Optical pulse propagation in fibers with random dispersion

The propagation of optical pulses in two types of fibers with randomly varying dispersion is investigated. The first type refers to a uniform fiber dispersion superimposed by random modulations with a zero mean. The second type is the dispersion-managed fiber line with fluctuating parameters of the dispersion map. Application of the mean field method leads to the nonlinear Schr\"odinger equation (NLSE) with a dissipation term, expressed by a 4th order derivative of the wave envelope. The prediction of the mean field approach regarding the decay rate of a soliton is compared with that of the perturbation theory based on the Inverse Scattering Transform (IST). A good agreement between these two approaches is found. Possible ways of compensation of the radiative decay of solitons using the linear and nonlinear amplification are explored. Corresponding mean field equation coincides with the complex Swift-Hohenberg equation. The condition for the autosolitonic regime in propagation of optical pulses along a fiber line with fluctuating dispersion is derived and the existence of autosoliton (dissipative soliton) is confirmed by direct numerical simulation of the stochastic NLSE. The dynamics of solitons in optical communication systems with random dispersion-management is further studied applying the variational principle to the mean field NLSE, which results in a system of ODE's for soliton parameters. Extensive numerical simulations of the stochastic NLSE, mean field equation and corresponding set of ODE's are performed to verify the predictions of the developed theory.Comment: 17 pages, 7 eps figure

Stable vortex and dipole vector solitons in a saturable nonlinear medium

We study both analytically and numerically the existence, uniqueness, and stability of vortex and dipole vector solitons in a saturable nonlinear medium in (2+1) dimensions. We construct perturbation series expansions for the vortex and dipole vector solitons near the bifurcation point where the vortex and dipole components are small. We show that both solutions uniquely bifurcate from the same bifurcation point. We also prove that both vortex and dipole vector solitons are linearly stable in the neighborhood of the bifurcation point. Far from the bifurcation point, the family of vortex solitons becomes linearly unstable via oscillatory instabilities, while the family of dipole solitons remains stable in the entire domain of existence. In addition, we show that an unstable vortex soliton breaks up either into a rotating dipole soliton or into two rotating fundamental solitons.Comment: To appear in Phys. Rev.

Toward a Systematic Holographic QCD: A Braneless Approach

Recently a holographic model of hadrons motivated by AdS/CFT has been proposed to fit the low energy data of mesons. We point out that the infrared physics can be developed in a more systematic manner by exploiting backreaction of the nonperturbative condensates. We show that these condensates can naturally provide the IR cutoff corresponding to confinement, thus removing some of the ambiguities from the original formulation of the model. We also show how asymptotic freedom can be incorporated into the theory, and the substantial effect it has on the glueball spectrum and gluon condensate of the theory. A simple reinterpretation of the holographic scale results in a non-perturbative running for alpha_s which remains finite for all energies. We also find the leading effects of adding the higher condensate into the theory. The difficulties for such models to reproduce the proper Regge physics lead us to speculate about extensions of our model incorporating tachyon condensation.Comment: 27 pages, LaTe

Instability of a Bose-Einstein Condensate with Attractive Interaction

We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an isolated condensate, with no gain or loss, we find that the system is stable (apart from quantum tunneling) if the particle number N is less than a critical number N_c. For N > N_c, the system collapses to high-density clumps in a region near the center of the trap. The time for the onset of collapse is on the order of 1 trap period. Within numerical uncertainty, the results are consistent with the formation of a "black hole" of infinite density fluctuations, as predicted by Ueda and Huang. We obtain numerically N_c approximately 1251. We then include gain-loss mechanisms, i.e., the gain of atoms from a surrounding "thermal cloud", and the loss due to two- and three-body collisions. The number N now oscillates in a steady state, with a period of about 145 trap periods. We obtain N_c approximately 1260 as the maximum value in the oscillations.Comment: Email correspondence to [email protected] ; 18 pages and 9 EPS figures, using REVTeX and BoxedEPS macro

Turbulent Thermalization

We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our prime motivation and application of the results. We identify three different stages of these processes. During the initial stage of ``parametric resonance'', only a small fraction of the initial inflaton energy is transferred to fluctuations in the physically relevant case of sufficiently large couplings. A major fraction is transfered in the prompt regime of driven turbulence. The subsequent long stage of thermalization classifies as free turbulence. During the turbulent stages, the evolution of particle distribution functions is self-similar. We show that wave kinetic theory successfully describes the late stages of our lattice calculation. Our analytical results are general and give estimates of reheating time and temperature in terms of coupling constants and initial inflaton amplitude.Comment: 27 pages, 13 figure

Unitarity bounds on low scale quantum gravity

We study the unitarity of models with low scale quantum gravity both in four dimensions and in models with a large extra-dimensional volume. We find that models with low scale quantum gravity have problems with unitarity below the scale at which gravity becomes strong. An important consequence of our work is that their first signal at the Large Hadron Collider would not be of a gravitational nature such as graviton emission or small black holes, but rather linked to the mechanism which fixes the unitarity problem. We also study models with scalar fields with non minimal couplings to the Ricci scalar. We consider the strength of gravity in these models and study the consequences for inflation models with non-minimally coupled scalar fields. We show that a single scalar field with a large non-minimal coupling can lower the Planck mass in the TeV region. In that model, it is possible to lower the scale at which gravity becomes strong down to 14 TeV without violating unitarity below that scale.Comment: 15 page

Not to normal order - Notes on the kinetic limit for weakly interacting quantum fluids

The derivation of the Nordheim-Boltzmann transport equation for weakly interacting quantum fluids is a longstanding problem in mathematical physics. Inspired by the method developed to handle classical dilute gases, a conventional approach is the use of the BBGKY hierarchy for the time-dependent reduced density matrices. In contrast, our contribution is motivated by the kinetic theory of the weakly nonlinear Schrodinger equation. The main observation is that the results obtained in the latter context carry over directly to weakly interacting quantum fluids provided one does not insist on normal order in the Duhamel expansion. We discuss the term by term convergence of the expansion and the equilibrium time correlation .Comment: 43 pages, corrected typos, updated assumptions in sec.

