Counterexamples to additivity of minimum output p-Renyi entropy for p close to 0

Complementing recent progress on the additivity conjecture of quantum information theory, showing that the minimum output p-Renyi entropies of channels are not generally additive for p>1, we demonstrate here by a careful random selection argument that also at p=0, and consequently for sufficiently small p, there exist counterexamples. An explicit construction of two channels from 4 to 3 dimensions is given, which have non-multiplicative minimum output rank; for this pair of channels, numerics strongly suggest that the p-Renyi entropy is non-additive for all p < 0.11. We conjecture however that violations of additivity exist for all p<1.Comment: 7 pages, revtex4; v2 added correct ref. [15]; v3 has more information on the numerical violation as well as 1 figure (2 graphs) - note that the explicit example was changed and the more conservative estimate of the bound up to which violations occur, additionally some other small issues are straightened ou

Supercooling of the disordered vortex lattice in Bi_2Sr_2CaCu_2O_8+d

Time-resolved local induction measurements near to the vortex lattice order-disorder transition in optimally doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ single crystals shows that the high-field, disordered phase can be quenched to fields as low as half the transition field. Over an important range of fields, the electrodynamical behavior of the vortex system is governed by the co-existence of the two phases in the sample. We interpret the results in terms of supercooling of the high-field phase and the possible first order nature of the order-disorder transition at the ``second peak''.Comment: 4 pages, 3 figures. Submitted to Nature, July 10th, 1999; Rejected August 8th for lack of broad interest Submitted to Physical Review Letters September 10th, 199

Visualizing the Anthropocene dialectically: Jessica Woodworth and Peter Brosens’ eco-crisis trilogy

The ambition of this article is to propose a way of visualizing the Anthropocene dialectically. As suggested by the Dutch atmospheric chemist Paul Crutzen and the professor of biology Eugene F. Stoermer, the term Anthropocene refers to a historical period in which humankind has turned into a geological force that transforms the natural environment in such a way that it is hard to distinguish between the human and the natural world. Crutzen and Stoermer explain that the Anthropocene has begun after the Holocene, the geological epoch that followed the last ice age and lasted until the industrial revolution. Drawing on a number of figures such as the “tenfold” increase in urbanisation, the extreme transformation of land surface by human action, the use of more than 50% of all accessible fresh water by humans, and the massive increase in greenhouse emissions, Crutzen and Stoermer conclude that the term Anthropocene describes aptly mankind's influence on ecological and geological cycles (Crutzen & Stoermer, 2000, p.17). The wager of this article is that we need to identify ways to visualize the Anthropocene dialectically and I proceed to do so using as a case study Jessica Woodworth's and Peter Brosen's trilogy on the conflict between humans and nature, which consists of Khadak (2006), Altiplano (2009), and The Fifth Season (La Cinquième Saison, 2012)

The pairing state in KFe2As2 studied by measurements of the magnetic vortex lattice

Understanding the mechanism and symmetry of electron pairing in iron-based superconductors represents an important challenge in condensed matter physics [1-3]. The observation of magnetic flux lines - "vortices" - in a superconductor can contribute to this issue, because the spatial variation of magnetic field reflects the pairing. Unlike many other iron pnictides, our KFe2As2 crystals have very weak vortex pinning, allowing small-angle-neutron-scattering (SANS) observations of the intrinsic vortex lattice (VL). We observe nearly isotropic hexagonal packing of vortices, without VL-symmetry transitions up to high fields along the fourfold c-axis of the crystals, indicating rather small anisotropy of the superconducting properties around this axis. This rules out gap nodes parallel to the c-axis, and thus d-wave and also anisotropic s-wave pairing [2, 3]. The strong temperature-dependence of the intensity down to T<<Tc indicates either widely different full gaps on different Fermi surface sheets, or nodal lines perpendicular to the axis.Comment: 13 pages, 3 figure

Low-Field Phase Diagram of Layered Superconductors: The Role of Electromagnetic Coupling

