Four electrons in a two-leg Hubbard ladder: exact ground states

In the case of a two-leg Hubbard ladder we present a procedure which allows the exact deduction of the ground state for the four particle problem in arbitrary large lattice system, in a tractable manner, which involves only a reduced Hilbert space region containing the ground state. In the presented case, the method leads to nine analytic, linear, and coupled equations providing the ground state. The procedure which is applicable to few particle problems and other systems as well is based on an r-space representation of the wave functions and construction of symmetry adapted orthogonal basis wave vectors describing the Hilbert space region containing the ground state. Once the ground state is deduced, a complete quantum mechanical characterization of the studied state can be given. Since the analytic structure of the ground state becomes visible during the use of the method, its importance is not reduced only to the understanding of theoretical aspects connected to exact descriptions or potential numerical approximation scheme developments, but is relevant as well for a large number of potential technological application possibilities placed between nano-devices and quantum calculations, where the few particle behavior and deep understanding are important key aspects to know.Comment: 19 pages, 5 figure

An instability criterion for nonlinear standing waves on nonzero backgrounds

A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a finite interval. Localized standing wave solutions on a non-zero background, e.g., dark solitons trapped by the inhomogeneity, are identified and studied. A novel instability criterion for such states is established through a topological argument. This allows instability to be determined quickly in many cases by considering simple geometric properties of the standing waves as viewed in the composite phase plane. Numerical calculations accompany the analytical results.Comment: 20 pages, 11 figure

Variational Approach to the Modulational Instability

We study the modulational stability of the nonlinear Schr\"odinger equation (NLS) using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODEs) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODEs, we re-derive the classical modulational instability criterion. The case (relevant to applications in optics and Bose-Einstein condensation) where the coefficients of the equation are time-dependent, is also examined

Optical Lattices: Theory

This chapter presents an overview of the properties of a Bose-Einstein condensate (BEC) trapped in a periodic potential. This system has attracted a wide interest in the last years, and a few excellent reviews of the field have already appeared in the literature (see, for instance, [1-3] and references therein). For this reason, and because of the huge amount of published results, we do not pretend here to be comprehensive, but we will be content to provide a flavor of the richness of this subject, together with some useful references. On the other hand, there are good reasons for our effort. Probably, the most significant is that BEC in periodic potentials is a truly interdisciplinary problem, with obvious connections with electrons in crystal lattices, polarons and photons in optical fibers. Moreover, the BEC experimentalists have reached such a high level of accuracy to create in the lab, so to speak, paradigmatic Hamiltonians, which were first introduced as idealized theoretical models to study, among others, dynamical instabilities or quantum phase transitions.Comment: Chapter 13 in Part VIII: "Optical Lattices" of "Emergent Nonlinear Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P. G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez (Springer Series on Atomic, Optical, and Plasma Physics, 2007) - pages 247-26

Nonlinear Waves in Bose-Einstein Condensates: Physical Relevance and Mathematical Techniques

The aim of the present review is to introduce the reader to some of the physical notions and of the mathematical methods that are relevant to the study of nonlinear waves in Bose-Einstein Condensates (BECs). Upon introducing the general framework, we discuss the prototypical models that are relevant to this setting for different dimensions and different potentials confining the atoms. We analyze some of the model properties and explore their typical wave solutions (plane wave solutions, bright, dark, gap solitons, as well as vortices). We then offer a collection of mathematical methods that can be used to understand the existence, stability and dynamics of nonlinear waves in such BECs, either directly or starting from different types of limits (e.g., the linear or the nonlinear limit, or the discrete limit of the corresponding equation). Finally, we consider some special topics involving more recent developments, and experimental setups in which there is still considerable need for developing mathematical as well as computational tools.Comment: 69 pages, 10 figures, to appear in Nonlinearity, 2008. V2: new references added, fixed typo

Dark solitons in atomic Bose-Einstein condensates: from theory to experiments

This review paper presents an overview of the theoretical and experimental progress on the study of matter-wave dark solitons in atomic Bose-Einstein condensates. Upon introducing the general framework, we discuss the statics and dynamics of single and multiple matter-wave dark solitons in the quasi one-dimensional setting, in higher-dimensional settings, as well as in the dimensionality crossover regime. Special attention is paid to the connection between theoretical results, obtained by various analytical approaches, and relevant experimental observations.Comment: 82 pages, 13 figures. To appear in J. Phys. A: Math. Theor

