Asymptotic formulas for probabilities of large deviations of ladder heights

Asymptotic formulas for large-deviation probabilities of a ladder height in a random walk generated by a sequence of sums of i.i.d. random variables are deduced. Two cases are considered: a) the distribution F(x) of summands is normal with a zero mean. b) F(x) belongs to the domain of the normal attraction of a stable law with the exponent 0 < α < 1. The method of Laplace transforms is applied in proofs

Anomalous crossover between thermal and shot noise in macroscopic diffusive conductors

We predict the existence of an anomalous crossover between thermal and shot noise in macroscopic diffusive conductors. We first show that, besides thermal noise, these systems may also exhibit shot noise due to fluctuations of the total number of carriers in the system. Then we show that at increasing currents the crossover between the two noise behaviors is anomalous, in the sense that the low frequency current spectral density displays a region with a superlinear dependence on the current up to a cubic law. The anomaly is due to the non-trivial coupling in the presence of the long range Coulomb interaction among the three time scales relevant to the phenomenon, namely, diffusion, transit and dielectric relaxation time.Comment: 4 pages, 2 figure

Shot Noise at High Temperatures

We consider the possibility of measuring non-equilibrium properties of the current correlation functions at high temperatures (and small bias). Through the example of the third cumulant of the current (${\cal{S}}_3$) we demonstrate that odd order correlation functions represent non-equilibrium physics even at small external bias and high temperatures. We calculate ${\cal{S}}_3=y(eV/T) e^2 I$ for a quasi-one-dimensional diffusive constriction. We calculate the scaling function $y$ in two regimes: when the scattering processes are purely elastic and when the inelastic electron-electron scattering is strong. In both cases we find that $y$ interpolates between two constants. In the low (high) temperature limit $y$ is strongly (weakly) enhanced (suppressed) by the electron-electron scattering.Comment: 11 pages 4 fig. submitted to Phys. Rev.

Theory of Interaction Effects in N-S Junctions out of Equilibrium

We consider a normal metal - superconductor (N-S) junction in the regime, when electrons in the normal metal are driven out of equilibrium. We show that the non-equilibrium fluctuations of the electron density in the N-layer cause the fluctuations of the phase of the order parameter in the S-layer. As a result, the density of states in the superconductor deviates from the BCS form, most notably the density of states in the gap becomes finite. This effect can be viewed as a result of the time reversal symmetry breaking due to the non-equilibrium, and can be described in terms of a low energy collective mode of the junction, which couples normal currents in N-layer and supercurrents. This mode is analogous to the Schmid-Sch\"{o}n mode. To interpret their measurements of the tunneling current, Pothier {\em et. al} [Phys. Rev. Lett. {\bf 79}, 3490 (1997)] had to assume that the energy relaxation rate in the normal metal is surprisingly high. The broadening of the BCS singularity of the density of states in the S-layer manifest itself similarly to the broadening of the distribution function. Mechanism suggested here can be a possible explanation of this experimental puzzle. We also propose an independent experiment to test our explanation.Comment: 16 pages, 2 .eps figure

Outlets of 2D invasion percolation and multiple-armed incipient infinite clusters

We study invasion percolation in two dimensions, focusing on properties of the outlets of the invasion and their relation to critical percolation and to incipient infinite clusters (IIC's). First we compute the exact decay rate of the distribution of both the weight of the kth outlet and the volume of the kth pond. Next we prove bounds for all moments of the distribution of the number of outlets in an annulus. This result leads to almost sure bounds for the number of outlets in a box B(2^n) and for the decay rate of the weight of the kth outlet to p_c. We then prove existence of multiple-armed IIC measures for any number of arms and for any color sequence which is alternating or monochromatic. We use these measures to study the invaded region near outlets and near edges in the invasion backbone far from the origin.Comment: 38 pages, 10 figures, added a thorough sketch of the proof of existence of IIC's with alternating or monochromatic arms (with some generalizations

Electron transport through interacting quantum dots

We present a detailed theoretical investigation of the effect of Coulomb interactions on electron transport through quantum dots and double barrier structures connected to a voltage source via an arbitrary linear impedance. Combining real time path integral techniques with the scattering matrix approach we derive the effective action and evaluate the current-voltage characteristics of quantum dots at sufficiently large conductances. Our analysis reveals a reach variety of different regimes which we specify in details for the case of chaotic quantum dots. At sufficiently low energies the interaction correction to the current depends logarithmically on temperature and voltage. We identify two different logarithmic regimes with the crossover between them occurring at energies of order of the inverse dwell time of electrons in the dot. We also analyze the frequency-dependent shot noise in chaotic quantum dots and elucidate its direct relation to interaction effects in mesoscopic electron transport.Comment: 21 pages, 4 figures. References added, discussion slightly extende

On the self-consistent spin-wave theory of layered Heisenberg magnets

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional (2D) Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the non-linear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.Comment: 46 pages, RevTeX, 7 figure

On limit theorems for continued fractions

It is shown that for sums of functionals of digits in continued fraction expansion the Kolmogorov-Feller weak laws of large numbers and the Khinchine-L\'evy-Feller-Raikov characterization of the domain of attraction of the normal law hold.Comment: 16 page

Evanescent wave transport and shot noise in graphene: ballistic regime and effect of disorder

We have investigated electrical transport and shot noise in graphene field effect devices. In large width over length ratio $W/L$ graphene strips, we have measured shot noise at low frequency ($f$ = 600--850 MHz) in the temperature range of 4.2--30 K. We observe a minimum conductivity of $\frac{4e^{2}}{\pi h}$ and a finite and gate dependent Fano factor reaching the universal value of 1/3 at the Dirac point, i.e. where the density of states vanishes. These findings are in good agreement with the theory describing that transport at the Dirac point should occur via evanescent waves in perfect graphene samples with large $W/L$. Moreover, we show and discuss how disorder and non-parallel leads affect both conductivity and shot noise.Comment: Extended version (19 pages, 10 figures) of Phys. Rev. Lett. 100, 196802 (2008). Additional data on the effect of disorder and non-parallel leads. Submitted for publication in Journal of Low Temperature Physics for the Proceedings of the International Symposium on Quantum Phenomena and Devices at Low Temperatures (ULTI 2008), Espoo, Finlan