M. Daumens

The super‐rotation Racah–Wigner calculus revisited

It is shown that, since the finite dimensional representations of the super‐rotation algebra are characterized by the superspin j and the parity λ of the representation space, all features of the Racah–Wigner calculus: Clebsch–Gordan coefficients, recoupling coefficients as well as the Wigner and Racah symbols depend on both j and λ. However, it is noticed that the dependence on the parities of the Wigner and Racah symbols can be factorized out into phases so that one can define parity‐independent super S3−j and S6−j symbols. The properties of these symbols are analyzed, in particular, it is shown that the S6−j symbols possess a symmetry similar to the Regge symmetry satisfied by the rotation 6−j symbols. Analytical and numerical tables of the symbols are given for the lowest values of their arguments.

Super angular momentum and super spherical harmonics

The usual quantum mechanics methods of defining angular momentum and spherical harmonics in the ordinary space E(3) are generalized to the real commuting super‐space E(3‖2). The super angular momentum, generators of the super‐rotation, is realized as differential operators acting on functions defined on E(3‖2). By solving the eigenvalue problem in spherical coordinates, a set of pseudo‐orthonormalized functions is constructed, the super‐spherical harmonics Ylmj, whose main properties are given.

Electrostatic analogies in the problems of vortex–defect interactions

Abstract We consider the general case of vortex interactions with different types of mesoscopic defects. When the distances of interest are smaller than the London penetration depth, a useful analogy with electrostatic problems can be formulated. We demonstrate how this analogy permits us to obtain the solutions to a number of problems of electromagnetic pinning of vortices (e.g., the vortex–elliptic hole interaction). We suggest a means of optimising conditions that should lead to higher critical currents. We also examine how the surface defects influence the field of the vortex entrance in superconductors and stress that such an effect is very important for layered superconductors, since it could reduce the theoretical entrance field by one or two orders of magnitude.

Regge Symmetries of Super 6 – j Symbols for the Superalgebra osp(1|2)

In this letter we show that the super 6 – j (s6 – j) symbols for the superalgebra osp(1|2) possess, in addition to the usual tetrahedral symmetry, a Regge symmetry. However, for an arbitrary s6 – j symbol, this additional symmetry is smaller than in the case of the rotation 6 – j symbols. Only in some particular cases does the s6 – j symbol possess the full Regge symmetry.

c-axis penetration depth in Bi2Sr2CaCu2O8+δ single crystals measured by ac-susceptibility and cavity perturbation technique

The c-axis penetration depth Δλc in Bi2Sr2CaCu2O8+δ (BSCCO) single crystals as a function of temperature has been determined using two techniques, namely, measurements of the ac-susceptibility at a frequency of 100 kHz and the surface impedance at 9.4 GHz. Both techniques yield an almost linear function Δλc(T)∝T in the temperature range T<0.5Tc. Electrodynamic analysis of the impedance anisotropy has allowed us to estimate λc(0)≈50 µm in BSCCO crystals overdoped with oxygen (Tc≈84 K) and λc(0)≈150 µm at the optimal doping level (Tc≈90 K).

A simple differential operator realization of the super‐rotation algebra

The super‐rotation algebra is realized as differential operators acting on functions defined on the E(1/2) superspace.

Tensor spherical harmonics and tensor multipoles. I. Euclidean space

Two bases in the Hilbert space of tensor fields on the unit sphere are discussed: the tensor spherical harmonics and the tensor multipoles. For vector fields these two bases are related by an orthonormal transformation whose coefficients are shown to be Clebsch–Gordan coefficients. This remark suggests a method of building multipole bases for higher order tensor fields. The second order tensor multipoles are studied in detail as well as their relations with the symmetric ones defined by several authors for application to the gravitational radiation.

Proximity effect in atomic-scaled hybrid superconductor/ferromagnet structures: Crucial role of electron spectra

We study the influence of the configuration of the majority and minority spin subbands of electron spectra on the properties of atomic-scaled superconductor/ferromagnet S/F/S and F/S/F hybrid structures. At low temperatures, the S/F/S junction is either a 0 or junction depending on the energy shift between S and F materials and the anisotropy of the Fermi surfaces. We found that the spin-switch effect in F/S/F system can be reversed if the minority spin electron spectra in F metal is of the hole-like type.

Canonical and differential realizations of OSP(3‖2) superalgebra

The osp(3‖2) superalgebra is realized, first by means of two supervectorial operators canonically conjugated, and then by differential operators acting on functions defined on E(3‖2). As for the vectorial representation of osp(1‖2) the eigenvalue problem yields to the superspherical harmonics.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4‐vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation.