Partial inner product spaces: Some categorical aspects

We make explicit in terms of categories a number of statements from the theory of partial inner product spaces (PIP spaces) and operators on them. In particular, we construct sheaves and cosheaves of operators on certain PIP spaces of practical interest.Comment: 21 page

Peculiar Nature of Snake States in Graphene

We study the dynamics of the electrons in a non-uniform magnetic field applied perpendicular to a graphene sheet in the low energy limit when the excitation states can be described by a Dirac type Hamiltonian. We show that as compared to the two-dimensional electron gas (2DEG) snake states in graphene exibit peculiar properties related to the underlying dynamics of the Dirac fermions. The current carried by snake states is locally uncompensated even if the Fermi energy lies between the first non-zero energy Landau levels of the conduction and valence bands. The nature of these states is studied by calculating the current density distribution. It is shown that besides the snake states in finite samples surface states also exist.Comment: 4 pages, 5 figure

Suppression of Giant Magnetoresistance by a superconducting contact

We predict that current perpendicular to the plane (CPP) giant magnetoresistance (GMR) in a phase-coherent magnetic multilayer is suppressed when one of the contacts is superconducting. This is a consequence of a superconductivity-induced magneto-resistive (SMR) effect, whereby the conductance of the ferromagnetically aligned state is drastically reduced by superconductivity. To demonstrate this effect, we compute the GMR ratio of clean (Cu/Co)_nCu and (Cu/Co)_nPb multilayers, described by an ab-initio spd tight binding Hamiltonian. By analyzing a simpler model with two orbitals per site, we also show that the suppression survives in the presence of elastic scattering by impurities.Comment: 5 pages, 4 figures. Submitted to PR

Why some fields might be rectangular: an exploration of agricultural landscapes between pre-capitalist and capitalist modes of production

This article is a preliminary investigation of possible spatial form which starts by rejecting the idea that spatial theory can be built from assumptions of isomorphism. It examines spatial form in high potential ridge valley areas which are densely populated, and identifies the transition in land configuration for pre-capitalist to capitalist modes of production. In building the argument simple geometric patterns that differentiate from the model are postulated. The basic drivers of the differing spatial systems are essentially the superstructural legal conditions which are postulated as a moving from communal, customary law to individual statutory property rights

Procyon-A and Eta-Bootis: Observational Frequencies Analyzed by the Local-Wave Formalism

In the present analysis of Procyon-A and Eta-Bootis, we use the local-wave formalism which, despite its lack of precision inherent to any semi-analytical method, uses directly the model profile without any modification when calculating the acoustic mode eigenfrequencies. These two solar-like stars present steep variations toward the center due to the convective core stratification, and toward the surface due to the very thin convective zone. Based on different boundary conditions, the frequencies obtained with this formalism are different from that of the classical numerical calculation. We point out that (1) the frequencies calculated with the local-wave formalism seem to agree better with observational ones. All the frequencies detected with a good confident level including those classified as 'noise' find an identification, (2) some frequencies can be clearly identified here as indications of the core limit.Comment: SOHO 18 / GONG 2006 / HELAS I Meetin

Quantum-limited mass flow of liquid 3^{3}He

We consider theoretically the possibility of observing unusual quantum fluid behavior in liquid $^{3}$He and solutions of $^{3}$He in $^{4}$He systems confined to nano-channels. In the case of pure ballistic flow at very low temperature conductance will be quantized in units of $2m^{2}/h$. We show that these steps should be sensitive to increases in temperature. We also use of a random scattering matrix simulation to study flow with diffusive wall scattering. Universal conductance fluctuations analogous to those seen in electron systems should then be observable. Finally we consider the possibility of the cross-over to a one-dimensional system at sufficiently low temperature where the system could form a Luttinger liquid

Superconducting Proximity Effect and Universal Conductance Fluctuations

We examine universal conductance fluctuations (UCFs) in mesoscopic normal-superconducting-normal (N-S-N) structures using a numerical solution of the Bogoliubov - de Gennes equation. We discuss two cases depending on the presence (``open'' structure) or absence (``closed'' structure) of quasiparticle transmission. In contrast to N-S structures, where the onset of superconductivity increases fluctuations, we find that UCFs are suppressed by superconductivity for N-S-N structures. We demonstrate that the fluctuations in ``open'' and ``closed'' structures exhibit distinct responses to an applied magnetic field and to an imposed phase variation of the superconducting order parameter.Comment: (4 pages, 5 figures). Corrected typos in equations, added references, changed Fig. 5 and its discussions. Phys. Rev. B, accepted for publicatio

Overcoming decoherence in the collapse and revival of spin Schr\"odinger cats

In addition to being a very interesting quantum phenomenon, Schr\"odinger cat swapping has the potential for application in the preparation of quantum states that could be used in metrology and other quantum processing. We study in detail the effects of field decoherence on a cat-swapping system comprising a set of identical qubits, or spins, all coupled to a field mode. We demonstrate that increasing the number of spins actually mitigates the effects of field decoherence on the collapse and revival of a spin Schr\"odinger cat, which could be of significant utility in quantum metrology and other quantum processing.Comment: 4 pages, 2 figure

Giant Backscattering Peak in Angle-Resolved Andreev Reflection

It is shown analytically and by numerical simulation that the angular distribution of Andreev reflection by a disordered normal-metal -- superconductor junction has a narrow peak at the angle of incidence. The peak is higher than the well-known coherent backscattering peak in the normal state, by a large factor G/G_0 (where G is the conductance of the junction and G_0=2e^2/h). The enhanced backscattering can be detected by means of ballistic point contacts.Comment: Instituut-Lorentz, Leiden, The Netherlands, 4 pages, REVTeX-3.0, 3 figure