12 research outputs found
Fractionalization of angular momentum at finite temperature around a magnetic vortex
Ambiguities in the definition of angular momentum of a quantum-mechanical
particle in the presence of a magnetic vortex are reviewed. We show that the
long-standing problem of the adequate definition is resolved in the framework
of the second-quantized theory at nonzero temperature. Planar relativistic
Fermi gas in the background of a point-like magnetic vortex with arbitrary flux
is considered, and we find thermal averages, quadratic fluctuations, and
correlations of all observables, including angular momentum, in this system.
The kinetic definition of angular momentum is picked out unambiguously by the
requirement of plausible behaviour for the angular momentum fluctuation and its
correlation with fermion number.Comment: 32 pages, submitted to Annals of Physic
On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree
In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum:
40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative
of the Legendre function of the first kind, , with respect to its
degree . In the present work, we extend these studies and construct
several representations of the derivative of the associated Legendre function
of the first kind, , with respect to the degree , for
. At first, we establish several contour-integral
representations of . They are then
used to derive Rodrigues-type formulas for with . Next, some closed-form
expressions for are
obtained. These results are applied to find several representations, both
explicit and of the Rodrigues type, for the associated Legendre function of the
second kind of integer degree and order, ; the explicit
representations are suitable for use for numerical purposes in various regions
of the complex -plane. Finally, the derivatives
, and , all with , are evaluated in terms
of .Comment: LateX, 40 pages, 1 figure, extensive referencin
Solution of generalized fractional reaction-diffusion equations
This paper deals with the investigation of a closed form solution of a
generalized fractional reaction-diffusion equation. The solution of the
proposed problem is developed in a compact form in terms of the H-function by
the application of direct and inverse Laplace and Fourier transforms.
Fractional order moments and the asymptotic expansion of the solution are also
obtained.Comment: LaTeX, 18 pages, corrected typo
Overcritical states of a superconductor strip in a magnetic environment
A current-carrying superconducting strip partly penetrated by magnetic flux
and surrounded by a bulk magnet of high permeability is considered. Two types
of samples are studied: those with critical current controlled by an edge
barrier dominating over the pinning, and those with high pinning-mediated
critical current masking the edge barrier.It is shown for both cases that the
current distribution in a central flux-free part of the strip is strongly
affected by the actual shape of the magnetic surroundings. Explicit analytical
solutions for the sheet current and self-field distributions are obtained which
show that, depending on the geometry, the effect may suppress the total
loss-free transport current of the strip or enhance it by orders of magnitude.
The effect depends strongly on the shape of the magnet and its distance to the
superconductor but only weakly on the magnetic permeability.Comment: 20 pages, 20 figure