The partition function versus boundary conditions and confinement in the Yang-Mills theory

We analyse dependence of the partition function on the boundary condition for the longitudinal component of the electric field strength in gauge field theories. In a physical gauge the Gauss law constraint may be resolved explicitly expressing this component via an integral of the physical transversal variables. In particular, we study quantum electrodynamics with an external charge and SU(2) gluodynamics. We find that only a charge distribution slowly decreasing at spatial infinity can produce a nontrivial dependence in the Abelian theory. However, in gluodynamics for temperatures below some critical value the partition function acquires a delta-function like dependence on the boundary condition, which leads to colour confinement.Comment: 14 pages, RevTeX, submitted to Phys. Rev.

Casimir force induced by imperfect Bose gas

We present a study of the Casimir effect in an imperfect (mean-field) Bose gas contained between two infinite parallel plane walls. The derivation of the Casimir force follows from the calculation of the excess grand canonical free energy density under periodic, Dirichlet, and Neumann boundary conditions with the use of the steepest descent method. In the one-phase region the force decays exponentially fast when distance $D$ between the walls tends to infinity. When Bose-Einstein condensation point is approached the decay length in the exponential law diverges with critical exponent $\nu_{IMP}=1$, which differs from the perfect gas case where $\nu_{P}=1/2$. In the two-phase region the Casimir force is long-range, and decays following the power law $D^{-3}$, with the same amplitude as in the perfect gas

The influence of an external magnetic field on the dynamic stress of an elastic conducting one-sided layer with a longitudinal shear crack

We study the interaction of a magnetoelastic shear wave with a curvilinear tunnel crack in an ideally conducting diamagnetic (resp. paramagnetic) one-sided (resp. two-sided) layer in the presence of an external static magnetic field. The bases of the one-sided layer are free of mechanical load, and the rim of the face is clamped or free. The corresponding linearized boundary-value problem of magnetoelasticity is reduced to a singular integrodifferential equation with subsequent implementation on a computer. We give numerical results that characterize the influence of the size of the preliminary magnetic field, the frequencies of the load, the curvature, and the orientation of the crack on the stress intensity factor. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2163

Comparative study of semiclassical approaches to quantum dynamics

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.Comment: 32 pages, 8 figures, corrected typos and added references; version as publishe

Dijet Event Shapes as Diagnostic Tools

Event shapes have long been used to extract information about hadronic final states and the properties of QCD, such as particle spin and the running coupling. Recently, a family of event shapes, the angularities, has been introduced that depends on a continuous parameter. This additional parameter-dependence further extends the versatility of event shapes. It provides a handle on nonperturbative power corrections, on non-global logarithms, and on the flow of color in the final state.Comment: 18 pages, 3 figure

The interaction of a magnetoelastic shear wave with longitudinal cavities in a conducting layer

We study the influence of a strong magnetic field on the interaction of a shear wave with longitudinal cylindrical cavities in an elastic ideally conducting layer. The resulting singular integral equation of the boundary-value problem under consideration is implemented numerically for the case of a single cavity. We present the results of computation of the stresses on the edge of a circular cavity and an elliptical cavity. When you are citing the document, use the following link http://essuir.sumdu.edu.ua/handle/123456789/2163

Investigation of the Chaotic Dynamics of an Electron Beam with a Virtual Cathode in an External Magnetic Field

The effect of the strength of the focusing magnetic field on chaotic dynamic processes occurring inan electron beam with a virtual cathode, as well as on the processes whereby the structures form in the beamand interact with each other, is studied by means of two-dimensional numerical simulations based on solving a self-consistent set of Vlasov-Maxwell equations. It is shown that, as the focusing magnetic field is decreased,the dynamics of an electron beam with a virtual cathode becomes more complicated due to the formation andinteraction of spatio-temporal longitudinal and transverse structures in the interaction region of a vircator. The optimum efficiency of the interaction of an electron beam with the electromagnetic field of the vircator isachieved at a comparatively weak external magnetic field and is determined by the fundamentally two-dimensional nature of the motion of the beam electrons near the virtual cathode.Comment: 12 pages, 8 figure

AdS_7/CFT_6, Gauss-Bonnet Gravity, and Viscosity Bound

We study the relation between the causality and the positivity of energy bounds in Gauss-Bonnet gravity in AdS_7 background and find a precise agreement. Requiring the group velocity of metastable states to be bounded by the speed of light places a bound on the value of Gauss-Bonnet coupling. To find the positivity of energy constraints we compute the parameters which determine the angular distribution of the energy flux in terms of three independent coefficients specifying the three-point function of the stress-energy tensor. We then relate the latter to the Weyl anomaly of the six-dimensional CFT and compute the anomaly holographically. The resulting upper bound on the Gauss-Bonnet coupling coincides with that from causality and results in a new bound on viscosity/entropy ratio.Comment: 21 page, harvmac; v2: reference adde