Affine spherical homogeneous spaces with good quotient by a maximal unipotent subgroup

For an affine spherical homogeneous space G/H of a connected semisimple algebraic group G, we consider the factorization morphism by the action on G/H of a maximal unipotent subgroup of G. We prove that this morphism is equidimensional if and only if the weight semigroup of G/H satisfies some simple condition.Comment: v2: title and abstract changed; v3: 16 pages, minor correction

Superconductivity and Cobalt Oxidation State in Metastable Na(x)CoO(2-delta)*yH2O (x ~ 1/3; y ~ 4x)

We report the synthesis and superconducting properties of a metastable form of the known superconductor NaxCoO2*yH2O (x ~ 1/3, y ~ 4x). Instead of using the conventional bromine-acetonitrile mixture for sodium deintercalation, we use an aqueous bromine solution. Using this method, we oxidize the sample to a point that the sodium cobaltate becomes unstable, leading to formation of other products if not controlled. This compound has the same structure as the reported superconductor, yet it exhibits a systematic variation of the superconducting transition temperature (Tc) as a function of time. Immediately after synthesis, this compound is not a superconductor, even though it contains appropriate amounts of sodium and water. The samples become superconducting with low Tc values after ~ 90 h. Tc continually increases until it reaches a maximum value (4.5 K) after about 260 h. Then Tc drops drastically, becoming non-superconducting approximately 100 h later. Corresponding time-dependent neutron powder diffraction data shows that the changes in superconductivity exhibited by the metastable cobaltate correspond to slow formation of oxygen vacancies in the CoO2 layers. In effect, the formation of these defects continually reduces the cobalt oxidation state causing the sample to evolve through its superconducting life cycle. Thus, the dome-shaped superconducting phase diagram is mapped as a function of cobalt oxidation state using a single sample. The width of this dome based on the formal oxidation state of cobalt is very narrow - approximately 0.1 valence units wide. Interestingly, the maximum Tc in NaxCoO2*yH2O occurs when the cobalt oxidation state is near 3.5. Thus, we speculate that the maximum Tc occurs near the charge ordered insulating state that correlates with the average cobalt oxidation state of 3.5.Comment: 22 pages, 9 figures, 1 tabl

Infrared stability of ABJ-like theories

We consider marginal deformations of the superconformal ABJM/ABJ models which preserve N=2 supersymmetry. We determine perturbatively the spectrum of fixed points and study their infrared stability. We find a closed line of fixed points which is IR stable. The fixed point corresponding to the ABJM/ABJ models is stable under marginal deformations which respect the original SU(2)xSU(2) invariance, while deformations which break this group destabilize the theory which then flows to a less symmetric fixed point. We discuss the addition of flavor degrees of freedom. We prove that in general a flavor marginal superpotential does not destabilize the system in the IR. An exception is represented by a marginal coupling which mixes matter charged under different gauge sectors. Finally, we consider the case of relevant deformations which should drive the system to a strongly coupled IR fixed point recently investigated in arXiv:0909.2036 [hep-th].Comment: 1+11 pages, 4 figures; v2: minor correction

FeCr₂S₄ in magnetic fields: possible evidence for a multiferroic ground state.

We report on neutron diffraction, thermal expansion, magnetostriction, dielectric, and specific heat measurements on polycrystalline FeCr2S4 in external magnetic fields. The ferrimagnetic ordering temperatures TC ≈ 170 K and the transition at TOO ≈ 10 K, which has been associated with orbital ordering, are only weakly shifted in magnetic fields up to 9 T. The cubic lattice parameter is found to decrease when entering the state below TOO. The magnetic moments of the Cr- and Fe-ions are reduced from the spin-only values throughout the magnetically ordered regime, but approach the spin-only values for fields >5.5 T. Thermal expansion in magnetic fields and magnetostriction experiments indicate a contraction of the sample below about 60 K. Below TOO this contraction is followed by a moderate expansion of the sample for fields larger than ~4.5 T. The transition at TOO is accompanied by an anomaly in the dielectric constant. The dielectric constant depends on both the strength and orientation of the external magnetic field with respect to the applied electric field for T < TOO. A linear correlation of the magnetic-field-induced change of the dielectric constant and the magnetic-field dependent magnetization is observed. This behaviour is consistent with the existence of a ferroelectric polarization and a multiferroic ground state below 10 K

