Michael Stone

Quantum Hall effect

This book is a compilation of reprint articles on one of the most intriguing phenomena in modern physics, the Quantum Hall Effect. Together with a detailed introduction by the editor, this volume is intended as a reference for students and research workers in condensed matter physics and for those with a particle physics background. The papers have been chosen with the intention of emphasizing the topological aspects of the Quantum Hall Effect and its connections with other branches of theoretical physics such as topological quantum field theories and string theory. The contents include sections on integer effect, fractional effect, effect of global topology, effective theories, edge states and non-Abelian statistics.

Landauer Conductance of Luttinger Liquids with Leads

We show that the dc conductance of a quantum wire containing a Luttinger liquid and attached to non-interacting leads is given by

Chiral symmetry restoration in baryon rich environments

e^2/h

Studies of chiral symmetry breaking in SU(2) lattice gauge theory

per spin orientation, regardless of the interactions in the wire. This explains the recent observations of the absence of conductance renormalization in long high-mobility

Supersymmetry and the Quantum Mechanics of Spin

GaAs

Problems with Finite Density Simulations of Lattice QCD

wires by Tarucha, Honda and Saku (Solid State Communications {\bf 94}, 413 (1995)).

Edge waves in the quantum Hall effect

Abstract Chiral symmetry restoration in an environment rich in baryons is studied by computer simulation methods in SU(2) and SU(3) gauge theories in the quenched approximation. The basic theory of symmetry restoration as a function of chemical potential is illusstrated and the implementation of the ideas on a lattice is made explicit. A simple mean field model is presented to guide ones expectations. The second order conjugate-gradient iterative method and the pseudo-fermion Monte Carlo procedure are convergent methods of calculating the fermion propagator in an environment rich in baryons. Computer simulations of SU(3) gauge theory show an abrupt chiral symmetry restoring transition and the critical chemical potential and induced baryon density are estimated crudely. A smoother transition is observed for the color group SU(2).

Edge modes, edge currents, and gauge invariance inpx+ipysuperfluids and superconductors

We study chiral symmetry breaking (χSB) in SU(2) lattice gauge theory with quarks in the l = 12, l = 1, l = 32, and l = 2 representations of the color group. We perform Monte Carlo evaluations of 〈ψψ〉 in the quenched approximation and extract the relevant length scales for χSB. We revise a previous estimate for the ratio between the chiral symmetry restoration temperatures for fundamental and adjoint quarks and obtain Tl = 1/Tl = 12 ∼ 8. Our results for the higher representations, l = 32and l = 2, are consistent with Casimir scaling and give C2gmom2 ∼ 4. Many aspects of our calculational method are explained in detail. The issues discussed include the relation between χSB in the quenched approximation and the spectrum of the Dirac operator, the flavor symmetries of euclidean staggered fermions, estimates of finite-size effects and the reliability of m → 0 extrapolations on finite lattices.

MEAN FIELD AND MONTE CARLO STUDIES OF SU(N) CHIRAL MODELS IN THREE DIMENSIONS

Abstract Bohr-Sommerfeld quantization is exact for a spin in a magnetic field. This well-known result is connected with the existence of a hidden supersymmetry. I discuss the supersymmetry and, in a broader context, the semiclassical quantum-mechanical interpretation of the Weyl character formula for compact, semisimple Lie groups.

The semiclassical propagator for spin coherent states

We present a discussion of problems that have arisen in attempts to understand the behavior of lattice QCD at high densities. The effects observed in the lattice simulations do not seem to be consistent with what we expect from the usual ideas of chiral symmetry breaking. In particular, at zero quark mass, there does not seem to be a massive baryon at finite density.