1, 2, and 6 qubits, and the Ramanujan-Nagell theorem

A conjecture of Ramanujan that was later proved by Nagell is used to show on the basis of matching dimensions that only three $n$-qubit systems, for $n=1, 2, 6$, can share an isomorphism of their symmetry groups with the rotation group of corresponding dimensions $3, 6, 91$. Topological analysis, however, rules out the last possibility

Anderson localization of solitons in optical lattices with random frequency modulation

We report on phenomenon of Anderson-type localization of walking solitons in optical lattices with random frequency modulation, manifested as dramatic enhancement of soliton trapping probability on lattice inhomogeneities with growth of the frequency fluctuation level. The localization process is strongly sensitive to the lattice depth since in shallow lattices walking solitons experience random refraction and/or multiple scattering in contrast to relatively deep lattices, where solitons are typically immobilized in the vicinity of local minimums on modulation frequency.Comment: 13 pages, 4 figures, to appear in Physical Review

Magnons versus electrons in thermal spin transport through metallic interfaces

We develop a theory for spin transport in magnetic metals that treats the contribution of magnons and electrons on equal footing. As an application we consider thermally-driven spin injection across an interface between a magnetic metal and a normal metal, i.e., the spin-dependent Seebeck effect. We show that the ratio between magnonic and electronic contribution scales as $\sqrt{T/T_C}T_F/T_C$, with the Fermi temperature $T_F$ and the Curie temperature $T_C$. Since, typically, $T_C \ll T_F$, the magnonic contribution may dominate the thermal spin injection, even though the interface is more transparent for electronic spin current.Comment: Contribution to the Special issue on Spincaloritronics in Journal of Physics D: Applied Physic

Spontaneous-Symmetry-Breaking Mechanism of Adiabatic Pumping

We consider heterostructures consisting of regions with a continuous symmetry in contact with regions wherein the symmetry is spontaneously broken. The low-frequency dynamics of the corresponding order parameter are shown to induce nonequilibrium transport, a ``pumping,'' out of the symmetry-broken regions, which is governed by the generator of the broken-symmetry operator. This pumping damps Goldstone-mode excitations and transfers them beyond traditional (static) proximity length scales. Our general conclusions are discussed for specific examples of order parameters in helimagnets, charge/spin-density waves, superconductors, and ferromagnets. We carry out a detailed calculation of such pumping for spiral magnetic orders in helimagnets possessing a duality in the representation of its symmetry-broken states.Comment: 5 pages, 2 figure

Transformation Optics with Photonic Band Gap Media

We introduce a class of optical media based on adiabatically modulated, dielectric-only, and potentially extremely low-loss, photonic crystals. The media we describe represent a generalization of the eikonal limit of transformation optics (TO). The foundation of the concept is the possibility to fit frequency isosurfaces in the k-space of photonic crystals with elliptic surfaces, allowing them to mimic the dispersion relation of light in anisotropic effective media. Photonic crystal cloaks and other TO devices operating at visible wavelengths can be constructed from optically transparent substances like glasses, whose attenuation coefficient can be as small as 10 dB/km, suggesting the TO design methodology can be applied to the development of optical devices not limited by the losses inherent to metal-based, passive metamaterials.Comment: 4 pages, 4 figure