Diffusive propagation of UHECR and the propagation theorem

We present a detailed analytical study of the propagation of ultra high energy (UHE) particles in extragalactic magnetic fields. The crucial parameter which affects the diffuse spectrum is the separation between sources. In the case of a uniform distribution of sources with a separation between them much smaller than all characteristic propagation lengths, the diffuse spectrum of UHE particles has a {\em universal} form, independent of the mode of propagation. This statement has a status of theorem. The proof is obtained using the particle number conservation during propagation, and also using the kinetic equation for the propagation of UHE particles. This theorem can be also proved with the help of the diffusion equation. In particular, it is shown numerically, how the diffuse fluxes converge to this universal spectrum, when the separation between sources diminishes. We study also the analytic solution of the diffusion equation in weak and strong magnetic fields with energy losses taken into account. In the case of strong magnetic fields and for a separation between sources large enough, the GZK cutoff can practically disappear, as it has been found early in numerical simulations. In practice, however, the source luminosities required are too large for this possibility.Comment: 16 pages, 13 eps figures, discussion of the absence of the GZK cut-off in strong magnetic field added, a misprint in figure 6 corrected, version accepted for publication in Ap

3D Simulations of MHD Jet Propagation Through Uniform and Stratified External Environments

We present a set of high-resolution 3D MHD simulations of steady light, supersonic jets, exploring the influence of jet Mach number and the ambient medium on jet propagation and energy deposition over long distances. The results are compared to simple self-similar scaling relations for the morphological evolution of jet-driven structures and to previously published 2D simulations. For this study we simulated the propagation of light jets with internal Mach numbers 3 and 12 to lengths exceeding 100 initial jet radii in both uniform and stratified atmospheres. The propagating jets asymptotically deposit approximately half of their energy flux as thermal energy in the ambient atmosphere, almost independent of jet Mach number or the external density gradient. Nearly one-quarter of the jet total energy flux goes directly into dissipative heating of the ICM, supporting arguments for effective feedback from AGNs to cluster media. The remaining energy resides primarily in the jet and cocoon structures. Despite having different shock distributions and magnetic field features, global trends in energy flow are similar among the different models. As expected the jets advance more rapidly through stratified atmospheres than uniform environments. The asymptotic head velocity in King-type atmospheres shows little or no deceleration. This contrasts with jets in uniform media with heads that are slowed as they propagate. This suggests that the energy deposited by jets of a given length and power depends strongly on the structure of the ambient medium. While our low-Mach jets are more easily disrupted, their cocoons obey evolutionary scaling relations similar to the high-Mach jets.Comment: Accepted in ApJ, 32 pages, 18 figures, animations available from: http://www.msi.umn.edu/Projects/twj/newsite/projects/radiojets/movies

Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice

There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appear to be a plethora of low energy excitations, predominantly singlets but also spin carrying, which suggest that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-1/2 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux-smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by (2+1)-dimensional quantum electrodynamics (QED$_3$) with an emergent $\mathrm{SU}(8)$ flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.Comment: 14 pages, 8 figure

Field-driven topological glass transition in a model flux line lattice

We show that the flux line lattice in a model layered HTSC becomes unstable above a critical magnetic field with respect to a plastic deformation via penetration of pairs of point-like disclination defects. The instability is characterized by the competition between the elastic and the pinning energies and is essentially assisted by softening of the lattice induced by a dimensional crossover of the fluctuations as field increases. We confirm through a computer simulation that this indeed may lead to a phase transition from crystalline order at low fields to a topologically disordered phase at higher fields. We propose that this mechanism provides a model of the low temperature field--driven disordering transition observed in neutron diffraction experiments on ${\rm Bi_2Sr_2CaCu_2O_8\, }$ single crystals.Comment: 11 pages, 4 figures available upon request via snail mail from [email protected]

Holographic Renormalization of Foliation Preserving Gravity and Trace Anomaly

From the holographic renormalizationg group viewpoint, while the scale transformation plays a primary role in the duality by providing the extra dimension, the special conformal transformation seems to only play a secondary role. We, however, claim that the space-time diffeomorphism is crucially related to the latter. For its demonstration, we study the holographic renormalization group flow of a foliation preserving diffeomophic theory of gravity (a.k.a. space-time flipped Horava gravity). We find that the dual field theory, if any, is only scale invariant but not conformal invariant. In particular, we show that the holographic trace anomaly in four-dimension predicts the Ricci scalar squared term that would be incompatible with the Wess-Zumino consistency condition if it were conformal. This illustrates how the foliation preserving diffeomophic theory of gravity could be inconsistent with a theorem of the dual unitary quantum field theory.Comment: 18 pages, v2: reference added, v3: comments on more recent literature added in response to referee's reques

Magnetic domain wall motion in a nanowire: depinning and creep

The domain wall motion in a magnetic nanowire is examined theoretically in the regime where the domain wall driving force is weak and its competition against disorders is assisted by thermal agitations. Two types of driving forces are considered; magnetic field and current. While the field induces the domain wall motion through the Zeeman energy, the current induces the domain wall motion by generating the spin transfer torque, of which effects in this regime remain controversial. The spin transfer torque has two mutually orthogonal vector components, the adiabatic spin transfer torque and the nonadiabatic spin transfer torque. We investigate separate effects of the two components on the domain wall depinning rate in one-dimensional systems and on the domain wall creep velocity in two-dimensional systems, both below the Walker breakdown threshold. In addition to the leading order contribution coming from the field and/or the nonadiabatic spin transfer torque, we find that the adiabatic spin transfer torque generates corrections, which can be of relevance for an unambiguous analysis of experimental results. For instance, it is demonstrated that the neglect of the corrections in experimental analysis may lead to incorrect evaluation of the nonadiabaticity parameter. Effects of the Rashba spin-orbit coupling on the domain wall motion are also analyzed.Comment: 14 pages, 3 figure

Dynamical Phase Transition in a Driven Disordered Vortex Lattice

Using Langevin dynamics, we have investigated the dynamics of vortices in a disordered two dimensional superconductor subjected to a uniform driving current. The results provide direct numerical evidence for a dynamical phase transition between a plastic flow regime and a moving ``hexatic glass." The simulated current-voltage characteristics are in excellent agreement with recent transport measurements on amorphous ${\rm Mo_{77}Ge_{23}}$ thin film superconductors.Comment: 13 pages, latex, revtex, 4 figures available upon request from [email protected]

Vacillation, indecision and hesitation in moment-by-moment decoding of monkey motor cortex

When choosing actions, we can act decisively, vacillate, or suffer momentary indecision. Studying how individual decisions unfold requires moment-by-moment readouts of brain state. Here we provide such a view from dorsal premotor and primary motor cortex. Two monkeys performed a novel decision task while we recorded from many neurons simultaneously. We found that a decoder trained using 'forced choices' (one target viable) was highly reliable when applied to 'free choices'. However, during free choices internal events formed three categories. Typically, neural activity was consistent with rapid, unwavering choices. Sometimes, though, we observed presumed 'changes of mind': the neural state initially reflected one choice before changing to reflect the final choice. Finally, we observed momentary 'indecision': delay forming any clear motor plan. Further, moments of neural indecision accompanied moments of behavioral indecision. Together, these results reveal the rich and diverse set of internal events long suspected to occur during free choice