Structure and Application of ATDP Suite for Electronic System States Detection and Evolution Operator Restoration

Structure and peculiarities of the Adaptive Testing Data Processing software Suite (ATDP Suite) are presented. It is applied for dynamic characteristics restoration from experimental time series of nonlinear and unstable electronic system. Basic methods realized in ATDP Suite are demonstrated. Application of ATDP Suite for electromagnetic tests of microwave receivers demonstrated the possibility to analyze and interpret the dynamic characteristics of complex nonlinear system.Представлены структура и особенности программного пакета адаптивной тестирующей обработки данных (ATDP Suite). Он применен к восстановлению динамических характеристик из экспериментальных временных рядов нелинейной и нестабильной электронной системы. Продемонстрированы основные методы, реализованные в ATDP Suite. Применение ATDP Suite для электромагнитного тестирования СВЧ приемников показало возможность анализировать и интерпретировать динамические характеристики сложной нелинейной системы.Представлено структуру та особливості програмного пакета адаптивної тестуючої обробки даних (ATDP Suite). Його застосовано для відтворення динамічних характеристик з експериментальних часових рядів нелінійної та нестабільної електронної системи. Продемонстровано основні методи, реалізовані в ATDP Suite. Застосування ATDP Suite для електромагнітного тестування НВЧ приймачів продемонструвало можливість аналізувати та інтерпретувати динамічні характеристики складної нелінійної системи

Solitons in high-energy QCD

We study the asymptotic solutions of the Schr\"odinger equation for the color-singlet reggeon compound states in multi-color QCD. We show that in the leading order of asymptotic expansion, quasiclassical reggeon trajectories have a form of the soliton waves propagating on the 2-dimensional plane of transverse coordinates. Applying methods of the finite-gap theory we construct their explicit form in terms of Riemann theta-functions and examine their properties.Comment: 26 pages, Latex style, 3 figures embedded with epsf.st

On Darboux-Treibich-Verdier potentials

It is shown that the four-parameter family of elliptic functions $$u_D(z)=m_0(m_0+1)\wp(z)+\sum_{i=1}^3 m_i(m_i+1)\wp(z-\omega_i)$$ introduced by Darboux and rediscovered a hundred years later by Treibich and Verdier, is the most general meromorphic family containing infinitely many finite-gap potentials.Comment: 8 page

Analytic and Reidemeister torsion for representations in finite type Hilbert modules

For a closed Riemannian manifold we extend the definition of analytic and Reidemeister torsion associated to an orthogonal representation of fundamental group on a Hilbert module of finite type over a finite von Neumann algebra. If the representation is of determinant class we prove, generalizing the Cheeger-M\"uller theorem, that the analytic and Reidemeister torsion are equal. In particular, this proves the conjecture that for closed Riemannian manifolds with positive Novikov-Shubin invariants, the L2 analytic and Reidemeister torsions are equal.Comment: 78 pages, AMSTe

High-frequency properties of the electron flow slowing down in a planar diode

The instability of the electron flow injected into a planar diode and slowed down in it under the action of the external electric field is investigated through the exact solution of the set of inhomogeneous hydrodynamic first-approximation equations of the stability theory. A dispersion equation has been derived, which relates the frequencies and increments (decrements) of arising electromagnetic oscillations to the parameters of the electron beam and the diode. The solution of the dispersion equation shows that in the diode, through which the slowing down electron beam is propagating, there arises the microwave oscillatory instability not described before. This instability occurs in the case when in the steady-state condition there is no potential minimum in the diode. The experiments have confirmed the occurrence of oscillatory instability with theoretically predicted frequencies and decrements in the corresponding beam and diode parameter regions.На основі точного рішення системи неоднорідних гідродинамічних рівнянь першого наближення теорії стійкості вивчена нестійкість електронного потоку, інжектованного у плоский діод і сповільненого в ньому під дією зовнішнього електричного поля. Отримано дисперсійне рівняння, що пов'язує частоти і інкременти (декременти) виникаючих електромагнітних коливань з параметрами електронного потоку і діода. Рішення дисперсійного рівняння показує, що в діоді, крізь який розповсюджується сповільнений електронний потік, виникає не описана раніше нестійкість коливань у СВЧ діапазоні. Ця нестійкість має місце, коли в стаціонарному стані мінімум потенціалу в діоді не утворюється. Експериментально підтверджено виникнення нестійкості коливань з передбаченими теоретично частотами і декрементами у відповідних областях параметрів пучка і діода.На основе точного решения системы неоднородных гидродинамических уравнений первого приближения теории устойчивости изучена неустойчивость электронного потока, который инжектирован в плоский диод и замедляется в нём под действием внешнего электрического поля. Получено дисперсионное уравнение, связывающее частоты и инкременты (декременты) возникающих электромагнитных колебаний с параметрами электронного потока и диода. Решение дисперсионного уравнения показывает, что в диоде, через который распространяется замедляющийся электронный поток, возникает не описанная ранее неустойчивость колебаний в СВЧ диапазоне. Эта неустойчивость имеет место, когда в стационарном состоянии минимум потенциала в диоде не образуется. Экспериментально подтверждено возникновение неустойчивости колебаний с предсказанными теоретически частотами и декрементами в соответствующих областях параметров пучка и диода

Combined effect of coherent Z exchange and the hyperfine interaction in atomic PNC

