"Level Curvature" Distribution for Diffusive Aharonov-Bohm Systems: analytical results

Abstract

We calculate analytically the distributions of "level curvatures" (LC) (the second derivatives of eigenvalues with respect to a magnetic flux) for a particle moving in a white-noise random potential. We find that the Zakrzewski-Delande conjecture is still valid even if the lowest weak localization corrections are taken into account. The ratio of mean level curvature modulus to mean dissipative conductance is proved to be universal and equal to $2\pi$ in agreement with available numerical data.

12 pages. Submitted to Phys.Rev.E

References in corpus (5)

• Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards
• Distribution of "level velocities" in quasi 1D disordered or chaotic systems with localization
• Universal Spectral Correlations in Diffusive Quantum Systems
• Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos
• Single Level Current and Curvature Distributions in Mesoscopic Systems

Cited by in corpus (24)

• Random Matrix Theories in Quantum Physics: Common Concepts
• Statistics of resonance poles, phase shifts and time delays in quantum chaotic scattering for systems with broken time reversal invariance
• Mesoscopic Fluctuations of Eigenfunctions and "Level Velocity" Distribution in Disordered Metals
• Semiclassical Quantization of Billiards with Mixed Boundary Conditions
• Level Curvatures and Conductances: A Numerical Study of the Thouless Relation
• Invariant Correlation Entropy and Complexity of Quantum States
• Energy level dynamics across the many-body localization transition
• Drude weight fluctuations in many-body localized systems
• Distribution of level curvatures for the Anderson model at the localization-delocalization transition
• Many-Body-Localization Transition : sensitivity to twisted boundary conditions
• Levy Diffusion and Classes of Universal Parametric Correlations
• Sensitivity of the eigenfunctions and the level curvature distribution in quantum billiards
• Nonuniversality in level dynamics
• Level Curvature distribution in a model of two uncoupled chaotic subsystems
• Non-universal corrections to the level curvature distribution beyond random matrix theory
• Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function
• Level Curvature Distribution and the Structure of Eigenfunctions in Disordered Systems
• Universal Voltage Fluctuations in Disordered Superconductors
• On the critical level-curvature distribution
• Level dynamics and avoided level crossings in driven disordered quantum dots
• Random Matrix Theory by the Supersymmetry Method Beyond the Sigma-Model
• Topological universality of level dynamics in quasi-one-dimensional disordered conductors
• Spectral properties of three-dimensional Anderson model
• Parametric Number Covariance in Quantum Chaotic Spectra