Supersymmetry for Systems with Unitary Disorder: Circular Ensembles
arXiv:chao-dyn/9609007 · doi:10.1088/0305-4470/29/22/013
Abstract
A generalized Hubbard-Stratonovitch transformation relating an integral over random unitary N times N matrices to an integral over Efetov's unitary sigma model manifold, is introduced. This transformation adapts the supersymmetry method to disordered and chaotic systems that are modeled not by a Hamiltonian but by their scattering matrix or time-evolution operator. In contrast to the standard method, no saddle-point approximation is made, and no massive modes have to be eliminated. This first paper on the subject applies the generalized Hubbard-Stratonovitch transformation to Dyson's Circular Unitary Ensemble. It is shown how to use a supersymmetric variant of the Harish-Chandra-Itzykson-Zuber formula to compute, in the large-N limit, the n-level correlation function for any n. Nontrivial applications to random network models, quantum chaotic maps, and lattice gauge theory, are expected.
19 pages, REVTEX, to appear in J. Phys. A (Math. and Gen.)
Cited by in corpus (65)
- Random Matrix Theories in Quantum Physics: Common Concepts
- Quantum Graphs: Applications to Quantum Chaos and Universal Spectral Statistics
- Solution of a minimal model for many-body quantum chaos
- The Microscopic Spectral Density of the QCD Dirac Operator
- Chaotic Scattering on Individual Quantum Graphs
- Systematic Analytical Approach to Correlation Functions of Resonances in Quantum Chaotic Scattering
- Toward a theory of the integer quantum Hall transition: continuum limit of the Chalker-Coddington model
- Universal spectral statistics in quantum graphs
- Point-Contact Conductances at the Quantum Hall Transition
- Effective Field Theory of the Random Flux Model
- Universal Quantum Graphs
- Derivation of determinantal structures for random matrix ensembles in a new way
- Quantum phase transitions in the quasi-periodic kicked rotor
- Generalizations of some integrals over the unitary group
- Characteristic polynomials of random Hermitian matrices and Duistermaat-Heckman localisation on non-compact Kaehler manifolds
- Eigenfunction Statistics on Quantum Graphs
- Howe pairs, supersymmetry, and ratios of random characteristic polynomials for the unitary groups U(N)
- Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations
- Localization of quasiparticles in a disordered vortex
- Spectral correlations of individual quantum graphs
- Planck's quantum-driven integer quantum Hall effect in chaos
- Universal Chaotic Scattering on Quantum Graphs
- On absolute moments of characteristic polynomials of a certain class of complex random matrices
- A few remarks on Colour-Flavour Transformations,truncations of random unitary matrices, Berezin reproducing kernels and Selberg type integrals
- Theory of localization and resonance phenomena in the quantum kicked rotor
- A field-theoretic approach to nonequilibrium work identities
- Replica treatment of non-Hermitian disordered Hamiltonians
- Field Theory of the Random Flux Model
- Microscopic Spectrum of the QCD Dirac Operator in Three Dimensions
- Chiral Metal as a Ferromagnetic Super Spin Chain
- Correlations between zeros and supersymmetry
- Quantum ergodicity on graphs
- Emergence of integer quantum Hall effect from chaos
- Sigma models for quantum chaotic dynamics
- Quantum relaxation in open chaotic systems
- On the mean density of complex eigenvalues for an ensemble of random matrices with prescribed singular values
- Correlation functions of the BC Calogero-Sutherland model
- Dirac Spectra of 2-dimensional QCD-like theories
- Quantum Network Models and Classical Localization Problems
- Probing the topological Anderson transition with quantum walks
- Color-Flavor Transformation for the Special Unitary Group
- Supersymmetry method for interacting chaotic and disordered systems: the SYK model
- Quantum Hall criticality in Floquet topological insulators
- Character expansion method for supergroups and extended superversions of the Leutwyler-Smilga and Berezin-Karpelevich integrals
- Chiral Lagrangians from lattice gauge theories in the strong coupling limit
- (1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation
- Det-Det Correlations for Quantum Maps: Dual Pair and Saddle-Point Analyses
- On the Efetov-Wegner terms by diagonalizing a Hermitian supermatrix
- Invariant integration on orthosymplectic and unitary supergroups
- Toda lattice representation for random matrix model with logarithmic confinement
- Bosonic color-flavor transformation for the special unitary group
- Effective field theory of random quantum circuits
- Spectral statistics of the uni-modular ensemble
- The Color-Flavor Transformation and Lattice QCD
- Howe Duality for an Induced Model of Lattice U(N) Yang-Mills Theory
- Linear Algebra with Disordered Sparse Matrices that have Spatial Structure: Theory and Computation
- On permanental polynomials of certain random matrices
- Statistics of the Random Matrix Spectral Form Factor
- Superbosonization in disorder and chaos: The role of anomalies
- A minimal approach for the local statistical properties of a one-dimensional disordered wire
- Supersymmetry approach to delocalization transitions in a network model of the weak field quantum Hall effect and related models
- Vicious walkers and random contraction matrices
- Exact generating function of a zero-dimensional supersymmetric non-linear sigma model
- Leading and beyond leading-order spectral form factor in chaotic quantum many-body systems across all Dyson symmetry classes
- Color-Flavor Transformation Revisited