The nuclear spin-dependent parity nonconserving (PNC) interaction arising from a combination of the hyperfine interaction and the coherent, spin-independent, PNC interaction from Z exchange is evaluated using many-body perturbation theory. For the 6s-7s transition in 133Cs, we obtain a result that is about 40% smaller than that found previously by Bouchiat and Piketty [Phys. Lett. B 269, 195 (1991)]. Applying this result to 133Cs, leads to an increase in the experimental value of nuclear anapole moment and exacerbates differences between constraints on PNC meson coupling constants obtained from the Cs anapole moment and those obtained from other nuclear parity violating experiments. Nuclear spin-dependent PNC dipole matrix elements, including contributions from the combined weak-hyperfine interaction, are also given for the 7s-8s transition in 211Fr and for transitions between ground-state hyperfine levels in K, Rb, Cs, Ba+, Au, Tl, Fr, and Ra+.Comment: Revtex4 preprint 19 pages 4 table

Inelastic X-ray scattering study of the collective dynamics in liquid sodium

Inelastic X-ray scattering data have been collected for liquid sodium at T=390 K, i.e. slightly above the melting point. Owing to the very high instrumental resolution, pushed up to 1.5 meV, it has been possible to determine accurately the dynamic structure factor, $S(Q,\omega)$, in a wide wavevector range, $1.5 \div 15$ nm$^{-1}$, and to investigate on the dynamical processes underlying the collective dynamics. A detailed analysis of the lineshape of $S(Q,\omega)$, similarly to other liquid metals, reveals the co-existence of two different relaxation processes with slow and fast characteristic timescales respectively. The present data lead to the conclusion that: i) the picture of the relaxation mechanism based on a simple viscoelastic model fails; ii) although the comparison with other liquid metals reveals similar behavior, the data do not exhibit an exact scaling law as the principle of corresponding state would predict.Comment: RevTex, 7 pages, 6 eps figures. Accepted by Phys. Rev.

Quantum phase transitions from topology in momentum space

Many quantum condensed matter systems are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the low-energy corner does not depend on the complicated details of the system and is relatively simple. It is determined by the nodes in the fermionic spectrum, which are protected by topology in momentum space (in some cases, in combination with the vacuum symmetry). Close to the nodes the behavior of the system becomes universal; and the universality classes are determined by the toplogical invariants in momentum space. When one changes the parameters of the system, the transitions are expected to occur between the vacua with the same symmetry but which belong to different universality classes. Different types of quantum phase transitions governed by topology in momentum space are discussed in this Chapter. They involve Fermi surfaces, Fermi points, Fermi lines, and also the topological transitions between the fully gapped states. The consideration based on the momentum space topology of the Green's function is general and is applicable to the vacua of relativistic quantum fields. This is illustrated by the possible quantum phase transition governed by topology of nodes in the spectrum of elementary particles of Standard Model.Comment: 45 pages, 17 figures, 83 references, Chapter for the book "Quantum Simulations via Analogues: From Phase Transitions to Black Holes", to appear in Springer lecture notes in physics (LNP

Measuring Black Hole Spin using X-ray Reflection Spectroscopy

I review the current status of X-ray reflection (a.k.a. broad iron line) based black hole spin measurements. This is a powerful technique that allows us to measure robust black hole spins across the mass range, from the stellar-mass black holes in X-ray binaries to the supermassive black holes in active galactic nuclei. After describing the basic assumptions of this approach, I lay out the detailed methodology focusing on "best practices" that have been found necessary to obtain robust results. Reflecting my own biases, this review is slanted towards a discussion of supermassive black hole (SMBH) spin in active galactic nuclei (AGN). Pulling together all of the available XMM-Newton and Suzaku results from the literature that satisfy objective quality control criteria, it is clear that a large fraction of SMBHs are rapidly-spinning, although there are tentative hints of a more slowly spinning population at high (M>5*10^7Msun) and low (M<2*10^6Msun) mass. I also engage in a brief review of the spins of stellar-mass black holes in X-ray binaries. In general, reflection-based and continuum-fitting based spin measures are in agreement, although there remain two objects (GROJ1655-40 and 4U1543-475) for which that is not true. I end this review by discussing the exciting frontier of relativistic reverberation, particularly the discovery of broad iron line reverberation in XMM-Newton data for the Seyfert galaxies NGC4151, NGC7314 and MCG-5-23-16. As well as confirming the basic paradigm of relativistic disk reflection, this detection of reverberation demonstrates that future large-area X-ray observatories such as LOFT will make tremendous progress in studies of strong gravity using relativistic reverberation in AGN.Comment: 19 pages. To appear in proceedings of the ISSI-Bern workshop on "The Physics of Accretion onto Black Holes" (8-12 Oct 2012). Revised version adds a missing source to Table 1 and Fig.6 (IRAS13224-3809) and corrects the referencing of the discovery of soft lags in 1H0707-495 (which were in fact first reported in Fabian et al. 2009

BGWM as Second Constituent of Complex Matrix Model

Earlier we explained that partition functions of various matrix models can be constructed from that of the cubic Kontsevich model, which, therefore, becomes a basic elementary building block in "M-theory" of matrix models. However, the less topical complex matrix model appeared to be an exception: its decomposition involved not only the Kontsevich tau-function but also another constituent, which we now identify as the Brezin-Gross-Witten (BGW) partition function. The BGW tau-function can be represented either as a generating function of all unitary-matrix integrals or as a Kontsevich-Penner model with potential 1/X (instead of X^3 in the cubic Kontsevich model).Comment: 42 page