arXiv subjects

V. E. Kravtsov

Publications and source records attributed to V. E. Kravtsov.

63 records · Page 4Linked to original sources

arXiv1996

Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function

It is shown that the quasi-localized states in weakly disordered systems can lead to the non-analytical distribution of level curvatures. In 2D systems the distribution function P(K) has a branching point at K=0. In quasi-1D systems the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all. Such a behavior confirms the conjecture that the branching at K=0 is due to the multi-fractality of wave functions and thus is a generic feature of all critical eigenstates. The relationsip between the branching power and the multi-fractality exponent $η(2)$ is derived.

cond-mat↗

arXiv1996

Non-universal corrections to the level curvature distribution beyond random matrix theory

The level curvature distribution function is studied beyond the random matrix theory for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the level curvature distribution is calculated using the nonlinear sigma-model. The sign of the correction depends on the presence or absence of the global gauge invariance and is different for perturbations caused by the constant vector-potential and by the random magnetic field. Scaling arguments are discussed that indicate on the qualitative difference in the level statistics in the dirty metal phase for space dimensionalities $d<4$ and $d>4$.

cond-mat↗

arXiv1996

Spectral Rigidity and Eigenfunction Correlations at the Anderson Transition

The statistics of energy levels for a disordered conductor are considered in the critical energy window near the mobility edge. It is shown that, if critical wave functions are multifractal, the one-dimensional gas of levels on the energy axis is ``compressible'', in the sense that the variance of the level number in an interval is $< (δN)^{2} > = χ $ for $ >> 1$. The compressibility, $χ=η/2d$, is given ``exactly'' in terms of the multifractal exponent $η=d-D_2$ at the mobility edge in a $d$-dimensional system.

cond-mat↗

arXiv1996

Spectral Statistics at the Anderson Transition: Multifractality of Wave Functions and the Violation of the Normalization Sum Rule

The statistics of energy levels of electrons in a random potential is considered in the critical energy window near the mobility edge. It is shown that the multifractality of critical wave functions results in the violation of the normalization sum rule in the thermodynamic limit and leads to the quasi-Poisson linear term in the level number variance. The slope of the linear term is equal to the sum rule deficiency which is expressed in terms of the fractal dimension D(2).

cond-mat↗

arXiv1996

Distribution of level curvatures for the Anderson model at the localization-delocalization transition

We compute the distribution function of single-level curvatures, $P(k)$, for a tight binding model with site disorder, on a cubic lattice. In metals $P(k)$ is very close to the predictions of the random-matrix theory (RMT). In insulators $P(k)$ has a logarithmically-normal form. At the Anderson localization-delocalization transition $P(k)$ fits very well the proposed novel distribution $P(k)\propto (1+k^μ)^{3/μ}$ with $μ\approx 1.58$, which approaches the RMT result for large $k$ and is non-analytical at small $k$. We ascribe such a non-analiticity to the spatial multifractality of the critical wave functions.

cond-mat↗

arXiv1995

Normalization Sum Rule and Spontaneous Breaking of U(N) Invariance in Random Matrix Ensembles

It is shown that the two-level correlation function $R(s,s')$ in the invariant random matrix ensembles (RME) with soft confinement exhibits a "ghost peak" at $s\approx -s'$. This lifts the sum rule prohibition for the level number variance to have a Poisson-like term ${\rm var}(n)=ηn$ that is typical of RME with broken U(N) symmetry. Thus we conclude that the U(N) invariance is broken spontaneously in the RME with soft confinement, $η$ playing the role of an order-parameter.

cond-mat↗

arXiv1994

Non-Universality in Random Matrix Ensembles with Soft Level Confinement

Two families of strongly non-Gaussian random matrix ensembles (RME) are considered. They are statistically equivalent to a one-dimensional plasma of particles interacting logarithmically and confined by the potential that has the long-range behavior $V(ε)\sim |ε|^α$ ($0<α<1$), or $V(ε)\sim \ln^{2}|ε|$. The direct Monte Carlo simulations on the effective plasma model shows that the spacing distribution function (SDF) in such RME can deviate from that of the classical Gaussian ensembles. For power-law potentials, this deviation is seen only near the origin $ε\sim 0$, while for the double-logarithmic potential the SDF shows the cross-over from the Wigner-Dyson to Poisson behavior in the bulk of the spectrum.

cond-mat↗

arXiv1994

The Level Spacing Distribution Near the Anderson Transition

For a disordered system near the Anderson transition we show that the nearest-level-spacing distribution has the asymptotics $P(s)\propto \exp(-A s^{2-γ})$ for $s\gg \av{s}\equiv 1$ which is universal and intermediate between the Gaussian asymptotics in a metal and the Poisson in an insulator. (Here the critical exponent $0<γ<1$ and the numerical coefficient $A$ depend only on the dimensionality $d>2$). It is obtained by mapping the energy level distribution to the Gibbs distribution for a classical one-dimensional gas with a pairwise interaction. The interaction, consistent with the universal asymptotics of the two-level correlation function found previously, is proved to be the power-law repulsion with the exponent $-γ$.

cond-mat↗

arXiv1994

Universal Spectral Correlations at the Mobility Edge

We demonstrate the level statistics in the vicinity of the Anderson transition in $d>2$ dimensions to be universal and drastically different from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. The variance of the number of levels $N$ in a given energy interval with $\langle N\rangle\gg1$ is proved to behave as $\langle N\rangle^γ$ where $γ=1-(νd)^{-1}$ and $ν$ is the correlation length exponent. The inequality $γ<1$, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function.

cond-mat↗