Heat Kernel and Loop Currents by the Generating Function Method

The generating function method is applied to the trace of the heat kernel and the one-loop effective action derived from the covariant perturbation theory. The basis of curvature invariants of second order for the heat kernel (Green function) is built and simple rules for form factor manipulations are proposed. The results are checked by deriving the Schwinger-DeWitt series of the heat kernel and divergences of one-loop currents.Comment: 12 pages, LaTeX, to appear in: Heat Kernel Techniques and Quantum Gravity, Discourses in Mathematics and Its Applications, No. 4, ed. by S. A. Fulling, (Texas A&M University, College Station, Texas, 1995

Thermoplastic waves in magnetars

Magnetar activity is generated by shear motions of the neutron star surface, which relieve internal magnetic stresses. An analogy with earthquakes and faults is problematic, as the crust is permeated by strong magnetic fields, which greatly constrain crustal displacements. We describe a new deformation mechanism that is specific to strongly magnetized neutron stars. The magnetically stressed crust begins to move because of a thermoplastic instability, which launches a wave that shears the crust and burns its magnetic energy. The propagating wave front resembles the deflagration front in combustion physics. We describe the conditions for the instability, the front structure and velocity, and discuss implications for observed magnetar activity.Comment: 5 pages, accepted to ApJ

Exact Multiparticle Amplitudes at Threshold in ϕ4\phi^4 Theories with Softly Broken O(∞)O(\infty) Symmetry

We consider the problem of multiparticle production at threshold in a $\phi^4$-theory with an $O(N_1$$+$$N_2)$ symmetry softly broken down to $O(N_1)\times O(N_2)$ by nonequal masses. We derive the set of recurrence relations between the multiparticle amplitudes which sums all relevant diagrams with arbitrary number of loops in the large-$N$ limit with fixed number of produced particles. We transform it into a quantum mechanical problem and show how it can be obtained directly from the operator equations of motion by applying the factorization at large $N$. We find the exact solutions to the problem by using the Gelfand--Diki\u{\i} representation of the diagonal resolvent of the Schr\"{o}dinger operator. The result coincides with the tree amplitudes while the effect of loops is the renormalization of the coupling constant and masses. The form of the solution is due to the fact that the exact amplitude of the process $2$\ra$n$ vanishes at $n$$>$$2$ on mass shell when averaged over the $O(N_{1,2})$-indices of incoming particles. We discuss what dynamical symmetry is behind this property. We also give an exact solution in the large-$N$ limit for the model of the $O(N)$$+$$singlet$ scalar particle with the spontaneous breaking of a reflection symmetry.Comment: Latex, 33 pages, NBI-HE-94-3

Bloch-mode analysis for retrieving effective parameters of metamaterials

We introduce a new approach for retrieving effective parameters of metamaterials based on the Bloch-mode analysis of quasi-periodic composite structures. We demonstrate that, in the case of single-mode propagation, a complex effective refractive index can be assigned to the structure, being restored by our method with a high accuracy. We employ both surface and volume averaging of the electromagnetic fields of the dominating (fundamental) Bloch modes to determine the Bloch and wave impedances, respectively. We discuss how this method works for several characteristic examples, and demonstrate that this approach can be useful for retrieval of both material and wave effective parameters of a broad range of metamaterials.Comment: 12 pages, 10 figure

Evolution of Neutron-Initiated Micro-Big-Bang in superfluid He 3B

A nuclear capture reaction of a single neutron by ultra-cold superfluid $^3$He results in a rapid overheating followed by the expansion and subsequent cooling of the hot subregion, in a certain analogy with the Big Bang of the early Universe. It was shown in a Grenoble experiment that a significant part of the energy released during the nuclear reaction was not converted into heat even after several seconds. It was thought that the missing energy was stored in a tangle of quantized vortex lines. This explanation, however, contradicts the expected lifetime of a bulk vortex tangle, $10^{-5}-10^{-4}\,$s, which is much shorter than the observed time delay of seconds. In this Letter we propose a scenario that resolves the contradiction: the vortex tangle, created by the hot spot, emits isolated vortex loops that take with them a significant part of the tangle's energy. These loops quickly reach the container walls. The dilute ensemble of vortex loops attached to the walls can survive for a long time, while the remaining bulk vortex tangle decays quickly.Comment: 5 pages, PRL submitte

The theory of transport in helical spin-structure crystals

We study helical structures in spin-spiral single crystals. In the continuum approach for the helicity potential energy the simple electronic band splits into two non-parabolic bands. For the Fermi energy greater than the splitting between the bands, the lower band is described by a surface with a saddle shape in the direction of the helicity axis. Using the Boltzmann equation with the relaxation due to acoustic phonons, we discover the dependence of the current on the angle between the electric field and helicity axis leading to the both parallel and perpendicular to the electric field components in the electroconductivity. In addition, we find that the transition rates depend on an electron spin allowing the transition between the bands. The electric conductivities exhibit nonlinear behaviors with respect to chemical potential. We explain this effect as the interference of the band anisotropy, spin conservation, and interband transitions. The proposed theory with the spherical model in the effective mass approximation for conduction electrons can elucidate nonlinear dependencies that can be identified in experiments. There is the excellent agreement between the theoretical and experimental data for parallel resistivity depending on temperature at the phase transition from helical to ferromagnetic state in a MnP single crystal. In addition, we predict that the perpendicular resistivity abruptly drops to zero in the ferromagnetic phase.Comment: 20 pages, 7 figures, 23 reference