Transitions in non-conserving models of Self-Organized Criticality

We investigate a random--neighbours version of the two dimensional non-conserving earthquake model of Olami, Feder and Christensen [Phys. Rev. Lett. {\bf 68}, 1244 (1992)]. We show both analytically and numerically that criticality can be expected even in the presence of dissipation. As the critical level of conservation, $\alpha_c$, is approached, the cut--off of the avalanche size distribution scales as $\xi\sim(\alpha_c-\alpha)^{-3/2}$. The transition from non-SOC to SOC behaviour is controlled by the average branching ratio $\sigma$ of an avalanche, which can thus be regarded as an order parameter of the system. The relevance of the results are discussed in connection to the nearest-neighbours OFC model (in particular we analyse the relevance of synchronization in the latter).Comment: 8 pages in latex format; 5 figures available upon reques

Universality of Electron Mobility in LaAlO3_3/SrTiO3_3 and bulk SrTiO3_3

Metallic LaAlO$_3$/SrTiO$_3$ (LAO/STO) interfaces attract enormous attention, but the relationship between the electron mobility and the sheet electron density, $n_s$, is poorly understood. Here we derive a simple expression for the three-dimensional electron density near the interface, $n_{3D}$, as a function of $n_s$ and find that the mobility for LAO/STO-based interfaces depends on $n_{3D}$ in the same way as it does for bulk doped STO. It is known that undoped bulk STO is strongly compensated with $N \simeq 5 \times 10^{18}~\rm{cm^{-3}}$ background donors and acceptors. In intentionally doped bulk STO with a concentration of electrons $n_{3D} < N$ background impurities determine the electron scattering. Thus, when $n_{3D} < N$ it is natural to see in LAO/STO the same mobility as in the bulk. On the other hand, in the bulk samples with $n_{3D} > N$ the mobility collapses because scattering happens on $n_{3D}$ intentionally introduced donors. For LAO/STO the polar catastrophe which provides electrons is not supposed to provide equal number of random donors and thus the mobility should be larger. The fact that the mobility is still the same implies that for the LAO/STO the polar catastrophe model should be revisited.Comment: 4 pages and 1 figur

Classical Trace Anomaly

We seek an analogy of the mathematical form of the alternative form of Einstein's field equations for Lovelock's field equations. We find that the price for this analogy is to accept the existence of the trace anomaly of the energy-momentum tensor even in classical treatments. As an example, we take this analogy to any generic second order Lagrangian and exactly derive the trace anomaly relation suggested by Duff. This indicates that an intrinsic reason for the existence of such a relation should perhaps be, classically, somehow related to the covariance of the form of Einstein's equations.Comment: Version 2: 21 pages, TeX file (using phyzzx.tex), added new section and references. Version 3: Just replaced Abstrac

Numerical indications on the semiclassical limit of the flipped vertex

We introduce a technique for testing the semiclassical limit of a quantum gravity vertex amplitude. The technique is based on the propagation of a semiclassical wave packet. We apply this technique to the newly introduced "flipped" vertex in loop quantum gravity, in order to test the intertwiner dependence of the vertex. Under some drastic simplifications, we find very preliminary, but surprisingly good numerical evidence for the correct classical limit.Comment: 4 pages, 8 figure

Cosmological Constraints on Dissipative Models of Inflation

(Abridged) We study dissipative inflation in the regime where the dissipative term takes a specific form, \Gamma=\Gamma(\phi), analyzing two models in the weak and strong dissipative regimes with a SUSY breaking potential. After developing intuition about the predictions from these models through analytic approximations, we compute the predicted cosmological observables through full numerical evolution of the equations of motion, relating the mass scale and scale of dissipation to the characteristic amplitude and shape of the primordial power spectrum. We then use Markov Chain Monte Carlo techniques to constrain a subset of the models with cosmological data from the cosmic microwave background (WMAP three-year data) and large scale structure (SDSS Luminous Red Galaxy power spectrum). We find that the posterior distributions of the dissipative parameters are highly non-Gaussian and their allowed ranges agree well with the expectations obtained using analytic approximations. In the weak regime, only the mass scale is tightly constrained; conversely, in the strong regime, only the dissipative coefficient is tightly constrained. A lower limit is seen on the inflation scale: a sub-Planckian inflaton is disfavoured by the data. In both weak and strong regimes, we reconstruct the limits on the primordial power spectrum and show that these models prefer a {\it red} spectrum, with no significant running of the index. We calculate the reheat temperature and show that the gravitino problem can be overcome with large dissipation, which in turn leads to large levels of non-Gaussianity: if dissipative inflation is to evade the gravitino problem, the predicted level of non-Gaussianity might be seen by the Planck satellite.Comment: 14 pages, 9 figures, Accepted by JCAP without text changes, References adde

Equations of Motion of Spinning Relativistic Particle in Electromagnetic and Gravitational Fields

We consider the motion of a spinning relativistic particle in external electromagnetic and gravitational fields, to first order in the external field, but to an arbitrary order in spin. The noncovariant spin formalism is crucial for the correct description of the influence of the spin on the particle trajectory. We show that the true coordinate of a relativistic spinning particle is its naive, common coordinate \r. Concrete calculations are performed up to second order in spin included. A simple derivation is presented for the gravitational spin-orbit and spin-spin interactions of a relativistic particle. We discuss the gravimagnetic moment (GM), a specific spin effect in general relativity. It is shown that for the Kerr black hole the gravimagnetic ratio, i.e., the coefficient at the GM, equals unity (just as for the charged Kerr hole the gyromagnetic ratio equals two). The equations of motion obtained for relativistic spinning particle in external gravitational field differ essentially from the Papapetrou equations.Comment: 32 pages, latex, Plenary talk at the Fairbank Meeting on the Lense--Thirring Effect, Rome-Pescara, 29/6-4/7 199