Adventures of the Coupled Yang-Mills Oscillators: II. YM-Higgs Quantum Mechanics

We continue our study of the quantum mechanical motion in the $x^2y^2$ potentials for $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. In the present paper, we develop a new approach to the calculation of the partition function $Z(t)$ beyond the Thomas-Fermi (TF) approximation by adding a harmonic (Higgs) potential and taking the limit $v\to 0$, where $v$ is the vacuum expectation value of the Higgs field. Using the Wigner-Kirkwood method to calculate higher-order corrections in $\hbar$, we show that the limit $v\to 0$ leads to power-like singularities of the type $v^{-n}$, which reflect the possibility of escape of the particle along the channels in the classical limit. We show how these singularities can be eliminated by taking into account the quantum fluctuations dictated by the form of the potential

Adventures of the Coupled Yang-Mills Oscillators: I. Semiclassical Expansion

We study the quantum mechanical motion in the $x^2y^2$ potentials with $n=2,3$, which arise in the spatially homogeneous limit of the Yang-Mills (YM) equations. These systems show strong stochasticity in the classical limit ($\hbar = 0$) and exhibit a quantum mechanical confinement feature. We calculate the partition function $Z(t)$ going beyond the Thomas-Fermi (TF) approximation by means of the semiclassical expansion using the Wigner-Kirkwood (WK) method. We derive a novel compact form of the differential equation for the WK function. After separating the motion in the channels of the equipotential surface from the motion in the central region, we show that the leading higher-order corrections to the TF term vanish up to eighth order in $\hbar$, if we treat the quantum motion in the hyperbolic channels correctly by adiabatic separation of the degrees of freedom. Finally, we obtain an asymptotic expansion of the partition function in terms of the parameter $g^2\hbar^4t^3$

Regular and chaotic interactions of two BPS dyons at low energy

We identify and analyze quasiperiodic and chaotic motion patterns in the time evolution of a classical, non-Abelian Bogomol'nyi-Prasad-Sommerfield (BPS) dyon pair at low energies. This system is amenable to the geodesic approximation which restricts the underlying SU(2) Yang-Mills-Higgs dynamics to an eight-dimensional phase space. We numerically calculate a representative set of long-time solutions to the corresponding Hamilton equations and analyze quasiperiodic and chaotic phase space regions by means of Poincare surfaces of section, high-resolution power spectra and Lyapunov exponents. Our results provide clear evidence for both quasiperiodic and chaotic behavior and characterize it quantitatively. Indications for intermittency are also discussed.Comment: 22 pages, 6 figures (v2 contains a few additional references, a new paragraph on intermittency and minor stylistic corrections to agree with the published version

The Partition Function and Level Density for Yang-Mills-Higgs Quantum Mechanics

We calculate the partition function $Z(t)$ and the asymptotic integrated level density $N(E)$ for Yang-Mills-Higgs Quantum Mechanics for two and three dimensions ($n = 2, 3$). Due to the infinite volume of the phase space $\Gamma$ on energy shell for $n= 2$, it is not possible to disentangle completely the coupled oscillators ($x^2 y^2$-model) from the Higgs sector. The situation is different for $n = 3$ for which $\Gamma$ is finite. The transition from order to chaos in these systems is expressed by the corresponding transitions in $Z(t)$ and $N(E)$, analogous to the transitions in adjacent level spacing distribution from Poisson distribution to Wigner-Dyson distribution. We also discuss a related system with quartic coupled oscillators and two dimensional quartic free oscillators for which, contrary to YMHQM, both coupling constants are dimensionless.Comment: 10 pages, LaTeX; minor changes; version accepted for publication as a Letter in J. Phys.

Azimuthal asymmetry in transverse energy flow in nuclear collisions at high energies

The azimuthal pattern of transverse energy flow in nuclear collisions at RHIC and LHC energies is considered. We show that the probability distribution of the event-by-event azimuthal disbalance in transverse energy flow is essentially sensitive to the presence of the semihard minijet component.Comment: 6 pages, 2 figure

Symmetry Decomposition of Potentials with Channels

We discuss the symmetry decomposition of the average density of states for the two dimensional potential $V=x^2y^2$ and its three dimensional generalisation $V=x^2y^2+y^2z^2+z^2x^2$. In both problems, the energetically accessible phase space is non-compact due to the existence of infinite channels along the axes. It is known that in two dimensions the phase space volume is infinite in these channels thus yielding non-standard forms for the average density of states. Here we show that the channels also result in the symmetry decomposition having a much stronger effect than in potentials without channels, leading to terms which are essentially leading order. We verify these results numerically and also observe a peculiar numerical effect which we associate with the channels. In three dimensions, the volume of phase space is finite and the symmetry decomposition follows more closely that for generic potentials --- however there are still non-generic effects related to some of the group elements

