Statistics of the One-Electron Current in a One-Dimensional Mesoscopic Ring at Arbitrary Magnetic Fields

The set of moments and the distribution function of the one-electron current in a one-dimensional disordered ring with arbitrary magnetic flux are calculated.Comment: 10 pages; Plain TeX; IFUM 448/FT; to appear in J. Stat. Phy

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

Optimal fluctuation approach to a directed polymer in a random medium

A modification of the optimal fluctuation approach is applied to study the tails of the free energy distribution function P(F) for an elastic string in quenched disorder both in the regions of the universal behavior of P(F) and in the regions of large fluctuations, where the behavior of P(F) is non-universal. The difference between the two regimes is shown to consist in whether it is necessary or not to take into account the renormalization of parameters by the fluctuations of disorder in the vicinity of the optimal fluctuation.Comment: 4 pages, no figure

Fresnel coefficients as hyperbolic rotations

We describe the action of a plane interface between two semi-infinite media in terms of a transfer matrix. We find a remarkably simple factorization of this matrix, which enables us to express the Fresnel coefficients as a hyperbolic rotation.Comment: 6 pages, 3 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

Periodic and Quasi-Periodic Compensation Strategies of Extreme Outages caused by Polarization Mode Dispersion and Amplifier Noise

Effect of birefringent disorder on the Bit Error Rate (BER) in an optical fiber telecommunication system subject to amplifier noise may lead to extreme outages, related to anomalously large values of BER. We analyze the Probability Distribution Function (PDF) of BER for various strategies of Polarization Mode Dispersion (PMD) compensation. A compensation method is proposed that is capable of more efficient extreme outages suppression, which leads to substantial improvement of the fiber system performance.Comment: 3 pages, 1 figure, Submitted to IEEE Photonics Letter

Tailoring porosity and rotational dynamics in a series of octacarboxylate metal-organic frameworks

Modulation and precise control of porosity of metal-organic frameworks (MOFs) are of critical importance to their materials function. Here we report the first modulation of porosity for a series of isoreticular octacarboxylate MOFs, denoted MFM-180 to MFM-185, via a strategy of selective elongation of metal-organic cages. Owing to the high ligand connectivity, these MOFs show absence of network interpenetration, robust structures and permanent porosity. Interestingly, activated MFM-185a shows a record high BET surface area of 4734 m2 g-1 for an octacarboxylate MOF. These MOFs show remarkable CH4 and CO2 adsorption properties, notably with simultaneously high gravimetric and volumetric deliverable CH4 capacities of 0.24 g g-1 and 163 v/v (298 K, 5-65 bar) recorded for MFM-185a due to selective elongation of tubular cages. Dynamics of molecular rotors in deuterated MFM-180a-d16 and MFM-181a-d16 were investigated by variable-temperature 2H solid state NMR spectroscopy to reveal the reorientation mechanisms within these materials. Analysis of the flipping modes of the mobile phenyl groups on the linkers, their rotational rates and transition temperatures, paves the way to controlling and understanding the role of molecular rotors through organic linker design within porous MOF materials

Universal and non-universal tails of distribution functions in the directed polymer and KPZ problems

The optimal fluctuation approach is applied to study the most distant (non-universal) tails of the free-energy distribution function P(F) for an elastic string (of a large but finite length L) interacting with a quenched random potential. A further modification of this approach is proposed which takes into account the renormalization effects and allows one to study the most close (universal) parts of the tails. The problem is analyzed for different dimensions of a space in which the polymer is imbedded. In terms the stochastic growth problem, the same distribution function describes the distribution of heights in the regime of a non-stationary growth in a situation when an interface starts to grow from a flat configuration.Comment: 17 pages, 2 figures, the final version, two paragraphs added to the conclusio

Viscous Instanton for Burgers' Turbulence

We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. We calculate high moments of the velocity gradient $\partial_xu$ and find out that they correspond to the PDF with $\ln[{\cal P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where ${\rm Re}$ is the Reynolds number. That stretched exponential form is valid for negative $\partial_xu$ with the modulus much larger than its root-mean-square (rms) value. The respective tail of PDF for negative velocity differences $w$ is steeper than Gaussian, $\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as single-point velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$. For high velocity derivatives $u^{(k)}=\partial_x^ku$, the general formula is found: $\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.Comment: 15 pages, RevTeX 3.