Time evolution of a pair of distinguishable interacting spins subjected to controllable and noisy magnetic fields

The quantum dynamics of a $\hat{\mathbf{J}}^2=(\hat{\mathbf{j}}_1+\hat{\mathbf{j}}_2)^2$-conserving Hamiltonian model describing two coupled spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ under controllable and fluctuating time-dependent magnetic fields is investigated. Each eigenspace of $\hat{\mathbf{J}}^2$ is dynamically invariant and the Hamiltonian of the total system restricted to any one of such $(j_1+j_2)-|j_1-j_2|+1$ eigenspaces, possesses the SU(2) structure of the Hamiltonian of a single fictitious spin acted upon by the total magnetic field. We show that such a reducibility holds regardless of the time dependence of the externally applied field as well as of the statistical properties of the noise, here represented as a classical fluctuating magnetic field. The time evolution of the joint transition probabilities of the two spins $\hat{\mathbf{j}}_1$ and $\hat{\mathbf{j}}_2$ between two prefixed factorized states is examined, bringing to light peculiar dynamical properties of the system under scrutiny. When the noise-induced non-unitary dynamics of the two coupled spins is properly taken into account, analytical expressions for the joint Landau-Zener transition probabilities are reported. The possibility of extending the applicability of our results to other time-dependent spin models is pointed out.Comment: 11 pages, 5 figure

Quantum orientational melting of mesoscopic clusters

By path integral Monte Carlo simulations we study the phase diagram of two - dimensional mesoscopic clusters formed by electrons in a semiconductor quantum dot or by indirect magnetoexcitons in double quantum dots. At zero (or sufficiently small) temperature, as quantum fluctuations of particles increase, two types of quantum disordering phenomena take place: first, at small values of quantum de Boer parameter q < 0.01 one can observe a transition from a completely ordered state to that in which different shells of the cluster, being internally ordered, are orientationally disordered relative to each other. At much greater strengths of quantum fluctuations, at q=0.1, the transition to a disordered (superfluid for the boson system) state takes place.Comment: 4 pages, 6 Postscript figure

Model of the Belousov-Zhabotinsky reaction

The article describes results of the modified model of the Belousov-Zhabotinsky reaction, which resembles rather well the limit set observed upon experimental performance of the reaction in the Petri dish. We discuss the concept of the ignition of circular waves and show that only the asymmetrical ignition leads to the formation of spiral structures. From the qualitative assumptions on the behavior of dynamic systems, we conclude that the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure

Josephson array of mesoscopic objects. Modulation of system properties through the chemical potential

The phase diagram of a two-dimensional Josephson array of mesoscopic objects is examined. Quantum fluctuations in both the modulus and phase of the superconducting order parameter are taken into account within a lattice boson Hubbard model. Modulating the average occupation number $n_0$ of the sites in the system leads to changes in the state of the array, and the character of these changes depends significantly on the region of the phase diagram being examined. In the region where there are large quantum fluctuations in the phase of the superconducting order parameter, variation of the chemical potential causes oscillations with alternating superconducting (superfluid) and normal states of the array. On the other hand, in the region where the bosons interact weakly, the properties of the system depend monotonically on $n_0$. Lowering the temperature and increasing the particle interaction force lead to a reduction in the width of the region of variation in $n_0$ within which the system properties depend weakly on the average occupation number. The phase diagram of the array is obtained by mapping this quantum system onto a classical two-dimensional XY model with a renormalized Josephson coupling constant and is consistent with our quantum Path-Integral Monte Carlo calculations.Comment: 12 pages, 8 Postscript figure

High-precision measurements of krypton and xenon isotopes with a new static-mode quadrupole ion trap mass spectrometer

