Level Curvature Distribution Beyond Random Matrix Theory

Kravtsov, V. E.; Yurkevich, Igor V.; Canali, Carlo M.

doi:10.1007/978-1-4615-4875-1_14

Cited by 3 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…. W denote the integration over W with the Gaussian weight exp{−S W [W ]}, and J[W ] is the Jacobian of the transformation (3.36), (3.37) from the variable Q to {Q 0 , W } (the Jacobian does not contribute to the leading order correction calculated here, but is important for higher-order calculations [45,46]). Expanding up to the order W 4 , we get…”

Section: Deviations From Universality Atmentioning

confidence: 99%

Statistics of energy levels and eigenfunctions in disordered systems

2000

View full text Add to dashboard Cite

The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial geometries are considered, with emphasis on low-dimensional (quasi-1D and 2D) systems. Calculations are based on the supermatrix σ-model approach. The method reproduces, in so-called zero-mode approximation, the universal random matrix theory (RMT) results for the energy-level and eigenfunction fluctuations. Going beyond this approximation allows us to study system-specific deviations from universality, which are determined by the diffusive classical dynamics in the system. These deviations are especially strong in the far "tails" of the distribution function of the eigenfunction amplitudes (as well as of some related quantities, such as local density of states, relaxation time, etc.). These asymptotic "tails" are governed by anomalously localized states which are formed in rare realizations of the random potential. The deviations of the level and eigenfunction statistics from their RMT form strengthen with increasing disorder and become especially pronounced at the Anderson metal-insulator transition. In this regime, the wave functions are multifractal, while the level statistics acquires a scale-independent form with distinct critical features. Fluctuations of the conductance and of the local intensity of a classical wave radiated by a point-like source in the quasi-1D geometry are also studied within the σ-model approach. For a ballistic system with rough surface an appropriately modified ("ballistic") σ-model is used. Finally, the interplay of the fluctuations and the electron-electron interaction in small samples is discussed, with application to the Coulomb blockade spectra.

show abstract

Section: Deviations From Universality Atmentioning

confidence: 99%

Statistics of energy levels and eigenfunctions in disordered systems

2000

View full text Add to dashboard Cite

show abstract

“…However, for critical values of the coupling constant, for which the localization length scales with the size of the sample, a linear dependence on n is predicted, i.e., Σ 2 (n) ∼ χn. In this regime, the slope has been related to the multifractality index of the wave functions [13,14].…”

Section: Introductionmentioning

confidence: 99%

Thouless energy and correlations of QCD Dirac eigenvalues

Osborn

Verbaarschot

1998

Nuclear Physics B

View full text Add to dashboard Cite

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences δE below an energy scale E c the eigenvalue correlations are given by Random Matrix Theories with the chiral symmetries of the QCD partition function. For eigenvalues near zero this energy scale shows a weak volume dependence that is not consistent with E c ∼ 1/L 2 which might be expected from the pion Compton wavelength and from the behavior of the Thouless energy in mesoscopic systems. However, the numerical value of E c for our largest volumes is in rough agreement with estimates from the pion Compton wavelength. A scaling behaviour consistent with E c ∼ 1/L 2 is found in the bulk of the spectrum. For δE > E c the number variance shows a linear dependence with a slope which is larger than the nonzero multifractality index of the wave functions. Finally, the average spectral density and the scalar susceptibilities are discussed in the context of quenched chiral perturbation theory. We argue that a nonzero value of the disconnected scalar susceptibility requires a linear dependence of the number variance on δE.

show abstract

Scattering, Transport & Stochasticity in Quantum Systems

Gaspard

2000

Dynamics: Models and Kinetic Methods for Non-Equilibrium Many Body Systems

View full text Add to dashboard Cite

Level Curvature Distribution Beyond Random Matrix Theory

Cited by 3 publications

References 27 publications

Statistics of energy levels and eigenfunctions in disordered systems

Statistics of energy levels and eigenfunctions in disordered systems

Thouless energy and correlations of QCD Dirac eigenvalues

Scattering, Transport & Stochasticity in Quantum Systems

Contact Info

Product

Resources

About