arXiv subjects

Igor V. Lerner

Publications and source records attributed to Igor V. Lerner.

41 records · Page 3Linked to original sources

arXiv1996

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

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.

cond-mat↗

arXiv1995

SPECTRAL CORRELATIONS IN DISORDERED ELECTRONIC SYSTEMS: CROSSOVER FROM METAL TO INSULATOR REGIME

We use the semiclassical approach combined with the scaling results for the diffusion coefficient to consider the two-level correlation function $R(\varepsilon)$ for a disordered electron system in the crossover region, characterized by the appearance of a macroscopic correlation or localization length, $ξ$, that diverges at the metal-insulator transition. We show new critical statistics, characterized by a nontrivial asymptotic behavior of $R(\varepsilon)$, to emerge on both sides of the transition at higher energies, and to expand to all energies larger than mean level spacing when $ξ$ exceeds the system size.

cond-mat↗

arXiv1995

LEVEL CORRELATIONS DRIVEN BY WEAK LOCALIZATION IN 2-D SYSTEMS

We consider the two-level correlation function in two-dimensional disordered systems. In the non-ergodic diffusive regime, at energy $ε>E_{c}$ ($E_{c}$ is the Thouless energy), it is shown to be completely determined by the weak localization effects, thus being extremely sensitive to time-reversal and spin symmetry breaking: it decreases drastically in the presence of magnetic field or magnetic impurities and changes its sign in the presence of a spin-orbit interaction. In contrast to this, the variance of the levels number fluctuations is shown to be almost unaffected by the weak localization effects.

cond-mat↗

arXiv1994

Mesoscopic Fluctuations in Models of Classical and Quantum Diffusion

It is shown that the characteristics of the mesoscopic fluctuations in the conventional quantum-diffusion model and the model of the non-coherent (`classical') diffusion in media with long-range correlated disorder are quite similar in the weak-disorder limit. The relative values of the variance and of the high-order moments of the fluctuations in one model are obtained from those in another one by substituting a proper weak-disorder parameter. As behaviour of the ensemble-averaged diffusion coefficient is quite different in these models, it suggests that the mesoscopic properties, including a possible universality in the distribution functions, could be independent of the behaviour of the averaged quantities.

cond-mat↗

arXiv1994

Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+ε$ dimensions, we calculate the localization length $ξ(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $ξ(B)$ by a numerical factor when the magnetic field is in the range $\ell\ll{\ell_{\!{_H}}}\altξ(0)$, $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $ξ(B)$ and $ξ(0)$. The effect of spin-orbit interaction is briefly considered as well.

cond-mat↗