Measuring the abundance and isotopic composition of noble gases in planetary atmospheres can answer fundamental questions in cosmochemistry and comparative planetology. However, noble gases are rare elements, a feature making their measurement challenging even on Earth. Furthermore, in space applications, power consumption, volume and mass constraints on spacecraft instrument accommodations require the development of compact innovative instruments able to meet the engineering requirements of the mission while still meeting the science requirements. Here we demonstrate the ability of the quadrupole ion trap mass spectrometer (QITMS) developed at the Jet Propulsion Laboratory (Caltech, Pasadena) to measure low quantities of heavy noble gases (Kr, Xe) in static operating mode and in the absence of a buffer gas such as helium. The sensitivity reaches 10^(13) cps Torr^(−1) (about 10^(11) cps Pa^(−1)) of gas (Kr or Xe). The instrument is able to measure gas in static mode for extended periods of time (up to 48 h) enabling the acquisition of thousands of isotope ratios per measurement. Errors on isotope ratios follow predictions of the counting statistics and the instrument provides reproducible results over several days of measurements. For example, 1.7 × 10^(−10) Torr (2.3 × 10^(−8) Pa) of Kr measured continuously for 7 hours yielded a 0.6‰ precision on the ^(86)Kr/^(84)Kr ratio. Measurements of terrestrial and extraterrestrial samples reproduce values from the literature. A compact instrument based upon the QITMS design would have a sensitivity high enough to reach the precision on isotope ratios (e.g. better than 1% for ^(129,131–136)Xe/^(130)Xe ratios) necessary for a scientific payload measuring noble gases collected in the Venus atmosphere

Pharmacoeconomic analysis of naft idrofuryl in patients with chronic obliterating diseases of lower limb arteries

Chronic obliterating diseases of lower limb arteries is a large group of socially significant diseases, characterized by persistent chronic progress, high probability of disabling complications as well as the emergence needs for expensive surgical treatment. This disease characterized by the association with other diseases of the cardiovascular system, making the conservative therapy especially relevant. Aim. To perform the pharmacoeconomic analysis (PHe) of the naft idrofuryl in the Russian Federation (RF) in patients aged 66 years and older with peripheral vascular disease, including atherosclerosis of the lower limbs arteries and the clinical picture, corresponding to Stage II of Fontaine. Methodology. Th is PHe is conducted perspective of public health organizations of the RF and considers only direct medical costs. Horizon of PHe adopted for 240 weeks (4.6 years). The source of data on the clinical eff ectiveness was taken from randomized controlled trials and meta-analyzes, which examined the efficacy, safety and tolerability comparable drugs. For criteria of clinical efficacy has been chosen the mean log expression of the maximum distance walk. As a criterion of utility were calculated the quality adjusted life years (QALY). In developed Markov model, the time horizon was broken down into a cycle of length for 1 week. On the basis of existing government standard of care was the assessment of costs in health care system for diagnosis and treatment in simulated groups, taking into consideration the cost of angioplasty. It was conducted cost-eff ectiveness (CEA), cost-utility (CUA), budget impact (BIA) and sensitivity analysis (SA), calculated cost-eff ectiveness threshold. Result. CER per patient at naft idrofuryl was 2,061 rubl., at pentoxifylline — 4,764 rubl. Since naft idrofuryl is not only superior to pentoxifylline in clinical effectiveness, but also was associated with a lower cost, the calculation of the ICER not needed. PHe show that CER per patient did not exceed the «willingness-to-pay ratio» none of the drugs, thus both of the drugs is relevant to reimbursement system. CUA demonstrated superiority naft idrofuryl both in terms of the net impact on the QALY, and in terms of utility costs (CUR), CUR of naft idrofuryl per patient totaled 144,992 rubl., pentoxifylline — 213,854 rubl. SA confi rmed the stability of these results. Analysis of BIA shows that the fi scal burden associated with naft idrofuryl, is lower by 183,9 million rubl. per year for every 3,000 treated patients on pentoxifylline, which can allow one to treat 1,321 patients more via a naft idrofuryl based therapeutic strategy. Conclusion. Excellence naft idrofuryl over pentoxifylline confi rmed in this pharmacoeconomic study. Naft idrofuryl dominates in terms of CER, CUR and reduce budget impact