Структура распределения генетических детерминант эффективности и безопасности нестероидных противовоспалительных препаратов в российской популяции: фокус на CYP2C8, PTGS1 и PTGS2

The efficacy and safety of non-steroidal anti-inflammatory drugs (NSAIDs) may be determined by the polymorphic nature of the CYP2C8, PTGS1 and PTGS2 genes.Objective: to analyze the nature of the distribution of CYP2C8*3 (rs10509681), CYP2C8*3 (rs11572080), PTGS1 (rs10306135), PTGS1 (rs12353214) and PTGS2 (rs20417) among residents of the North Caucasus.Patients and methods. The study involved 676 volunteers from Russian, Balkar, Kabardian and Ossetian ethnic groups. Carriage of polymorphic markers CYP2C8, PTGS1 and PTGS2 was determined using real-time polymerase chain reaction.Results and discussion. There were no significant differences between the groups in the rs10509681 and rs11572080 variants of the CYP2C8 gene. In all groups, the carriage of a combination of CYP2C8 and CYP2C9 alleles, encoding the phenotype of normal metabolizers, prevailed with a frequency of about 75% or more. The rs10306135 variant of the PTGS1 gene was found in 5.9% of Russians, 1.1% of Balkars, 5.3% of Kabardians, and 10.6% of Ossetians; variant rs12353214 – in 19.1; 9.4; 10.8 and 9.2%, rs20417 polymorphism of the PTGS2 gene in 0.4; 5; 2.8 and 3.1% respectively.Conclusion. The data obtained can be used to develop a more rational approach to the prescription of NSAIDs, taking into account the genetic characteristics of the local population in ethnic regions.Эффективность и безопасность применения нестероидных противовоспалительных препаратов (НПВП) может определяться полиморфной природой генов CYP2C8, PTGS1 и PTGS2.Цель исследования – анализ характера распределения CYP2C8*3 (rs10509681), CYP2C8*3 (rs11572080), PTGS1 (rs10306135), PTGS1 (rs12353214) и PTGS2 (rs20417) среди жителей Северного Кавказа.Пациенты и методы. В исследовании участвовали 676 добровольцев из русской, балкарской, кабардинской и осетинской этнических групп. Носительство полиморфных маркеров CYP2C8, PTGS1 и PTGS2 определялось с помощью полимеразной цепной реакции в режиме реального времени.Результаты и обсуждение. Значимых различий между группами по вариантам rs10509681 и rs11572080 гена CYP2C8 не получено. Во всех группах преобладало носительство комбинации аллелей CYP2C8 и CYP2C9, кодирующих фенотип нормальных метаболизаторов с частотой около 75% и более. Вариант rs10306135 гена PTGS1 выявлен у 5,9% русских, 1,1% балкарцев, 5,3% кабардинцев и 10,6% осетин; вариант rs12353214 – у 19,1; 9,4; 10,8 и 9,2%, полиморфизм rs20417 гена PTGS2 – у 0,4; 5; 2,8 и 3,1% соответственно.Заключение. Полученные данные могут быть использованы при разработке более рационального подхода к назначению НПВП, учитывающего генетические особенности местного населения в этнических регионах

Experimental characterization of anomalous strong scattering of mm-waves in TEXTOR plasmas with rotating islands

Anomalous scattering of high power millimetre waves from gyrotrons at 140 and 110 GHz is investigated for plasma with rotating islands at TEXTOR. The magnetic field and plasma density influence the spectral content of the scattered waves and their power levels significantly. Anomalous strong scattering occurs in two density regimes, one at low densities and one at high densities, that also depend on the magnetic field. The two regimes are separated by a quiescent regime without anomalous scattering. Investigations suggest that scattering in the high-density regime is generated at the low-field side intersection of the gyrotron beam and the island position. The transition from the quiescent regime to the high-density regime occurs when the gyrotron frequency is twice the upper hybrid frequency at this position. There is some evidence that the scattering in the low-density regime is generated near the plasma centre. Under this assumption all the observed scattering is generated when the gyrotron frequency is near or below twice the upper hybrid frequency