Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State

We show the exact solution of Bogoliubov equations at zero-energy in the critical supercurrent state for arbitrary shape of potential barrier. With use of this solution, we prove the absence of perfect transmission of excitations in the low-energy limit by giving the explicit expression of transmission coefficient. The origin of disappearance of perfect transmission is the emergence of zero-energy density fluctuation near the potential barrier.Comment: 6 pages, 3 figures; Proceedings of QFS200

Glauber dynamics in the continuum via generating functionals evolution

We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in time) solution which, under certain initial conditions, might be extended to a global one. An application of this approach to Vlasov-type scaling in terms of generating functionals is considered as well.Comment: 24 page

Complete description of polarization effects in e^+e^- pair production by a photon in the field of a strong laser wave

We consider production of a e^+e^- pair by a high-energy photon in the field of a strong laser wave. A probability of this process for circularly or linearly polarized laser photons and for arbitrary polarization of all other particles is calculated. We obtain the complete set of functions which describe such a probability in a compact invariant form. Besides, we discuss in some detail the polarization effects in the kinematics relevant to the problem of electron-photon conversion at photon-photon and electron-photon colliders.Comment: 14 pages, 8 figure

Fast k-NN classifier for documents based on a graph structure

In this paper, a fast k nearest neighbors (k-NN) classifier for documents is presented. Documents are usually represented in a high-dimensional feature space, where terms appeared on it are treated as features and the weight of each term reflects its importance in the document. There are many approaches to find the vicinity of an object, but their performance drastically decreases as the number of dimensions grows. This problem prevents its application for documents. The proposed method is based on a graph index structure with a fast search algorithm. It’s high selectivity permits to obtain a similar classification quality than exhaustive classifier, with a few number of computed distances. Our experimental results show that it is feasible the use of the proposed method in problems of very high dimensionality, such as Text Mining

Observations of temporal group delays in slow-light multiple coupled photonic crystal cavities

We demonstrate temporal group delays in coherently-coupled high-Q multi-cavity photonic crystals, in an all-optical analogue to electromagnetically induced transparency. We report deterministic control of the group delay up to 4× the single cavity lifetime in our CMOS-fabricated room-temperature chip. Supported by three-dimensional numerical simulations and theoretical analyses, our multi-pump beam approach enables control of the multi-cavity resonances and inter-cavity phase, in both single and double transparency peaks. The standing-wave wavelength-scale photon localization allows direct scalability for chip-scale optical pulse trapping and coupled-cavity QED

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate

We study tunneling properties of collective excitations in spin-1 Bose-Einstein condensates. In the absence of magnetic fields, the total transmission in the long wavelength limit occurs in all kinds of excitations but the quadrupolar spin mode in the ferromagnetic state. The quadrupolar spin mode alone shows the total reflection. A difference between those excitations comes from whether the wavefunction of an excitation corresponds to that of the condensate in the long wavelength limit. The correspondence results in the total transmission as in the spinless BEC.Comment: 6 pages, 5 figure

Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page

Landau and dynamical instabilities of Bose-Einstein condensates with superfluid flow in a Kronig-Penney potential

We study the elementary excitations of Bose-Einstein condensates in a one-dimensional periodic potential and discuss the stability of superfluid flow based on the Kronig-Penney model. We analytically solve the Bogoliubov equations and calculate the excitation spectrum. The Landau and dynamical instabilities occur in the first condensate band when the superfluid velocity exceeds certain critical values, which agrees with the result of condensates in a sinusoidal potential. It is found that the onset of the Landau instability coincides with the point where the perfect transmission of low-energy excitations is forbidden, while the dynamical instability occurs when the effective mass is negative. It is well known that the condensate band has a peculiar structure called swallowtail when the periodic potential is shallow compared to the mean field energy. We find that the upper side of the swallowtail is dynamically unstable although the excitations have the linear dispersion reflecting the positive effective mass.Comment: 6 pages, 2 figures, Proceedings of the International Symposium on Quantum Fluids and Solids (QFS2006

High-pressure behaviors of carbon nanotubes

In this paper, we have reviewed the experimental and theoretical studies on pressure-induced polygonization, ovalization, racetrack–shape deformation, and polymerization of carbon nanotubes (CNTs). The corresponding electronic, optical, and mechanical changes accompanying these behaviors have been discussed. The transformations of armchair (n, n) CNT bundles (n = 2, 3, 4, 6, and 8) under hydrostatic or nonhydrostatic pressure into new carbons, including recently proposed superhard bct-C₄, Cco-C₈, and B-B1AL2R2 carbon phases have also been demonstrated. Given the diversity of CNTs from various chiralities, diameters, and arrangements, pressure-induced CNT polymerization provides a promising approach to produce numerous novel metastable carbons exhibiting unique electronic, optical, and mechanical characteristics.Розглянуто експериментальні та теоретичні дослідження з індукованою тиском полігонізації, овалізації, деформації у формі бігової доріжки і полімеризації вуглецевих нанотрубок (ВНТ). Обговорено відповідні електронні, оптичні і механічні зміни, що супроводжують ці процеси. Також продемонстровано перетворення в ВНТ у формі крісла (n, n), зібраних в пучок (n = 2, 3, 4, 6 і 8) під гідростатичним або негідростатичним тиском в нові вуглецеві алотропи, в тому числі недавно запропоновані надтверді bct-C₄, Cco-C₈ і B-B1AL2R2-вуглецеві фази. Різноманітність ВНТ з різними хіральністю, діаметрами та упаковками, а також полімеризація ВНТ, викликана тиском, забезпечує перспективний підхід для отримання численних нових метастабільних вуглецевих фаз, що демонструють унікальні електронні, оптичні і механічні характеристики.Рассмотрены экспериментальные и теоретические исследования по индуцированной давлением полигонизации, овализации, деформации в форме беговой дорожки и полимеризации углеродных нанотрубок (УНТ). Обсуждены соответствующие электронные, оптические и механические изменения, сопровождающие эти процессы. Также продемонстрированы преобразования в УНТ в форме кресла (n, n), собранных в пучок (n = 2, 3, 4, 6 и 8) под гидростатическим или негидростатическим давлением в новые углеродные аллотропы, в том числе недавно предложенные сверхтвердые bct-C₄, Cco-C₈ и B-B1AL2R2-углеродные фазы. Разнообразие УНТ с различными хиральностью, диаметрами и упаковками, а также полимеризация УНТ, вызванная давлением, обеспечивает перспективный подход для получения многочисленных новых метастабильных углеродных фаз, демонстрирующих уникальные электронные, оптические и механические характеристики