Об одном достаточном условии нерегулярности языков

The article deals with a proof of one sufficient condition for the irregularity of languages. This condition is related to the properties of certain relations on the set of natural numbers, namely relations possessing the property, referred to as strong separability. In turn, this property is related to the possibility of decomposition of an arithmetic vector space into a direct sum of subspaces. We specify languages in some finite alphabet through the properties of a vector that shows the number of occurrences of each letter of the alphabet in the language words and is called the word distribution vector in the word. The main result of the paper is the proof of the theorem according to which a language given in such a way that the vector of distribution of letters in each word of the language belongs to a strongly separable relation on the set of natural numbers is not regular. Such an approach to the proof of irregularity is based on the Myhill-Nerode theorem known in the theory of formal languages, according to which the necessary and sufficient condition for the regularity of a language consists in the finiteness of the index of some equivalence relation defined by the language.The article gives a definition of a strongly separable relation on the set of natural numbers and examines examples of such relations. Also describes a construction covering a considerably wide class of strongly separable relations and connected with decomposition of the even-dimensional vector space into a direct sum of subspaces of the same dimension. Gives the proof of the lemma to assert an availability of an infinite sequence of vectors, any two terms of which are pairwise disjoint, i.e. one belongs to some strongly separable relation, and the other does not. Based on this lemma, there is a proof of the main theorem on the irregularity of a language defined by a strongly separable relation.This result sheds additional light on the effectiveness of regularity / irregularity analysis tools based on the Myhill-Neroud theorem. In addition, the proved theorem and analysis of some examples of strongly separable relations allows us to establish non-trivial connections between the theory of formal languages and the theory of linear spaces, which, as analysis of sources shows, is relevant.In terms of development of the obtained results, the problem of the general characteristic of strongly separable relations is of interest, as well as the analysis of other properties of numerical sets that are important from the point of view of regularity / irregularity analysis of languages.Данная статья посвящена доказательству одного достаточного условия нерегулярности языков. Это условие связано со свойствами некоторых отношений на множестве натуральных чисел, а именно отношений, обладающих свойством, названное сильной отделимостью. В свою очередь, это свойство связано с возможностью разложения арифметического векторного пространства в прямую сумму подпространств. Мы задаем языки в некотором конечном алфавите через свойства вектора, показывающего числа вхождений каждой буквы алфавита в слова языка и называемого вектором распределения букв в слове. Основной результат статьи состоит в доказательстве теоремы, согласно которой язык, задаваемый таким образом, что вектор распределения букв в каждом слове языка принадлежит сильно отделимому отношению на множестве натуральных чисел, нерегулярен. Такой подход к доказательству нерегулярности основан на известной в теории формальных языков теореме Майхилла-Нероуда, согласно которой необходимое и достаточное условие регулярности языка состоит в конечности индекса некоторого отношения эквивалентности, определяемого языком.В статье дается определение сильно отделимого отношения на множестве натуральных чисел и рассматриваются примеры таких отношений. Дается также описание конструкции, покрывающей весьма широкий класс сильно отделимых отношений и связанной с разложением векторного пространства четной размерности в прямую сумму подпространств одинаковой размерности. Доказывается лемма, утверждающая существование бесконечной последовательности векторов, любые два члена которой попарно дизъюнктны, т.е. один принадлежит некоторому сильно отделимому отношению, а другой нет. На основании этой леммы доказывается основная теорема о нерегулярности языка, определяемым сильно отделимым отношением.Этот результат проливает дополнительный свет на эффективность инструментов анализа регулярности/нерегулярности языков, базирующихся на теореме Майхилла-Нероуда. Кроме того, доказанная теорема и анализ некоторых примеров сильно отделимых отношений позволяет установить нетривиальные связи между теорией формальных языков и теорией линейных пространств, что, как показывает анализ источников, является актуальной проблематикой.В плане развития полученных результатов интерес представляет задача общей характеристики сильно отделимых отношений, а также анализ других свойств числовых множеств, важных с точки зрения анализа регулярности/нерегулярности языков

Quantum effects on the BKT phase transition of two-dimensional Josephson arrays

The phase diagram of two dimensional Josephson arrays is studied by means of the mapping to the quantum XY model. The quantum effects onto the thermodynamics of the system can be evaluated with quantitative accuracy by a semiclassical method, the {\em pure-quantum self-consistent harmonic approximation}, and those of dissipation can be included in the same framework by the Caldeira-Leggett model. Within this scheme, the critical temperature of the superconductor-to-insulator transition, which is a Berezinskii-Kosterlitz-Thouless one, can be calculated in an extremely easy way as a function of the quantum coupling and of the dissipation mechanism. Previous quantum Monte Carlo results for the same model appear to be rather inaccurate, while the comparison with experimental data leads to conclude that the commonly assumed model is not suitable to describe in detail the real system.Comment: 4 pages, 2 figures, to be published in Phys. Rev.