

Suppose there is a mesoscopic system connected to single channel leads. If the system is non-chaotic or non-ergodic then the thermodynamic and transport properties do not depend on impurity averaged density of states. We show that the partial density of states as well as density of states of a given system can be determined exactly from the asymptotic wave-function (or scattering matrix) at the resonances. The asymptotic wave-function can be determined experimentally without any knowledge about the quantum mechanical potential (including electron-electron interaction) or wave function in the interior of the system. Some counter intuitive relations derived here can allow this.