Fictitious Level Dynamics: A Novel Approach to Spectral Statistics in Disordered Conductors

Abstract

We establish a new approach to calculating spectral statistics in disordered conductors, by considering how energy levels move in response to changes in the impurity potential. We use this fictitious dynamics to calculate the spectral form factor in two ways. First, describing the dynamics using a Fokker-Planck equation, we make a physically motivated decoupling, obtaining the spectral correlations in terms of the quantum return probability. Second, from an identity which we derive between two- and three-particle correlation functions, we make a mathematically controlled decoupling to obtain the same result. We also calculate weak localization corrections to this result, and show for two dimensional systems (which are of most interest) that corrections vanish to three-loop order.

35 pages in REVTeX format including 10 postscript figures; to be published in a special issue (on Topics in Mesoscopic Physics) of the Journal of Mathematical Physics, October 1996

References in corpus (1)

• Random Walks through the Ensemble: Linking Spectral Statistics with Wavefunction Correlations in Disordered Metals

Cited by in corpus (17)

• The Ergodic Side of the Many-Body Localization Transition
• Fluctuations of the inverse participation ratio at the Anderson transition
• Multifractality and critical fluctuations at the Anderson transition
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Critical quantum chaos and the one dimensional Harper model
• Coherent forward scattering as a signature of Anderson metal-insulator transitions
• Spectral statistics in disordered metals: a trajectories approach
• Energy levels and their correlations in quasicrystals
• Surprising relations between parametric level correlations and fidelity decay
• Parametric Spectral Statistics in Unitary Random Matrix Ensembles: From Distribution Functions to Intra-Level Correlations
• Critical Conductance of a Mesoscopic System: Interplay of the Spectral and Eigenfunction Correlations at the Metal-Insulator Transition
• Correlations in the Adiabatic Response of Chaotic Systems
• Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials
• Effect of dephasing on mesoscopic conductance fluctuations in quantum dots with single channel leads
• Parametric Statistics of Individual Energy Levels in Random Hamiltonians
• The Quantum-Classical Crossover in the Adiabatic Response of Chaotic Systems
• Weak localization in disordered systems at the ballistic limit