Magnetization and specific heat of the dimer system CuTe2O5

We report on magnetization and specific heat measurements on single-crystalline CuTe2O5. The experimental data are directly compared to theoretical results for two different spin structures, namely an alternating spin-chain and a two-dimensional (2D) coupled dimer model, obtained by Das et al. [Phys. Rev. B 77, 224437 (2008)]. While the analysis of the specific heat does not allow to distinguish between the two models, the magnetization data is in good agreement with the 2D coupled dimer model.Comment: 5 pages, 3 figure

ИССЛЕДОВАНИЕ ЭФФЕКТИВНОСТИ ЛЕЧЕНИЯ ЭССЕНЦИАЛЬНОГО ТРЕМОРА С ИСПОЛЬЗОВАНИЕМ ТРЕМОРОГРАФИИ

Background: Essential tremor is one of the most prevalent extrapyramidal disorders, while treatment efficacy in such patients remains low. Clinical polymorphism of essential tremor requires a  differentiated treatment approach, that should be implemented with consideration of objective tremor parameters. Aim: To study efficacy of treatment of essential tremor based on tremorography. Materials and methods: We followed up 85  patients with essential tremor (mean age, 69.05±1.2  years) who were treated with anticonvulsants as monotherapy (primidone or topiramate), or with combination treatment with non-selective beta-blockers (propranolol), anxiolytics (hydroxizine, etifoxine) and aminophenylbutyric acid. During the treatment, we assessed changes in functional status by Fahn-Tolosa-Marin Tremor Severity Scale and by tremorography. Results: Under treatment with primidone, there was a decrease in global tremor assessment of postural tremor (p=0.036) and of action tremor (p=0.001). During treatment with topiramate, there was a decrease in global tremor assessment in all tests performed (p0.0002). Non-specific treatment (anxiolytics) exerted a positive effect on the functional state of patients with essential tremor. Conclusion: Tremor amplitude and duration are the objective parameters that define its severity. The treatment guidelines for essential tremor in the elderly patients have been developed.Актуальность. Эссенциальный тремор  – одно из наиболее распространенных экстрапирамидных заболеваний, вместе с  тем эффективность лечения таких пациентов остается невысокой. Клинический полиморфизм при эссенциальном треморе определяет необходимость дифференцированного подхода к  лечению, которое должно проводиться с  учетом объективизации параметров тремора. Цель  – изучение эффективности лечения тремора эссенциального типа с  использованием метода треморографии.  Материал и  методы. Обследованы 85  пациентов с  эссенциальным тремором (средний возраст – 69,05±1,2 года) на фоне лечения антиконвульсантами в качестве монотерапии (примидон или топирамат) либо получавших комбинированную терапию неселективными бета-блокаторами (пропранолол), анксиолитиками (гидроксизин, этифоксин) и  препаратами аминофенилмасляной кислоты. Проведена оценка динамики функционального состояния пациентов на фоне лечения с использованием шкалы оценки тяжести тремора Fahn  – Tolosa  – Marin, метода треморографии. Результаты. Уменьшение общей оценки тремора у  пациентов, получавших примидон, было выявлено для постурального тремора (p=0,036) и  для тремора удержания стандартного груза (p=0,001). На фоне лечения топираматом отмечено снижение общей оценки тремора во всех проводимых пробах (p0,0002). Показано положительное влияние неспецифической терапии (анксиолитиками) на функциональное состояние больных с  эссенциальным тремором. Заключение. Значения амплитуды и протяженности тремора во времени выступают в качестве объективных параметров, определяющих его тяжесть. Выработаны рекомендации по лечению эссенциального тремора у  пациентов старшей возрастной группы

Actual fecundity of the Arctic squid Gonatus fabricii (Cephalopoda) based on the examination of a rarely encountered spent female

Gonatus fabricii (Lichtenstein, 1818) is an ecologically important squid that spends its entire life cycle within the Arctic where it is the most abundant cephalopod. Due to the rarity of mature and reproducing females, it is unknown how many eggs females spawn (actual fecundity). Among 47,000 specimens studied between 2005 and 2019 one spent, degenerated and gelatinous female with a mantle length of 230 mm was caught in West Greenland in 2019. Examination allowed the first detailed description of fecundity and spawning pattern in the species. Oocyte development shows that the most considerable maturation of mid-vitellogenic oocytes to late vitellogenic and then to ripe stages occurs immediately after the first ripe oocytes appear in the ovary. There were no ripe oocytes in the ovary or oviducts. The ovary contained an estimated 6561 oocytes and 2551 post-ovulatory follicles and hence the total fecundity was 9112. This specimen of G. fabricii realised 28.0% of its potential fecundity which is comparable to Berryteuthis magister, which also belongs to Gonatidae, and lower than in the majority of studied deep-sea squids (including other gonatids). Spent females may provide clues as to where the major spawning areas of this abundant but poorly known squid are located