We determine the position and shape of the melting line in a layered superconductor taking the electromagnetic coupling between layers into account. In the limit of vanishing Josephson coupling we obtain a new generic reentrant low-field melting line. Finite Josephson coupling pushes the melting line to higher temperatures and fields and a new line shape $B_{{\rm m}} \propto (1-T/T_c)^{3/2}$ is found. We construct the low-field phase diagram including melting and decoupling lines and discuss various experiments in the light of our new results.Comment: 12 pages, 1 figure attached as compressed and uuencoded postscrip

Dirac Nodes and Quantized Thermal Hall Effect in the Mixed State of d-wave Superconductors

We consider the vortex state of d-wave superconductors in the clean limit. Within the linearized approximation the quasiparticle bands obtained are found to posess Dirac cone dispersion (band touchings) at special points in the Brillouin zone. They are protected by a symmetry of the linearized Hamiltonian that we call T_Dirac. Moreover, for vortex lattices that posess inversion symmetry, it is shown that there is always a Dirac cone centered at zero energy within the linearized theory. On going beyond the linearized approximation and including the effect of the smaller curvature terms (that break T_Dirac), the Dirac cone dispersions are found to acquire small gaps (0.5 K/Tesla in YBCO) that scale linearly with the applied magnetic field. When the chemical potential for quasiparticles lies within the gap, quantization of the thermal-Hall conductivity is expected at low temperatures i.e. kappa_{xy}/T = n[(pi k_B)^2/(3h)] with the integer `n' taking on values n=+2, -2, 0. This quantization could be seen in low temperature thermal transport measurements of clean d-wave superconductors with good vortex lattices.Comment: (23 pages in all [7 pages in appendices], 9 figures

Entanglement on mixed stabilizer states: normal forms and reduction procedures

Published versio

First-Order Melting and Dynamics of Flux Lines in a Model for YBa2_2Cu3_3O7−δ_{7-\delta}

We have studied the statics and dynamics of flux lines in a model for YBCO, using both Monte Carlo simulations and Langevin dynamics. For a clean system, both approaches yield the same melting curve, which is found to be weakly first order with a heat of fusion of about $0.02 k_BT_m$ per vortex pancake at a field of $50 {\rm kG}.$ The time averaged magnetic field distribution experienced by a fixed spin is found to undergo a qualitative change at freezing, in agreement with NMR and $\mu {\rm SR}$ experiments. Melting in the clean system is accompanied by a proliferation of free disclinations which show a clear B-dependent 3D-2D crossover from long disclination lines parallel to the c-axis at low fields, to 2D ``pancake'' disclinations at higher fields. Strong point pins produce a logarithmical $\ln t$ relaxation which results from slow annealing out of disclinations in disordered samples.Comment: 31 pages, latex, revtex, 12 figures available upon request, No major changes to the original text, but some errors in the axes scale for Figures 6 and 7 were corrected(new figures available upon request), to be published in Physical Review B, July 199

Possible new vortex matter phases in BSCCO

The vortex matter phase diagram of BSCCO crystals is analyzed by investigating vortex penetration through the surface barrier in the presence of a transport current. The strength of the effective surface barrier, its nonlinearity, and asymmetry are used to identify a possible new ordered phase above the first-order transition. This technique also allows sensitive determination of the depinning temperature. The solid phase below the first-order transition is apparently subdivided into two phases by a vertical line extending from the multicritical point.Comment: 11 pages, 3 figures, accepted for publication in PR

Freezing transition of the vortex liquid in anisotropic superconductors

We study the solid-liquid transition of a model of pancake vortices in laminar superconductors using a density functional theory of freezing. The physical properties of the system along the melting line are discussed in detail. We show that there is a very good agreement with experimental data in the shape and position of the first order transition in the phase diagram and in the magnitude and temperature dependence of the magnetic induction jump at the transition. We analyze the validity of the Lindemann melting criterion and the Hansen-Verlet freezing criterion. Both criteria are shown to be good to predict the phase diagram in the region where a first order phase transition is experimentally observed.Comment: 9 pages, 10 figure