Threshold J/ψ−J/\psi- production in nucleon-nucleon collisions

We analyze $J/\psi-$ production in nucleon-nucleon collisions near threshold in the framework of a general model independent formalism, which can be applied to any reaction $N+N\to N+N+V^0$, where $V^0=\omega$, $\phi$, or $J/\psi$. Such reactions show large isotopic effects: a large difference for $pp$- and $pn$-collisions, which is due to the different spin structure of the corresponding matrix elements. The analysis of the spin structure and of the polarization observables is based on symmetry properties of the strong interaction. Using existing experimental data on the different decays of $J/\psi-$meson, we suggest a model for $N+N\to N+N+J/\psi$, based on $t-$channel $\eta+\pi$-exchanges. We predict polarization phenomena for the $n+p\to n+p+J/\psi$-reaction and the ratio of cross sections for $np$ and $pp$-collisions. For the processes $\eta(\pi)+N\to N+J/\psi$ we apply two different approaches: vector meson exchange and local four-particle interaction. In both cases we find larger $J/\psi$-production in $np$-collisions, with respect to $pp$-collisions.Comment: 17 pages, 6 figure

Злокачественная гипертермия (обзор литературы)

   The objective – to summarize the current literature data on the etiology, pathogenesis, diagnosis and treatment of malignant hyperthermia.   The search and analysis of literature data on malignant hyperthermia in the medical information systems PubMed, Сochrane librarу, Cyberleninka for the last 10 years was performed with using the keywords: «malignant hyperthermia», «dantrolene», «general anesthesia», «succinylcholine», «inhalation anesthetics». The search criteria were met by 96 publications. In addition, references to selected articles were manually checked for applicable articles including recent reports of malignant hyperthermia, in addition to works of historical significance. It was shown that malignant hyperthermia develops in susceptible individuals during or after general anesthesia with the use of trigger agents – inhaled halogen-containing anesthetics and succinylcholine. Until recently, the problem of treatment in Russia remained unresolved, since specific therapy for this syndrome was not available. In connection with the official registration of Dantrolene in the Russian Federation, this problem no longer has a life-threatening potential. Doctors should recognize the symptoms of this disease as early as possible in order to quickly begin the pathogenetic treatment of malignant hyperthermia in order to prevent fatal complications. The material is intended for a wide audience of anesthesiologists, resuscitators and surgeons who may encounter this pathology in clinical practice.   Цель – обобщить текущие литературные данные по этиологии, патогенезу, диагностике и лечению злокачественной гипертермии.   Выполнен поиск и анализ литературных данных по злокачественной гипертермии в медицинских информационных системах PubMed, Сochrane librarу, Cyberleninka за последние 10 лет с использованием ключевых слов: «злокачественная гипертермия», «дантролен», «общая анестезия», «сукцинилхолин», «ингаляционные анестетики». Критериям поиска удовлетворяли 96 публикаций. В дополнение к этому ссылки на выбранные статьи были вручную проверены на наличие применимых статей, включающих последние сообщения о злокачественной гипертермии, помимо работ, имеющих историческое значение. Показано, что злокачественная гипертермия развивается у восприимчивых к ней лиц во время или после проведения общей анестезии с применением триггерных агентов – ингаляционных галогенсодержащих анестетиков и сукцинилхолина. До недавнего времени проблема лечения в России оставалась нерешенной, поскольку специфическая терапия данного синдрома была недоступна. В связи с официальной регистрацией препарата «Дантролен» в Российской Федерации данная проблема более не носит жизнеугрожающий потенциал. Врачу следует как можно раньше распознать симптомы данного заболевания, чтобы быстрее начать патогенетическое лечение злокачественной гипертермии с целью предотвращения фатальных осложнений. Материал предназначен для широкой аудитории врачей анестезиологов-реаниматологов, хирургов, которые могут встретиться с данной патологией в клинической практике

The initial gluon multiplicity in heavy ion collisions

The initial gluon multiplicity per unit area per unit rapidity, dN/L^2/d\eta, in high energy nuclear collisions, is equal to f_N (g^2\mu L) (g^2\mu)^2/g^2, with \mu^2 proportional to the gluon density per unit area of the colliding nuclei. For an SU(2) gauge theory, we compute f_N (g^2\mu L)=0.14\pm 0.01 for a wide range in g^2\mu L. Extrapolating to SU(3), we predict dN/L^2/d\eta for values of g^2\mu L in the range relevant to the Relativistic Heavy Ion Collider and the Large Hadron Collider. We compute the initial gluon transverse momentum distribution, dN/L^2/d^2 k_\perp, and show it to be well behaved at low k_\perp.Comment: LaTex 10 pgs., 3 figure