abstract

General approach to decomposition of the tangent bundle of pseudo-Riemannian manifolds, and the associated decomposition of geometric objects are constructed on the basis of the invariantly defined split structure. We define the main geometric objects characterizing decomposition. Invariant non-holonomic generalizations of the Gauss–Codazzi–Ricci’s relations have been obtained. All the known types of decompositions (used in theory of frames of reference for the general relativity, in the Hamiltonian formulation for gravity, in the Cauchy problem, in the theory of stationary spaces, and so on) follow from the present work as special cases when fixing the basis and dimensions of subbundles, and parametrization of a basis of decomposition. Method of decomposition have been applied here for the relativistic configurations of a perfect fluid. Discussing an invariant form of the equations of motion we have found the invariant equilibrium conditions and their (3+1) decomposed form. The invariant formulation of the conservation law for the curl have been obtained.

abstract

We study barrier crossing of Brownian particles in a bistable symmetric potential and transport of Brownian particles in spatially periodic structures, driven by both kangaroo fluctuations and thermal equilibrium noise of zero mean values. We consider exponentially and algebraically correlated kangaroo fluctuations. Starting with the full Newton–Langevin equation for the Brownian particle and by introducing scaling as well as dimensionless variables, we show that the equation is very well approximated by overdamped dynamics in which inertial effects can be neglected. We analyze properties of selected macroscopic characteristics of the system such as the mean first passage time (MFPT) of particles from one minimum of the bistable potential to the other and mean stationary velocity of particles moving in a spatially periodic potential. In dependence upon statistics of kangaroo fluctuations and temperature of the system, macroscopic characteristics exhibit distinctive non-monotonic behavior. Accordingly, there exist optimal statistics of fluctuations optimizing macroscopic characteristics.

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We motivate and use the concept of free random variables for the study of the de-pinning transition of flux lines in superconductors as recently discussed by Hatano and Nelson in one dimension. Our analysis yields naturally to a generalization of the concept of Coherent Phase Appproximation (CPA) for nonhermitean Hamiltonians, and is exact for Cauchy randomness. We derive analytical conditions for the critical points of the complex eigenvalue distribution, in very good agreement with numerical calculations. We suggest a relation between dimensionally reduced nonhermitean quantum mechanics and weak nonhermiticity.

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We study evolution of colour gluons and prove the possibility of gluon squeezed states at the nonperturbative QCD jet stage. Angular and rapidity dependences of squeezed gluon second correlation function are studied. We demonstrate that the new gluon states can have both sub-poissonian and super-poissonian statistics corresponding to antibunching and bunching of gluons.

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The instanton-induced multiple events in high energy collisions are considered in nonperturbative quantum chromodynamics (QCD). Here we obtained unusual behaviour of ratio of correlation moments \(H_q\) for such processes which can be used for experimental search of instantons.

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The static vortex solution in Abelian Higgs model with small ratio of vector and Higgs particle masses is considered. Several formulae approximating this solution are discussed. The accuracy of these approximations is tested by numerical computations.

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The eigenvalue problem for a bound state solution of three quarks requires deep analysis to even start a numerical attempt. A power series solution to the three body Dirac equation solved in hypercentral approximation is sought. A scalar linear flux tube three body string potential is used to confine the quarks. In addition one gluon exchange potentials (OGEP) between quark pairs are considered to model the short range interactions. The angular momentum barrier is found to dominate the wave function behavior at the origin when including only the magnetic part of the OGEP. This occurs when the Coulomb part of the OGEP is neglected, or canceled by terms of opposite sign from the scalar potential. Recurrence relations for the power series coefficients are determined. When the Coulomb part of the OGEP is included, the initial ratios of the composite three quark wave function components are also determined. In this case, the Coulomb strength of the OGEP combines with the angular momenta to determine the wave function behavior near the origin.

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We discuss the current picture of the standard Higgs sector at strong coupling and the phenomenological implications for direct searches at the LHC.

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We discuss the possibility of measuring entropy of the system created in heavy ion collisions using the Ma coincidence method. The same method can also be used to test whether the system in question is in a state of equilibrium.

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An analytical fit to the experimental data on the mean square charge radius and to QCD-calculations of the neutron charge distribution is given and used to recognize the neutron charge distribution when calculating the charge density distribution in a finite nucleus. Relativistic Thomas–Fermi calculations of lead isotopes are performed and the effect of the neutron charge distribution on charge density distributions and rms charge radii of lead isotopes is discussed.

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We investigate the influence of the nuclear deformation on the decay rates of some cluster emission processes. The interaction between the daughter and the cluster is given by a double folding potential including quadrupole and hexadecupole deformed densities of both fragments. The nuclear part of the nucleus–nucleus interaction is density dependent and at small distances a repulsive core in the potential will occur. In the frame of the WKB-approximation the assault frequency of the cluster will depend on the geometric properties of the potential pocket whereas the penetrability will be sensitive to changes in the barrier location. The results obtained in this paper point out that various combinations of cluster and daughter deformations may account for the measured values of the decay rate. The decay rates are however more sensitive to the changes in the daughter deformation due to the large mass asymmetry of the process.

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Multiplicities of neutrons using \(4\pi \) detection system accompanying projectile-like fragments in \(^{40}\)Ar\(+^{159}\)Tb collision were measured. For the system studied the results suggest a broad range of reaction mechanisms. The experimental results were compared with predictions of the random walk model supplemented by a statistical evaporation.

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The hadronic particle production data from relativistic nuclear Pb–Pb 158 \(A\) GeV collisions are successfully described within the chemical non-equilibrium model, provided that the analysis treats \({\mit \Omega }\) and \(\overline {\mit \Omega }\) abundances with care. We further show that there is a subtle influence of the Coulomb potential on strange quarks in quark matter which is also seen in our data analysis, and this Coulomb effect confirms the finding made by chemical analysis in the S–Au/W/Pb 200 \(A\) GeV collisions that the hadron particle source is deconfined with respect to strange quark propagation. Physical freeze-out conditions (pressure, specific energy, entropy, and strangeness) are evaluated and considerable universality of hadron freeze-out between the two different collision systems is established.