Passive scalar convection in 2D long-range delta-correlated velocity field: Exact results

The letter presents new field-theoretical approach to 2D passive scalar problem. The Gaussian form of the distribution for the Lyapunov exponent is derived and its parameters are found explicitly.Comment: 11 pages, RevTex 3.0, IFUM-94/455/January-F

Doping-Induced Interband Gain in InAs/AlSb Quantum Wells

A paper describes a computational study of effects of doping in a quantum well (QW) comprising a 10-nm-thick layer of InAs sandwiched between two 21-nm-thick AlSb layers. Heretofore, InAs/AlSb QWs have not been useful as interband gain devices because they have type-II energy-band-edge alignment, which causes spatial separation of electrons and holes, thereby leading to weak interband dipole matrix elements. In the doping schemes studied, an interior sublayer of each AlSb layer was doped at various total areal densities up to 5 X 10(exp 12) / square cm. It was found that (1) proper doping converts the InAs layer from a barrier to a well for holes, thereby converting the heterostructure from type II to type I; (2) the resultant dipole matrix elements and interband gains are comparable to those of typical type-I heterostructures; and (3) dipole moments and optical gain increase with the doping level. Optical gains in the transverse magnetic mode can be almost ten times those of other semiconductor material systems in devices used to generate medium-wavelength infrared (MWIR) radiation. Hence, doped InAs/AlSb QWs could be the basis of an alternative material system for devices to generate MWIR radiation

The Lyapunov Spectrum of a Continuous Product of Random Matrices

We expose a functional integration method for the averaging of continuous products $\hat{P}_t$ of $N\times N$ random matrices. As an application, we compute exactly the statistics of the Lyapunov spectrum of $\hat{P}_t$. This problem is relevant to the study of the statistical properties of various disordered physical systems, and specifically to the computation of the multipoint correlators of a passive scalar advected by a random velocity field. Apart from these applications, our method provides a general setting for computing statistical properties of linear evolutionary systems subjected to a white noise force field.Comment: Latex, 9 page

T-duality in supersymmetric theory of disordered quantum systems

A new super-symmetric representation for quantum disordered systems is derived. This representation is exact and is dual to that of the nonlinear sigma-model. The new formalism is tested by calculating the distribution of wave function amplitudes in the 1d Anderson model. The deviation from the distribution found for a thick wire is detected near the band center E=0.Comment: 4 page

Statistics of anomalously localized states at the center of band E=0 in the one-dimensional Anderson localization model

We consider the distribution function $P(|\psi|^{2})$ of the eigenfunction amplitude at the center-of-band (E=0) anomaly in the one-dimensional tight-binding chain with weak uncorrelated on-site disorder (the one-dimensional Anderson model). The special emphasis is on the probability of the anomalously localized states (ALS) with $|\psi|^{2}$ much larger than the inverse typical localization length $\ell_{0}$. Using the solution to the generating function $\Phi_{an}(u,\phi)$ found recently in our works we find the ALS probability distribution $P(|\psi|^{2})$ at $|\psi|^{2}\ell_{0} >> 1$. As an auxiliary preliminary step we found the asymptotic form of the generating function $\Phi_{an}(u,\phi)$ at $u >> 1$ which can be used to compute other statistical properties at the center-of-band anomaly. We show that at moderately large values of $|\psi|^{2}\ell_{0}$, the probability of ALS at E=0 is smaller than at energies away from the anomaly. However, at very large values of $|\psi|^{2}\ell_{0}$, the tendency is inverted: it is exponentially easier to create a very strongly localized state at E=0 than at energies away from the anomaly. We also found the leading term in the behavior of $P(|\psi|^{2})$ at small $|\psi|^{2}<< \ell_{0}^{-1}$ and show that it is consistent with the exponential localization corresponding to the Lyapunov exponent found earlier by Kappus and Wegner and Derrida and Gardner.Comment: 25 pages, 9 figure

Statistics of soliton-bearing systems with additive noise

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a further development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governing by noisy Nonlinear Schr\"odinger Equation (NSE). We then apply our method to optical soliton transmission systems using signal control elements (filters, amplitude and phase modulators).Comment: 4 pages. Submitted to PR

Spin and Charge Correlations in Quantum Dots: An Exact Solution

The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an {\it exact} analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We calculate several observables, including the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotropic spin interaction. Our results could be tested in nearly ferromagnetic materials.Comment: JETPL class, 6 pages, 2 figure

Notes about Passive Scalar in Large-Scale Velocity Field

We consider advection of a passive scalar theta(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model the whole PDF's (probability distribution functions) for the single-point statistics of theta and for the passive scalar difference theta(r_1)-theta(r_2) (for separations r_1-r_2 lying in the convective interval) are found.Comment: 19 pages, RevTe