Hamiltonian formalism for Fermi excitations in a plasma with a non-Abelian interaction

The Hamiltonian theory for the collective longitudinally polarized colorless gluon excitations (plasmons) and for collective quark-antiquark excitations with abnormal relation between chirality and helicity (plasminos) in a high-temperature quark-gluon plasma (QGP) is developed. For this purpose, Zakharov's formalism for constructing the wave theory in nonlinear media with dispersion is used. A generalization of the Poisson superbracket involving both commuting and anticommuting variables to the case of a continuous medium is performed and the corresponding Hamilton equations are presented. The canonical transformations including simultaneously both bosonic and fermionic degrees of freedom of the collective excitations in QGP are discussed and a complete system of the canonicity conditions for these transformations is written out. An explicit form of the effective fourth-order Hamiltonians describing the elastic scattering of plasmino off plasmino and plasmino off plasmon is found and the Boltzmann type kinetic equations describing the processes of elastic scattering are obtained. A detailed comparison of the effective amplitudes defined within the (pseudo)classical Hamiltonian theory, with the corresponding matrix elements calculated early in the framework of high-temperature quantum chromodynamics in the so-called hard thermal loop approximation is performed. This enables one to obtain, in particular, an explicit form of the vertex and coefficient functions in the effective amplitudes and in the canonical transformations, correspondingly, and also to define the validity of a purely pseudoclassical approach in the Hamiltonian description of the dynamics of a quark-gluon plasma. The problem of determining the higher-order coefficient functions in the canonical transformations of fermionic and bosonic normal variables is considered.Comment: 69 pages, 2 figures, typos corrected and references adde

Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction I: plasmon -- hard particle scattering

The Hamiltonian theory for the collective longitudinally polarized gluon excitations (plasmons) coupling with classical high-energy test color-charged particle propagating through a high-temperature gluon plasma is developed. A generalization of the Lie-Poisson bracket to the case of a continuous medium involving bosonic normal field variable $a^{\phantom{\ast}\!\!a}_{\hspace{0.03cm}{\bf k}}$ and a non-Abelian color charge $Q^{\hspace{0.03cm}a}$ is performed and the corresponding Hamilton equations are presented. The canonical transformations including simultaneously both bosonic degrees of freedom of the soft collective excitations and degree of freedom of hard test particle connecting with its color charge in the hot gluon plasma are written out. A complete system of the canonicity conditions for these transformations is derived. The notion of the plasmon number density ${\mathcal N}^{a\hspace{0.03cm}a^{\prime}_{\phantom{1}}\!}_{{\bf k}}$, which is a nontrivial matrix in the color space, is introduced. An explicit form of the effective fourth-order Hamiltonian describing elastic scattering of plasmon off a hard color particle is found and the self-consistent system of Boltzmann type kinetic equations taking into account the time evolution of the mean value of the color charge of the hard particle is obtained. On the basis of these equations, a model problem of interaction of two infinitly narrow wave packets is considered. A system of nonlinear first-order ordinary differential equations defining the dynamics of the interaction of the colorless $N^{l}_{\bf k}$ and color $W^{l}_{\bf k}$ components of the plasmon number density is derived. The problem of determining the third- and fourth-order coefficient functions entering into the canonical transformations of the original bosonic variable $a^{\phantom{\ast}\!\!a}_{{\bf k}}$ and color charge $Q^{\hspace{0.03cm}a}$ is discussed.Comment: 57 pages, 5 figure

Ryanodine Receptors Coupling Causes a Calcium Leak in Cardiac Cell

Here we introduce results of a mathematical modeling of calcium sparks in cardiac cells. We developed a model of the calcium release unit which includes a single sarcoplasmic reticulum (SR) lumen, a regular 9×9 cluster of RyRs and a dyadic space. 2D diffusion problem of Ca2+ ions across the dyadic space was solved thereby we reproduced Calcium-fnduced-Calcium-Release (CICR) effect and domino-like RyRs activation in the cluster. We take into account allosteric and Ca2+-induced coupling between RyRs. We show, that coupling between RyRs leads to the stability of Ca2+ sparks in amplitude and frequency. However, a sudden stop of spontaneous Ca2+ releases can be a result of strong allosteric coupling between RyRs. © 2018 Creative Commons Attribution.Russian Foundation for Basic Research, RFBR: 16-34-60223The project is supported by RFBR grant 16-34-60223. The work was carried out within the framework of the IIF UrB RAS theme No AAAA-A18-118020590031-8 and RF Government Act 211 of March 16, 2013 (agreement 02.A03.21.0006)

