251 research outputs found
The spatial statistical properties of wave functions in a disordered finite one-dimensional sample
For a given wave function one can define a quantity having a meaning
of its inverse spatial size. The Laplace transform of the distribution function
is calculated analytically for a 1D disordered sample with a finite
length .Comment: LaTEX, 7 pages, Preprint IFUM-456/FT, Milano, Jan.199
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
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
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 of random matrices. As an application, we
compute exactly the statistics of the Lyapunov spectrum of . 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
Resonant transparency of materials with negative permittivity
It is shown that the transparency of opaque material with negative
permittivity exhibits resonant behavior. The resonance occurs as a result of
the excitation of the surface waves at slab boundaries. Dramatic field
amplification of the incident evanescent fields at the resonance improves the
resolution of the the sub-wavelength imaging system (superlens). A finite
thickness slab can be totally transparent to a \textit{p}-polarized obliquely
incident electromagnetic wave for certain values of the incidence angle and
wave frequency corresponding to the excitation of the surface modes. At the
resonance, two evanescent waves have a finite phase shift providing non-zero
energy flux through the non-transparent region
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