Bright vector solitons in cross-defocusing nonlinear media

We study two-dimensional soliton-soliton vector pairs in media with self-focusing nonlinearities and defocing cross-interactions. The general properties of the stationary states and their stability are investigated. The different scenarios of instability are observed using numerical simulations. The quasi-stable propagation regime of the high-power vector solitons is revealed.Comment: 6 pages, 7 figure

Mean Field Approach to the Giant Wormhole Problem

We introduce a gaussian probability density for the space-time distribution of wormholes, thus taking effectively into account wormhole interaction. Using a mean-field approximation for the free energy, we show that giant wormholes are probabilistically suppressed in a homogenous isotropic ``large'' universe.Comment: 10 pages, Late

The spatial statistical properties of wave functions in a disordered finite one-dimensional sample

For a given wave function one can define a quantity $\mu_E$ having a meaning of its inverse spatial size. The Laplace transform of the distribution function $P(\mu_E)$ is calculated analytically for a 1D disordered sample with a finite length $L$.Comment: LaTEX, 7 pages, Preprint IFUM-456/FT, Milano, Jan.199

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

Displaced dynamics of binary mixtures in linear and nonlinear optical lattices

The dynamical behavior of matter wave solitons of two-component Bose-Einstein condensates (BEC) in combined linear and nonlinear optical lattices (OLs) is investigated. In particular, the dependence of the frequency of the oscillating dynamics resulting from initially slightly displaced components is investigated both analytically, by means of a variational effective potential approach for the reduced collective coordinate dynamics of the soliton, and numerically, by direct integrations of the mean field equations of the BEC mixture. We show that for small initial displacements binary solitons can be viewed as point masses connected by elastic springs of strengths related to the amplitude of the OL and to the intra and inter-species interactions. Analytical expressions of symmetric and anti-symmetric mode frequencies, are derived and occurrence of beatings phenomena in the displaced dynamics is predicted. These expressions are shown to give a very good estimation of the oscillation frequencies for different values of the intra-species interatomic scattering length, as confirmed by direct numerical integrations of the mean field Gross-Pitaevskii equations (GPE) of the mixture. The possibility to use displaced dynamics for indirect measurements of BEC mixture characteristics such as number of atoms and interatomic interactions is also suggested.Comment: 8 pages, 21 figure

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

Outage probability for soliton transmission

PACS. 78.55.Qr – Amorphous materials; glasses and other disordered solids. PACS. 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion. Abstract. – We study the interplay between amplifier noise and birefringent disorder in the case of strongly nonlinear (soliton) type of transmission in optical fibers. Assuming both noise and disorder to be weak, we evaluate the probability distribution function (PDF) of the Bit-Error-Rate (BER) for the values of BER that are much larger than the typical (average) value. The PDFtail that describes probability of the system outage shows log-normal shape, strongly dependent on the fiber length. We also discuss a simple timing shift technique capable of the outage compensation. Nonlinear information transmission in optical fibers when elementary bits are represented by optical solitons constitutes a promising technology that has been a subject of intensive research over the past decades [1, 2]. In idealfibers, the information carried by the solitons would be transmitted without any loss. In practice, however, various impairments lead to information loss. Amplifier noise and birefringent disorder represent the two major impairments in both linear and nonlinear transmission regimes. The noise generated by spontaneous emissio

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

Проблемы международно-правовой ответственности международных организаций

Колоколов А. Е. Проблемы международно-правовой ответственности международных организаций / А. Е. Колоколов // Міжнародні читання з міжнародного права пам’яті професора П.Є. Казанського : матер. третьої міжнар. наук. конф. (м. Одеса, 2–3 листопада 2012 р.) / відп. за випуск М. І. Пашковський ; НУ «ОЮА». – Одеса : Фенікс, 2012. – С. 150-154.Автор статьи считает, что практика в вопросе ответственности ММО не слишком богата и на данный момент к международным организациям применяются mutatis mutandis общие положения Статей об ответственности государств. Приведенный автором статьи перечень проблем далеко себя не исчерпывает. В основном они возникают из специфики правосубъектности международных организаций и учитывая, что КМП до сихпор работает над ПСОМО и он еще не принят, решение данного вопроса еще далеко от завершения