Spectroscopic and physical parameters of Galactic O-type stars. II. Observational constraints on projected rotational and extra broadening velocities as a function of fundamental parameters and stellar evolution

Rotation is of key importance for the evolution of hot massive stars, however, the rotational velocities of these stars are difficult to determine. Based on our own data for 31 Galactic O stars and incorporating similar data for 86 OB supergiants from the literature, we aim at investigating the properties of rotational and extra line-broadening as a function of stellar parameters and at testing model predictions about the evolution of stellar rotation. Fundamental stellar parameters were determined by means of the code FASTWIND. Projected rotational and extra broadening velocities originate from a combined Ft + GOF method. Model calculations published previously were used to estimate the initial evolutionary masses. The sample O stars with Minit > 50 Msun rotate with less that 26% of their break-up velocity, and they also lack objects with v sin i 35 Msun on the hotter side of the bi-stability jump, the observed and predicted rotational rates agree quite well; for those on the cooler side of the jump, the measured velocities are systematically higher than the predicted ones. In general, the derived extra broadening velocities decrease toward cooler Teff, whilst for later evolutionary phases they appear, at the same v sin i, higher for high-mass stars than for low-mass ones. None of the sample stars shows extra broadening velocities higher than 110 km/s. For the majority of the more massive stars, extra broadening either dominates or is in strong competition with rotation. Conclusions: For OB stars of solar metallicity, extra broadening is important and has to be accounted for in the analysis. When appearing at or close to the zero-age main sequence, most of the single and more massive stars rotate slower than previously thought. Model predictions for the evolution of rotation in hot massive stars may need to be updated.Comment: 15 pages, 10 figures, accepted for publication in A &

Second-layer nucleation in coherent Stranski-Krastanov growth of quantum dots

We have studied the monolayer-bilayer transformation in the case of the coherent Stranski-Krastanov growth. We have found that the energy of formation of a second layer nucleus is largest at the center of the first-layer island and smallest on its corners. Thus nucleation is expected to take place at the corners (or the edges) rather than at the center of the islands as in the case of homoepitaxy. The critical nuclei have one atom in addition to a compact shape, which is either a square of i*i or a rectangle of i*(i-1) atoms, with i>1 an integer. When the edge of the initial monolayer island is much larger than the critical nucleus size, the latter is always a rectangle plus an additional atom, adsorbed at the longer edge, which gives rise to a new atomic row in order to transform the rectangle into the equilibrium square shape.Comment: 6 pages, 4 figures. Accepted version, minor change

Hamiltonian formalism for Bose excitations in a plasma with a non-Abelian interaction

We have developed the Hamiltonian theory for collective longitudinally polarized colorless excitations (plasmons) in a high-temperature gluon plasma using the general formalism for constructing the wave theory in nonlinear media with dispersion, which was developed by V.E. Zakharov. In this approach, we have explicitly obtained a special canonical transformation that makes it possible to simplify the Hamiltonian of interaction of soft gluon excitations and, hence, to derive a new effective Hamiltonian. The approach developed here is used for constructing a Boltzmann-type kinetic equation describing elastic scattering of collective longitudinally polarized excitations in a gluon plasma as well as the effect of the so-called nonlinear Landau damping. We have performed detailed comparison of the effective amplitude of the plasmon-plasmon interaction, which is determined using the classical Hamilton theory, with the corresponding matrix element calculated in the framework of high-temperature quantum chromodynamics; this has enabled us to determine applicability limits for the purely classical approach described in this study.Comment: 21 pages, 2 figure

Dynamical Quantum Phase Transition Without An Order Parameter

Short-time dynamics of many-body systems may exhibit non-analytical behavior of the systems' properties at particular times, thus dubbed dynamical quantum phase transition. Simulations showed that in the presence of disorder new critical times appear in the quench evolution of the Ising model. We study the physics behind these new critical times. We discuss the spectral features of the Ising model responsible for the disorder-induced phase transitions. We found the critical value of the disorder sufficient to induce the dynamical phase transition as a function of the number of spins. Most importantly, we argue that this dynamical phase transition while non-topological lacks a local order parameter.Comment: 15 pages, 6 figure