Proximity effect for asymmetrical three-layered F/S structures in external magnetic field

We study the critical temperature T c of the three-layered ferromagnet/superconductor (F/S) structures in the external magnetic field H parallel to the film. For the F1/S/F2 and F1/F2/S asymmetrical trilayers, the triplet superconducting component is generated at noncollinear magnetizations of the F layers. Assuming that all S and F layers are dirty, we solve boundary problem for the Usadel function. The results of numerical calculations for T c as function thicknesses both F1 and F2 layers at various parameters F/S structure are presented. The application to the spin-switch problem is discussed. We found that asymmetry can essentially change the spin-switch observation condition. The re-entrant superconductivity caused by external magnetic field is predicted for the F1/F2/S trilayer. © 2013 The Korean Physical Society

Harmonic analysis on spherical homogeneous spaces with solvable stabilizer

For all spherical homogeneous spaces G/H, where G is a simply connected semisimple algebraic group and H a connected solvable subgroup of G, we compute the spectra of the representations of G on spaces of regular sections of homogeneous line bundles over G/H.Comment: v2: 14 pages, minor correction

Variational approach for electrolyte solutions: from dielectric interfaces to charged nanopores

A variational theory is developed to study electrolyte solutions, composed of interacting point-like ions in a solvent, in the presence of dielectric discontinuities and charges at the boundaries. Three important and non-linear electrostatic effects induced by these interfaces are taken into account: surface charge induced electrostatic field, solvation energies due to the ionic cloud, and image charge repulsion. Our variational equations thus go beyond the mean-field theory. The influence of salt concentration, ion valency, dielectric jumps, and surface charge is studied in two geometries. i) A single neutral air-water interface with an asymmetric electrolyte. A charge separation and thus an electrostatic field gets established due to the different image charge repulsions for coions and counterions. Both charge distributions and surface tension are computed and compared to previous approximate calculations. For symmetric electrolyte solutions close to a charged surface, two zones are characterized. In the first one, with size proportional to the logarithm of the coupling parameter, strong image forces impose a total ion exclusion, while in the second zone the mean-field approach applies. ii) A symmetric electrolyte confined between two dielectric interfaces as a simple model of ion rejection from nanopores. The competition between image charge repulsion and attraction of counterions by the membrane charge is studied. For small surface charge, the counterion partition coefficient decreases with increasing pore size up to a critical pore size, contrary to neutral membranes. For larger pore sizes, the whole system behaves like a neutral pore. The prediction of the variational method is also compared with MC simulations and a good agreement is observed.Comment: This version is accepted for publication in Phys. Rev. E

Electrostatic correlations on the ionic selectivity of cylindrical membrane nanopores

We characterize the role of electrostatic fluctuations on the charge selectivity of cylindrical nanopores confining electrolyte mixtures. To this end, we develop an extended one-loop theory that can account for correlation effects induced by the surface charge, nanoconfinement of the electrolyte, and interfacial polarization charges associated with the low permittivity membrane. We validate the quantitative accuracy of the theory by comparisons with previously obtained Monte-Carlo simulation data from the literature, and scrutinize in detail the underlying forces driving the ionic selectivity of the nanopore. In the biologically relevant case of electrolytes with divalent cations such as CaCl2 in negatively charged nanopores, electrostatic correlations associated with the dense counterion layer in the channel result in an increase of the pore coion density with the surface charge. This peculiarity analogous to the charge inversion phenomenon remains intact for dielectrically inhomogeneous pores, which indicates that the effect should be observable in nanofiltration membranes or DNA-blocked nanopores characterized by a low membrane permittivity. Our results show that a quantitatively accurate consideration of correlation effects is necessary to determine the ionic selectivity of nanopores in the presence of electrolytes with multivalent counterions.Peer reviewe