16,936 research outputs found
Integrable nonlinear field equations and loop algebra structures
We apply the (direct and inverse) prolongation method to a couple of
nonlinear Schr{\"o}dinger equations. These are taken as a laboratory field
model for analyzing the existence of a connection between the integrability
property and loop algebras. Exploiting a realization of the Kac-Moody type of
the incomplete prolongation algebra associated with the system under
consideration, we develop a procedure with allows us to generate a new class of
integrable nonlinear field equations containing the original ones as a special
case.Comment: 13 pages, latex, no figures
The Prolongation Problem for the Heavenly Equation
We provide an exact regular solution of an operator system arising as the
prolongation structure associated with the heavenly equation. This solution is
expressed in terms of operator Bessel coefficients.Comment: 9 pages, Proc. SIGRAV Conference (Bari 1998
"Soft" Anharmonic Vortex Glass in Ferromagnetic Superconductors
Ferromagnetic order in superconductors can induce a {\em spontaneous} vortex
(SV) state. For external field , rotational symmetry guarantees a
vanishing tilt modulus of the SV solid, leading to drastically different
behavior than that of a conventional, external-field-induced vortex solid. We
show that quenched disorder and anharmonic effects lead to elastic moduli that
are wavevector-dependent out to arbitrarily long length scales, and non-Hookean
elasticity. The latter implies that for weak external fields , the magnetic
induction scales {\em universally} like , with
. For weak disorder, we predict the SV solid is a
topologically ordered vortex glass, in the ``columnar elastic glass''
universality class.Comment: minor corrections; version published in PR
Quaternionic eigenvalue problem
We discuss the (right) eigenvalue equation for , and
linear quaternionic operators. The possibility to introduce an
isomorphism between these operators and real/complex matrices allows to
translate the quaternionic problem into an {\em equivalent} real or complex
counterpart. Interesting applications are found in solving differential
equations within quaternionic formulations of quantum mechanics.Comment: 13 pages, AMS-Te
Quantum coherent transport in a three-arm beam splitter and a Braess paradox
The Braess paradox encountered in classical networks is a counterintuitive
phenomenon when the flow in a road network can be impeded by adding a new road
or, more generally, the overall net performance can degrade after addition of
an extra available choice. In this work, we discuss the possibility of a
similar effect in a phase-coherent quantum transport and demonstrate it by
example of a simple Y-shaped metallic fork. To reveal the Braess-like partial
suppression of the charge flow in such device, it is proposed to transfer two
outgoing arms into a superconducting state. We show that the differential
conductance-vs-voltage spectrum of the hybrid fork structure varies
considerably when the extra link between the two superconducting leads is added
and it can serve as an indicator of quantum correlations which manifest
themselves in the quantum Braess paradox.Comment: 9 pages, 3 figures, the author version presented at the Quantum 2017
Workshop (Torino, Italy, 7-13 May 2017) and submitted to the International
Journal of Quantum Information; v2: reference 9 added and the introduction
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