Supersymmetry in Disorder and Chaos

Abstract

The development of the supersymmetry technique has led to significant advances in the study of disordered metals and semiconductors. The technique has proved to be of great use in the analysis of modern mesoscopic quantum devices, but is also finding applications in a broad range of other topics, such as localization and quantum chaos. This book provides a comprehensive treatment of the ideas and uses of supersymmetry. The first four chapters of the book set out the basic results and some straightforward applications of the technique. Thereafter, a range of topics is covered in detail, including random matrix theory, persistent currents in mesoscopic rings, transport in mesoscopic devices, localization in quantum wires and films, and the quantum Hall effect. Each topic is covered in a self-contained manner, and the book will be of great interest to graduate students and researchers in condensed matter physics and quantum chaos.

Dirac spectrum of the Wilson-Dirac operator for QCD with two colors

“…This choice differs with respect to some other works [47,48] where the sign of the supertrace is reversed and the superdeterminant is the inverse of the definition here. The invariant measure dµ(U ) is given by…”

Superbosonization via Riesz Superdistributions

“…The elements of O(S, E) are called E-valued superfunctions on S. Observe that since Γ (O S ) is nuclear by Proposition C.6, we might have taken any other locally convex tensor product topology in the definition [45]. PROPOSITION C. 10. Let E be a locally convex supervector space.…”

“…Although this relationship is indeed intimate and fundamental, supersymmetry is also deeply rooted in the physics of condensed matter. The so-called supersymmetry method, developed by Efetov and Wegner [10], has been used to great effect in the study of disordered systems, and in particular in connection to the metal-insulator transition; or in other words, in the analysis of localization and delocalization for certain random matrix ensembles [47,48].…”

Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

“…In fact, controlled external perturbations such as magnetic field or gate potential often serve as important experimental tools to study statistical properties of such systems. Thus, instead of a sequence of random steps dV one is lead to consider finite mappings H → H ′ = H + V , where V is a fixed matrix with the same symmetry as the ensemble from which the matrices H are drawn † [6,7,8,9].…”