Heat Kernel Expansion for Operators of the Type of the Square Root of the Laplace Operator

A method is suggested for the calculation of the DeWitt-Seeley-Gilkey (DWSG) coefficients for the operator $\sqrt{-\nabla^2 + V(x)}$ basing on a generalization of the pseudodifferential operator technique. The lowest DWSG coefficients for the operator $\sqrt{-\nabla^2} + V(x)$ are calculated by using the method proposed. It is shown that the method admits a generalization to the case of operators of the type $(-\nabla^2 + V(X))^{1/{\rm m}}$, where m is an arbitrary rational number. A more simple method is proposed for the calculation of the DWSG coefficients for the case of strictly positive operators under the sign of root. By using this method, it is shown that the problem of the calculation of the DWSG coefficients for such operators is exactly solvable. Namely, an explicit formula expressing the DWSG coefficients for operators with root through the DWSG coefficients for operators without root is deduced.Comment: 17 pages, LaTeX, no figure

Dynamics and phase diagram of the ν=0\nu=0 quantum Hall state in bilayer graphene

Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $\nu=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tilde{\Delta}_0,B)$, where $\tilde{\Delta}_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $\Delta E\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.Comment: 14 pages, 4 figure

Surprises in relativistic matter in a magnetic field

A short review of recent advances in understanding the dynamics of relativistic matter in a magnetic field is presented. The emphasis is on the dynamics related to the generation of the chiral shift parameter in the normal ground state. We argue that the chiral shift parameter contributes to the axial current density, but does not modify the conventional axial anomaly relation. The analysis based on gauge invariant regularization schemes in the Nambu-Jona-Lasinio model suggests that these findings should be valid also in gauge theories. It is pointed out that the chiral shift parameter can affect observable properties of compact stars and modify the key features of the chiral magnetic effect in heavy ion collisions.Comment: 7 pages, 1 figure. V2: references added. Talk presented at Int. School of Nuclear Physics "From Quarks and Gluons to Hadrons and Nuclei", Erice-Sicily, 16 - 24 September, 201

Dynamical stabilization of runaway potentials at finite density

We study four dimensional non-abelian gauge theories with classical moduli. Introducing a chemical potential for a flavor charge causes moduli to become unstable and start condensing. We show that the moduli condensation in the presence of a chemical potential generates nonabelian field strength condensates. These condensates are homogeneous but non-isotropic. The end point of the condensation process is a stable homogeneous, but non-isotropic, vacuum in which both gauge and flavor symmetries and the rotational invariance are spontaneously broken. Possible applications of this phenomenon for the gauge theory/string theory correspondence and in cosmology are briefly discussed.Comment: revtex4, 4 pages; v.2: journal versio

Crossover from BCS to Composite Boson (Local Pair) Superconductivity in Quasi-2D systems

The crossover from cooperative Cooper pairing to independent bound state (composite bosons) formation and condensation in quasi-2D systems is studied. It is shown that at low carrier density the critical superconducting temperature is equal to the temperature of Bose-condensation of ideal quasi-2D Bose-gas with heavy dynamical mass, meanwhile at high densities the BCS result remains valid. The evident nonmonotoneous behaviour of the critical temperature as function of the coupling constant (the energy of the two particle bound state) is a qualitative difference of quasi-2D crossover from 3D one.Comment: 9 pages, LaTeX, no figures. (The latest version which appeared in the journal