Counterexamples to the discrete and continuous weighted Weiss conjectures

Counterexamples are presented to weighted forms of the Weiss conjecture in discrete and continuous time. In particular, for certain ranges of $\alpha$, operators are constructed that satisfy a given resolvent estimate, but fail to be $\alpha$-admissible. For $\alpha \in (-1,0)$ the operators constructed are normal, while for $\alpha \in (0,1)$ the operator is the unilateral shift on the Hardy space $H^2(\mathbb{D})$.Comment: 16 page

Preparation and Characterization of Homogeneous YBCO Single Crystals with Doping Level near the SC-AFM Boundary

High-purity and homogeneous YBa2Cu3Oy single crystals with carrier doping level near the AFM-SC boundary have been obtained in the oxygen content range between y = 6.340 and 6.370. The crystals are ortho-II phase at room temperature and undergo the orthorhombic to tetragonal transition at about 140_Degree_C. They show sharp superconducting transitions, with Tc between 4 and 20 K. Tc changes by 0.8 K when the oxygen content y is changed by 0.001, and is also sensitive to annealing conditions near room temperature, due to the dependence of doping on oxygen ordering correlation lengths. Crystals with oxygen content y lower than 6.345 are non-superconducting.Comment: 6 page

Possible Z2 phase and spin-charge separation in electron doped cuprate superconductors

The SU(2) slave-boson mean-field theory for the tt'J model is analyzed. The role of next-nearest-neighbor hopping t' on the phase-diagram is studied. We find a pseudogap phase in hole-doped materials (where t'<0). The pseudo-gap phase is a U(1) spin liquid (the staggered-flux phase) with a U(1) gauge interaction and no fractionalization. This agrees with experiments on hole doped samples. The same calculation also indicates that a positive t' favors a Z2 state with true spin-charge separation. The Z2 state that exists when t' > 0.5J can be a candidate for the pseudo-gap phase of electron-doped cuprates (if such a phase exists). The experimental situation in electron-doped materials is also addressed.Comment: 6 pages, 2 figures, RevTeX4. Homepage http://dao.mit.edu/~wen

Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet

We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.Comment: 22 pages, 14 figures. Further minor changes. To appear in Phys. Rev.

Fluxoid dynamics in superconducting thin film rings

We have measured the dynamics of individual magnetic fluxoids entering and leaving photolithographically patterned thin film rings of the underdoped high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, using a variable sample temperature scanning SQUID microscope. These results can be qualitatively described using a model in which the fluxoid number changes by thermally activated nucleation of a Pearl vortex in, and transport of the Pearl vortex across, the ring wall.Comment: 9 pages, 10 figures, fixed typo

Accretion, Outflows, and Winds of Magnetized Stars

Many types of stars have strong magnetic fields that can dynamically influence the flow of circumstellar matter. In stars with accretion disks, the stellar magnetic field can truncate the inner disk and determine the paths that matter can take to flow onto the star. These paths are different in stars with different magnetospheres and periods of rotation. External field lines of the magnetosphere may inflate and produce favorable conditions for outflows from the disk-magnetosphere boundary. Outflows can be particularly strong in the propeller regime, wherein a star rotates more rapidly than the inner disk. Outflows may also form at the disk-magnetosphere boundary of slowly rotating stars, if the magnetosphere is compressed by the accreting matter. In isolated, strongly magnetized stars, the magnetic field can influence formation and/or propagation of stellar wind outflows. Winds from low-mass, solar-type stars may be either thermally or magnetically driven, while winds from massive, luminous O and B type stars are radiatively driven. In all of these cases, the magnetic field influences matter flow from the stars and determines many observational properties. In this chapter we review recent studies of accretion, outflows, and winds of magnetized stars with a focus on three main topics: (1) accretion onto magnetized stars; (2) outflows from the disk-magnetosphere boundary; and (3) winds from isolated massive magnetized stars. We show results obtained from global magnetohydrodynamic simulations and, in a number of cases compare global simulations with observations.Comment: 60 pages, 44 figure

Changes in meltwater chemistry over a 20-year period following a thermal regime switch from polythermal to cold-based glaciation at Austre Broggerbreen, Svalbard

Our long-term study gives a rare insight into meltwater hydrochemistry following the transition of Austre Brøggerbreen from polythermal to cold-based glaciation and its continued retreat. We find that the processes responsible for ion acquisition did not change throughout the period of records but became more productive. Two regimes before and after July/August 2000 were identified from changes in solute concentrations and pH. They resulted from increased chemical weathering occurring in ice-marginal and proglacial environments that have become progressively exposed by glacier retreat. Carbonate carbonation nearly doubled between 2000 and 2010, whilst increases in the weathering of silicate minerals were also marked. In addition, the end of ablation season chemistry was characterized by reactions in long residence time flow paths like those in subglacial environments, in spite of their absence in the watershed. Furthermore, the retreat of the glacier caused the sudden re-routing of meltwaters through its immediate forefield during 2009, which more than doubled crustal ion yields in this particular year and influenced chemical weathering in 2010 regardless of a low water flux. Such a “flush” of crustally derived ions can be meaningful for downstream terrestrial and marine ecosystems. We therefore find that, during glacier retreat, the recently exposed forefield is the most chemically active part of the watershed, making high rates of weathering possible, even when ice losses have caused a switch to cold-based conditions with no delayed subglacial drainage flowpaths. In addition, the drainage system reorganization events result in significant pCO2 depletion in an otherwise high pCO2 system