Optical sum rule violation, superfluid weight and condensation energy in the cuprates

The model of hole superconductivity predicts that the superfluid weight in the zero-frequency $\delta$-function in the optical conductivity has an anomalous contribution from high frequencies, due to lowering of the system's kinetic energy upon entering the superconducting state. The lowering of kinetic energy, mainly in-plane in origin, accounts for both the condensation energy of the superconductor as well as an increased potential energy due to larger Coulomb repulsion in the paired state. It leads to an apparent violation of the conductivity sum rule, which in the clean limit we predict to be substantially larger for in-plane than for c-axis conductivity. However, because cuprates are in the dirty limit for c-axis transport, the sum rule violation is found to be greatly enhanced in the c-direction. The model predicts the sum rule violation to be largest in the underdoped regime and to decrease with doping, more rapidly in the c-direction that in the plane. So far, experiments have detected sum rule violation in c-axis transport in several cuprates, as well as a decrease and disappearance of this violation for increasing doping, but no violation in-plane. We explore the predictions of the model for a wide range of parameters, both in the absence and in the presence of disorder, and the relation with current experimental knowledge.Comment: submitted to Phys.Rev.

Flat Information Geometries in Black Hole Thermodynamics

The Hessian of either the entropy or the energy function can be regarded as a metric on a Gibbs surface. For two parameter families of asymptotically flat black holes in arbitrary dimension one or the other of these metrics are flat, and the state space is a flat wedge. The mathematical reason for this is traced back to the scale invariance of the Einstein-Maxwell equations. The picture of state space that we obtain makes some properties such as the occurence of divergent specific heats transparent.Comment: 14 pages, one figure. Dedicated to Rafael Sorkin's birthda

Optical Sum Rule anomalies in the High-Tc Cuprates

We provide a brief summary of the observed sum rule anomalies in the high-T$_c$ cuprate materials. A recent issue has been the impact of a non-infinite frequency cutoff in the experiment. In the normal state, the observed anomalously high temperature dependence can be explained as a `cutoff effect'. The anomalous rise in the optical spectral weight below the superconducting transition, however, remains as a solid experimental observation, even with the use of a cutoff frequency.Comment: 4 pages, 2 figures, very brief review of optical sum rule anomal

Conductivity sum rule, implication for in-plane dynamics and c-axis response

Recently observed $c$-axis optical sum rule violations indicate non-Fermi liquid in-plane behavior. For coherent $c$-axis coupling, the observed flat, nearly frequency independent $c$-axis conductivity $\sigma_{1}(\omega)$ implies a large in-plane scattering rate $\Gamma$ around $(0,\pi)$ and therefore any pseudogap that might form at low frequency in the normal state will be smeared. On the other hand incoherent $c$-axis coupling places no restriction on the value of $\Gamma$ and gives a more consistent picture of the observed sum rule violation which, we find in some cases, can be less than half.Comment: 3 figures. To appear in PR

Evolution of high-frequency gravitational waves in some cosmological models

We investigate Isaacson's high-frequency gravitational waves which propagate in some relevant cosmological models, in particular the FRW spacetimes. Their time evolution in Fourier space is explicitly obtained for various metric forms of (anti--)de Sitter universe. Behaviour of high-frequency waves in the anisotropic Kasner spacetime is also described.Comment: 14 pages, 8 figures, to appear in Czech. J. Phy

The Electric Dipole Moment of the Nucleons in Holographic QCD

We introduce the strong CP-violation in the framework of AdS/QCD model and calculate the electric dipole moments of nucleons as well as the CP-violating pion-nucleon coupling. Our holographic estimate of the electric dipole moments gives for the neutron d_n=1.08 X 10^{-16} theta (e cm), which is comparable with previous estimates. We also predict that the electric dipole moment of the proton should be precisely the minus of the neutron electric dipole moment, thus leading to a new sum rule on the electric dipole moments of baryons.Comment: 22 pages, no figures. v2: A reference and an acknowledgment added. v3: One more reference, to appear in JHE

Activated Random Walkers: Facts, Conjectures and Challenges

We study a particle system with hopping (random walk) dynamics on the integer lattice $\mathbb Z^d$. The particles can exist in two states, active or inactive (sleeping); only the former can hop. The dynamics conserves the number of particles; there is no limit on the number of particles at a given site. Isolated active particles fall asleep at rate $\lambda > 0$, and then remain asleep until joined by another particle at the same site. The state in which all particles are inactive is absorbing. Whether activity continues at long times depends on the relation between the particle density $\zeta$ and the sleeping rate $\lambda$. We discuss the general case, and then, for the one-dimensional totally asymmetric case, study the phase transition between an active phase (for sufficiently large particle densities and/or small $\lambda$) and an absorbing one. We also present arguments regarding the asymptotic mean hopping velocity in the active phase, the rate of fixation in the absorbing phase, and survival of the infinite system at criticality. Using mean-field theory and Monte Carlo simulation, we locate the phase boundary. The phase transition appears to be continuous in both the symmetric and asymmetric versions of the process, but the critical behavior is very different. The former case is characterized by simple integer or rational values for critical exponents ($\beta = 1$, for example), and the phase diagram is in accord with the prediction of mean-field theory. We present evidence that the symmetric version belongs to the universality class of conserved stochastic sandpiles, also known as conserved directed percolation. Simulations also reveal an interesting transient phenomenon of damped oscillations in the activity density

The Fayet-Iliopoulos D-term and its renormalisation in the MSSM

We consider the renormalisation of the Fayet-Iliopoulos D-term in a softly-broken supersymmetric gauge theory with a non-simple gauge group containing an abelian factor, and present the associated beta-function through three loops. We also include in an appendix the result for several abelian factors. We specialise to the case of the minimal supersymmetric standard model (MSSM), and investigate the behaviour of the Fayet-Iliopoulos coupling for various boundary conditions at the unification scale. We focus particularly on the case of non-standard soft supersymmetry breaking couplings, for which the Fayet-Iliopoulos coupling evolves significantly between the unification scale and the weak scale.Comment: 18 pages, Revtex, 2 figures. Expanded version including general results for gauge groups with several abelian factors. Minor typos correcte

Constraints on the Local Sources of Ultra High-Energy Cosmic Rays

Ultra high-energy cosmic rays (UHECRs) are believed to be protons accelerated in magnetized plasma outflows of extra-Galactic sources. The acceleration of protons to ~10^{20} eV requires a source power L>10^{47} erg/s. The absence of steady sources of sufficient power within the GZK horizon of 100 Mpc, implies that UHECR sources are transient. We show that UHECR "flares" should be accompanied by strong X-ray and gamma-ray emission, and that X-ray and gamma-ray surveys constrain flares which last less than a decade to satisfy at least one of the following conditions: (i) L>10^{50} erg/s; (ii) the power carried by accelerated electrons is lower by a factor >10^2 than the power carried by magnetic fields or by >10^3 than the power in accelerated protons; or (iii) the sources exist only at low redshifts, z<<1. The implausibility of requirements (ii) and (iii) argue in favor of transient sources with L>10^{50} erg/s.Comment: 7 pages, 1 figure, submitted to JCA

An Emerging Model of Creative Game-based Learning

We consider the integration of creative approaches to problem solving into pervasive games is a natural extension of play for creative thinking – one that can innovatively drive technology-led changes to the facilitation of creative thinking and pose a new genre in serious gaming for learning. This paper presents an initial proposal of a new model of creative game-base learning (CGBL), which emerged through mapping of established characteristics of climates that encourage creativity and innovation to characteristics of effective serious games