# Publications by John Chalker

## Spin textures, screening, and excitations in dirty quantum Hall ferromagnets.

Phys Rev Lett **88** (2002) 036801-

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential. Describing these systems with a classical nonlinear sigma model and using analytical estimates supported by results from numerical simulations, we examine the nature of the ground state as a function of disorder strength, Delta, and deviation, deltanu, of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration, and in the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at small Delta and /deltanu/ to a spin glass at larger Delta or /deltanu/. We examine ground-state response functions and excitations.

## The two-dimensional random-bond Ising model, free fermions and the network model

Physical Review B: Condensed Matter and Materials Physics **65** (2002) 054425 18pp-

## Spin textures, screening and excitations in dirty quantum Hall ferromagnets

Physical Review Letters **88** (2002) 036801 4pp-

## Some Generic Aspects of Bosonic Excitations in Disordered Systems

Physical Review Letters **89** (2002) 136801 4pp-

## Spin quantum Hall transition in disordered superconductors

PHYSICA E **9** (2001) 352-355

We study a delocalization transition for non-interacting quasiparticles moving in two dimensions, which belongs to a new symmetry class. This symmetry class can be realized in a dirty, gapless superconductor in which time-reversal symmetry for orbital motion is broken, but spin rotation symmetry is intact. We find a direct transition between two insulating phases with quantized Hall conductances of zero and two for the conserved quasiparticles. The energy of quasiparticles acts as a relevant, symmetry-breaking field at the critical point, which splits the direct transition into two conventional plateau transitions. (C) 2001 Elsevier Science B.V. All rights reserved.

## Spectrum of the fokker-planck operator representing diffusion in a random velocity field

Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics **61** (2000) 196-203

We study spectral properties of the Fokker-Planck operator that represents particles moving via a combination of diffusion and advection in a time-independent random velocity field, presenting in detail work outlined elsewhere [J. T. Chalker and Z. J. Wang, Phys. Rev. Lett. 79, 1797 (1997)]. We calculate analytically the ensemble-averaged one-particle Green function and the eigenvalue density for this Fokker-Planck operator, using a diagrammatic expansion developed for resolvents of non-Hermitian random operators, together with a mean-field approximation (the self-consistent Born approximation) which is well controlled in the weak-disorder regime for dimension d>2. The eigenvalue density in the complex plane is nonzero within a wedge that encloses the negative real axis. Particle motion is diffusive at long times, but for short times we find a novel time dependence of the mean-square displacement, <r(2)> approximately t(2/d) in dimension d>2, associated with the imaginary parts of eigenvalues.

## Eigenvector correlations in non-Hermitian random matrix ensembles

ANN PHYS-BERLIN **7** (1998) 427-436

We analyse correlations of eigenvectors in Ginibre's and Girko's ensembles of Gaussian, non-Hermitian random N x N matrices J. We study the ensemble average of [L-alpha/L-beta] [R-beta/R-alpha], where [L-alpha\ and \R-beta] are the left and right eigenvectors of J. The case of Ginibre's ensemble, in which the real and imaginary parts of each element of J are independent random variables, is sufficiently symmetric to allow for an exact solution. In the more general case of Girko's ensemble, we rely on approximations which become exact in the limit of N --> infinity.

## Eigenvector statistics in non-hermitian random matrix ensembles

Physical Review Letters **81** (1998) 3367-3370

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre’s complex Gaussian ensemble, in which the real and imaginary parts of each element of an N × N matrix, J, are independent random variables. Calculating ensemble averages based on the quantity ⟨Lα|Lβ⟩ ⟨Rβ|Rα⟩, where ⟨Lα| and |Rβ⟩ are left and right eigenvectors of J, we show for large N that eigenvectors associated with a pair of eigenvalues are highly correlated if the two eigenvalues lie close in the complex plane. We examine consequences of these correlations that are likely to be important in physical applications. © 1998 The American Physical Society.

## Multiple scattering in the presence of absorption: A theoretical treatment for quasi one-dimensional systems

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL **29** (1996) 3761-3768

## LOCALIZATION IN A RANDOM MAGNETIC-FIELD - THE SEMICLASSICAL LIMIT

PHYSICAL REVIEW B **50** (1994) 5272-5285

## EXACT RESULTS FOR THE LEVEL DENSITY AND 2-POINT CORRELATION-FUNCTION OF THE TRANSMISSION-MATRIX EIGENVALUES IN QUASI-ONE-DIMENSIONAL CONDUCTORS

PHYSICAL REVIEW B **49** (1994) 4695-4702

## COMPLETE CHARACTERIZATION OF UNIVERSAL FLUCTUATIONS IN QUASI-ONE-DIMENSIONAL MESOSCOPIC CONDUCTORS

PHYSICAL REVIEW LETTERS **71** (1993) 3693-3696

## COULOMB INTERACTIONS AND THE INTEGER QUANTUM HALL-EFFECT - SCREENING AND TRANSPORT

PHYSICAL REVIEW B **48** (1993) 4530-4544

## SCATTERING-THEORY, TRANSFER-MATRICES, AND ANDERSON LOCALIZATION

PHYSICAL REVIEW LETTERS **70** (1993) 982-985

## EIGENFUNCTION FLUCTUATIONS AND CORRELATIONS AT THE MOBILITY EDGE IN A 2-DIMENSIONAL SYSTEM WITH SPIN ORBIT SCATTERING

JOURNAL OF PHYSICS-CONDENSED MATTER **5** (1993) 485-490

## EFFECTS OF SPIN-ORBIT INTERACTIONS IN DISORDERED CONDUCTORS - A RANDOM-MATRIX APPROACH

PHYSICAL REVIEW B **46** (1992) 14985-14994

## Ground-state disorder in the spin-1/2 kagomé Heisenberg antiferromagnet.

Physical review. B, Condensed matter **46** (1992) 14201-14204

## Hidden order in a frustrated system: Properties of the Heisenberg Kagomé antiferromagnet.

Physical review letters **68** (1992) 855-858

## PROCEEDINGS OF THE INTERNATIONAL-CONFERENCE ON LOCALIZATION HELD AT IMPERIAL-COLLEGE, LONDON, 13-15 AUGUST 1990 - PREFACE

INSTITUTE OF PHYSICS CONFERENCE SERIES (1991) R5-R5