Shifts of Random Energy Levels by a Local Perturbation

We consider the effect of a local perturbation on the energy levels of a system described by random matrix theory. An analytic expression for the joint distribution function of initial and final energy levels is obtained. In the case of unitary ensemble we also find the two-point correlation function of initial and final densities of states.Comment: 4 page

Theory of Dephasing by External Perturbation in Open Quantum Dots

We propose a random matrix theory describing the influence of a time dependent external field on the average magnetoresistance of open quantum dots. The effect is taken into account in all orders of perturbation theory, and the result is applicable to both weak and strong external fields.Comment: 4 pages, 3 figure

Divergence of the Classical trajectories and Weak Localization

We study the weak localization correction (WLC) to transport coefficients of a system of electrons in a static long-range potential (e.g. an antidot array or ballistic cavity). We found that the weak localization correction to the current response is delayed by the large time $t_E = \lambda^{-1} |\ln \hbar|$, where $\lambda$ is the Lyapunov exponent. In the semiclassical regime $t_E$ is much larger than the transport lifetime. Thus, the fundamental characteristic of the classical chaotic motion, Lyapunov exponent, may be found by measuring the frequency or temperature dependence of WLC.Comment: 23 pages, 4 .eps figures; Major revisions in Secs. 3, 4, and 6; To appear in Phys. Rev. B, Nov. 15, 199

Landau levels in deformed bilayer graphene at low magnetic fields

We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, instead of ff=+-8 in unperturbed bilayer at a weak magnetic field. To mention, in one of the strain regimes, the activation gap at ff=+-4 is, down to very low fields, weakly dependent on the strength of the magnetic field.Comment: 14 single-column pages, 5 figures, more details on material presented in arXiv:1104.502