The Onset of Intermittency in Stochastic Burgers Hydrodynamics

We study the onset of intermittency in stochastic Burgers hydrodynamics, as characterized by the statistical behavior of negative velocity gradient fluctuations. The analysis is based on the response functional formalism, where specific velocity configurations - the viscous instantons - are assumed to play a dominant role in modeling the left tails of velocity gradient probability distribution functions. We find, as expected on general grounds, that the field theoretical approach becomes meaningful in practice only if the effects of fluctuations around instantons are taken into account. Working with a systematic cumulant expansion, it turns out that the integration of fluctuations yields, in leading perturbative order, to an effective description of the Burgers stochastic dynamics given by the renormalization of its associated heat kernel propagator and the external force-force correlation function.Comment: 10 pages, 6 figure

Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride

DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a perturbative expansion of the density matrix. This allows a microscopic description of the quadratic response to an electromagnetic field in these materials, which we analyze as a function of temperature and electron density. We find that the intrinsic response is robust across these systems and allows for currents in the range of pA cm/W to nA cm/W. At the independent-particle level, the response of hBN-based structures is significant only in the ultra-violet due to their sizeable band-gap. However, when Coulomb interactions are accounted for by explicit solution of the Bethe-Salpeter equation, we find that the photoconductivity is strongly modified by transitions involving exciton levels in the gap region, whose spectral weight dominates in the overall frequency range. Biased bilayers and gapped monolayers of graphene have a strong photoconductivity in the visible and infrared window, allowing for photocurrent densities of several nA cm/W. We further show that the richer electronic dispersion of BBG at low energies and the ability to change its band-gap on demand allows a higher tunability of the photocurrent, including not only its magnitude but also, and significantly, its polarity.Comment: Updating with published version and respective references; 14 pages, 11 figure

Dynamics of molecular nanomagnets in time-dependent external magnetic fields: Beyond the Landau-Zener-St\"{u}ckelberg model

The time evolution of the magnetization of a magnetic molecular crystal is obtained in an external time-dependent magnetic field, with sweep rates in the kT/s range. We present the 'exact numerical' solution of the time dependent Schr\"{o}dinger equation, and show that the steps in the hysteresis curve can be described as a sequence of two-level transitions between adiabatic states. The multilevel nature of the problem causes the transition probabilities to deviate significantly from the predictions of the Landau-Zener-St\"{u}ckelberg model. These calculations allow the introduction of an efficient approximation method that accurately reproduces the exact results. When including phase relaxation by means of an appropriate master equation, we observe an interplay between coherent dynamics and decoherence. This decreases the size of the magnetization steps at the transitions, but does not modify qualitatively the physical picture obtained without relaxation.Comment: 8 pages, 7 figure

Tkachenko polarons in vortex lattices

We analyze the properties of impurities immersed in a vortex lattice formed by ultracold bosons in the mean field quantum Hall regime. In addition to the effects of a periodic lattice potential, the impurity is dressed by collective modes with parabolic dispersion (Tkachenko modes). We derive the effective polaron model, which contains a marginal impurity-phonon interaction. The polaron spectral function exhibits a Lorentzian broadening for arbitrarily small wave vectors even at zero temperature, in contrast with the result for optical or acoustic phonons. The anomalous damping of Tkachenko polarons could be detected experimentally using momentum-resolved spectroscopy.Comment: 10 pages, 2 figure

Kinematics of a Spacetime with an Infinite Cosmological Constant

A solution of the sourceless Einstein's equation with an infinite value for the cosmological constant \Lambda is discussed by using Inonu-Wigner contractions of the de Sitter groups and spaces. When \Lambda --> infinity, spacetime becomes a four-dimensional cone, dual to Minkowski space by a spacetime inversion. This inversion relates the four-cone vertex to the infinity of Minkowski space, and the four-cone infinity to the Minkowski light-cone. The non-relativistic limit c --> infinity is further considered, the kinematical group in this case being a modified Galilei group in which the space and time translations are replaced by the non-relativistic limits of the corresponding proper conformal transformations. This group presents the same abstract Lie algebra as the Galilei group and can be named the conformal Galilei group. The results may be of interest to the early Universe Cosmology.Comment: RevTex, 7 pages, no figures. Presentation changes, including a new Title. Version to appear in Found. Phys. Let

Gravitation and the Local Symmetry Group of Spacetime

According to general relativity, the interaction of a matter field with gravitation requires the simultaneous introduction of a tetrad field, which is a field related to translations, and a spin connection, which is a field assuming values in the Lie algebra of the Lorentz group. These two fields, however, are not independent. By analyzing the constraint between them, it is concluded that the relevant local symmetry group behind general relativity is provided by the Lorentz group. Furthermore, it is shown that the minimal coupling prescription obtained from the Lorentz covariant derivative coincides exactly with the usual coupling prescription of general relativity. Instead of the tetrad, therefore, the spin connection is to be considered as the fundamental field representing gravitation.Comment: 8 pages, no figures. Some signs and references corrected; version to appear in Int. J. Theor. Phy