Critical State in Thin Anisotropic Superconductors of Arbitrary Shape

A thin flat superconductor of arbitrary shape and with arbitrary in-plane and out-of-plane anisotropy of flux-line pinning is considered, in an external magnetic field normal to its plane. It is shown that the general three-dimensional critical state problem for this superconductor reduces to the two-dimensional problem of an infinitely thin sample of the same shape but with a modified induction dependence of the critical sheet current. The methods of solving the latter problem are well known. This finding thus enables one to study the critical states in realistic samples of high-Tc superconductors with various types of anisotropic flux-line pinning. As examples, we investigate the critical states of long strips and rectangular platelets of high-Tc superconductors with pinning either by the ab-planes or by extended defects aligned with the c-axis.Comment: 13 pages including 13 figure files in the tex

Analytic Solution for the Critical State in Superconducting Elliptic Films

A thin superconductor platelet with elliptic shape in a perpendicular magnetic field is considered. Using a method originally applied to circular disks, we obtain an approximate analytic solution for the two-dimensional critical state of this ellipse. In the limits of the circular disk and the long strip this solution is exact, i.e. the current density is constant in the region penetrated by flux. For ellipses with arbitrary axis ratio the obtained current density is constant to typically 0.001, and the magnetic moment deviates by less than 0.001 from the exact value. This analytic solution is thus very accurate. In increasing applied magnetic field, the penetrating flux fronts are approximately concentric ellipses whose axis ratio b/a < 1 decreases and shrinks to zero when the flux front reaches the center, the long axis staying finite in the fully penetrated state. Analytic expressions for these axes, the sheet current, the magnetic moment, and the perpendicular magnetic field are presented and discussed. This solution applies also to superconductors with anisotropic critical current if the anisotropy has a particular, rather realistic form.Comment: Revtex file and 13 postscript figures, gives 10 pages of text with figures built i

The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples

A theory has been developed to explain the anomalous behavior of the magnetic susceptibility of a normal metal-superconductor ($NS$) structure in weak magnetic fields at millikelvin temperatures. The effect was discovered experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting samples covered with a thin normal pure metal layer, the susceptibility exhibited a reentrant effect: it started to increase unexpectedly when the temperature lowered below 100 mK. The effect was observed in mesoscopic $NS$ structures when the $N$ and $S$ metals were in good electric contact. The theory proposed is essentially based on the properties of the Andreev levels in the normal metal. When the magnetic field (or temperature) changes, each of the Andreev levels coincides from time to time with the chemical potential of the metal. As a result, the state of the $NS$ structure experiences strong degeneracy, and the quasiparticle density of states exhibits resonance spikes. This generates a large paramagnetic contribution to the susceptibility, which adds up to the diamagnetic contribution thus leading to the reentrant effect. The explanation proposed was obtained within the model of free electrons. The theory provides a good description for experimental results [10]

Non-linear electromagnetic interactions in thermal QED

We examine the behavior of the non-linear interactions between electromagnetic fields at high temperature. It is shown that, in general, the log(T) dependence on the temperature of the Green functions is simply related to their UV behavior at zero-temperature. We argue that the effective action describing the nonlinear thermal electromagnetic interactions has a finite limit as T tends to infinity. This thermal action approaches, in the long wavelength limit, the negative of the corresponding zero-temperature action.Comment: 7 pages, IFUSP/P-111

High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the 1PI one-loop diagrams and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for $d$ space-time dimensions. This result is valid whenever the external fields are all bosonic.Comment: 15 pages, 11 figures. To be published in Physical Review

Thermal Effective Lagrangian of Static Gravitational Fields

We compute the effective Lagrangian of static gravitational fields interacting with thermal fields. Our approach employs the usual imaginary time formalism as well as the equivalence between the static and space-time independent external gravitational fields. This allows to obtain a closed form expression for the thermal effective Lagrangian in $d$ space-time dimensions.Comment: Accepted for publication in the Physical Review

Seiberg-Witten maps and anomalies in noncommutative Yang-Mills theories

A BRST-cohomological analysis of Seiberg-Witten maps and results on gauge anomalies in noncommutative Yang-Mills theories with general gauge groups are reviewed.Comment: 9 pages, talk at 9th Adriatic Meeting, Dubrovnik, Croatia, 4-14 Sept. 200