Conformal Invariance and Shape-Dependent Conductance of Graphene Samples

For a sample of an arbitrary shape, the dependence of its conductance on the longitudinal and Hall conductivity is identical to that of a rectangle. We use analytic results for a conducting rectangle, combined with the semicircle model for transport coefficients, to study properties of the monolayer and bilayer graphene. A conductance plateau centered at the neutrality point, predicted for square geometry, is in agreement with recent experiments. For rectangular geometry, the conductance exhibits maxima at the densities of compressible quantum Hall states for wide samples, and minima for narrow samples. The positions and relative sizes of these features are different in the monolayer and bilayer cases, indicating that the conductance can be used as a tool for sample diagnostic.Comment: 9 pages, 6 figure

Wave of nonequilibrium ionization in a gas

Propagation model for plane ionization wave in uniform electric fiel

Strong-field dipole resonance. I. Limiting analytical cases

We investigate population dynamics in N-level systems driven beyond the linear regime by a strong external field, which couples to the system through an operator with nonzero diagonal elements. As concrete example we consider the case of dipolar molecular systems. We identify limiting cases of the Hamiltonian leading to wavefunctions that can be written in terms of ordinary exponentials, and focus on the limits of slowly and rapidly varying fields of arbitrary strength. For rapidly varying fields we prove for arbitrary $N$ that the population dynamics is independent of the sign of the projection of the field onto the dipole coupling. In the opposite limit of slowly varying fields the population of the target level is optimized by a dipole resonance condition. As a result population transfer is maximized for one sign of the field and suppressed for the other one, so that a switch based on flopping the field polarization can be devised. For significant sign dependence the resonance linewidth with respect to the field strength is small. In the intermediate regime of moderate field variation, the integral of lowest order in the coupling can be rewritten as a sum of terms resembling the two limiting cases, plus correction terms for N>2, so that a less pronounced sign-dependence still exists.Comment: 34 pages, 1 figur

Magnetic screening in proximity effect Josephson-junction arrays

The modulation with magnetic field of the sheet inductance measured on proximity effect Josephson-junction arrays (JJAs) is progressively vanishing on lowering the temperature, leading to a low temperature field-independent response. This behaviour is consistent with the decrease of the two-dimensional penetration length below the lattice parameter. Low temperature data are quantitatively compared with theoretical predictions based on the XY model in absence of thermal fluctuations. The results show that the description of a JJA within the XY model is incomplete and the system is put well beyond the weak screening limit which is usually assumed in order to invoke the well known frustrated XY model describing classical Josephson-junction arrays.Comment: 6 pages, 5 figure

Effective Drag Between Strongly Inhomogeneous Layers: Exact Results and Applications

We generalize Dykhne's calculation of the effective resistance of a 2D two-component medium to the case of frictional drag between the two parallel two-component layers. The resulting exact expression for the effective transresistance, $\rho^D_{eff}$, is analyzed in the limits when the resistances and transresistances of the constituting components are strongly different - situation generic for the vicinity of the {\em classical} (percolative) metal-insulator transition (MIT). On the basis of this analysis we conclude that the evolution of $\rho^D_{eff}$ across the MIT is determined by the type of correlation between the components, constituting the 2D layers. Depending on this correlation, in the case of two electron layers, $\rho^D_{eff}$ changes either monotonically or exhibits a sharp maximum. For electron-hole layers $\rho^D_{eff}$ is negative and $|\rho^D_{eff}|$ exhibits a sharp minimum at the MIT.Comment: 7 pages, 3 figure

Dielectric breakdown in spin polarized Mott insulator

Nonlinear response of a Mott insulator to external electric field, corresponding to dielectric breakdown phenomenon, is studied within of a one-dimensional half-filled Hubbard model. It is shown that in the limit of nearly spin polarized insulator the decay rate of the ground state into excited holon-doublon pairs can be evaluated numerically as well to high accuracy analytically. Results show that the threshold field depends on the charge gap as $F_{th} \propto \Delta^{3/2}$. Numerical results on small systems indicate on the persistence of a similar mechanism for the breakdown for decreasing magnetization down to unpolarised system.Comment: 4 pages, 6 figure

Ionization Instability of a Plasma with Hot Electrons

Ionization instability of plasma with hot electron

Establishment of the spectra of kinetic turbulence

An analysis of kinetic equations describing the establishment of Langmuir turbulence spectra is presented. Secondary turbulence occurs where stationary distribution consists of many peaks. The position of peaks is established and their amplitudes complete undamped oscillations. It is pointed out that establishing spectra can occur only during adiabatic inclusion of pumping. It is significant here that the adiabiatic condition is more rigid than the ordinary by several hundred times

Level crossings in a cavity QED model

In this paper I study the dynamics of a two-level atom interacting with a standing wave field. When the atom is subjected to a weak linear force, the problem can be turned into a time dependent one, and the evolution is understood from the band structure of the spectrum. The presence of level crossings in the spectrum gives rise to Bloch oscillations of the atomic motion. Here I investigate the effects of the atom-field detuning parameter. A variety of different level crossings are obtained by changing the magnitude of the detuning, and the behaviour of the atomic motion is strongly affected due to this. I also consider the situation in which the detuning is oscillating in time and its impact on the atomic motion. Wave packet simulations of the full problem are treated numerically and the results are compared with analytical solutions given by the standard Landau-Zener and the three-level Landau-Zener models.Comment: 12 pages, 10 figure