Density-matrix spectra for integrable models

The spectra which occur in numerical density-matrix renormalization group (DMRG) calculations for quantum chains can be obtained analytically for integrable models via corner transfer matrices. This is shown in detail for the transverse Ising chain and the uniaxial XXZ Heisenberg model and explains in particular their exponential character in these cases.Comment: 14 pages, 7 figures, to appear in Ann. Physi

On network representations of antennas inside resonating environments

We discuss network representations of dipole antennas within electromagnetic cavities. It is pointed out that for a given configuration these representations are not unique. For an efficient evaluation a network representation should be chosen such that it involves as few network elements as possible. The field theoretical analogue of this circumstance is the possibility to express electromagnetic cavities' Green's functions by representations which exhibit different convergence properties. An explicit example of a dipole antenna within a rectangular cavity clarifies the corresponding interrelation between network theory and electromagnetic field theory. As an application, current spectra are calculated for the case that the antenna is nonlinearly loaded and subject to a two-tone excitation

On Measuring Gravitomagnetism via Spaceborne Clocks: A Gravitomagnetic Clock Effect

DOI:10.1002/(SICI)1521-3889(199902)8:2<135The difference in the proper azimuthal periods of revolution of two standard clocks in direct and retrograde orbits about a central rotating mass is proportional to J/Mc^2, where J and M are, respectively, the proper angular momentum and mass of the source. In connection with this gravitomagnetic clock effect, we explore the possibility of using spaceborne standard clocks for detecting the gravitomagnetic field of the Earth. It is shown that this approach to the measurement of the gravitomagnetic field is, in a certain sense, theoretically equivalent to the Gravity Probe-B concept.This work has been supported in part by the Alexander von Humboldt Foundation

Non Singular Origin of the Universe and its Present Vacuum Energy Density

We consider a non singular origin for the Universe starting from an Einstein static Universe, the so called "emergent universe" scenario, in the framework of a theory which uses two volume elements $\sqrt{-{g}}d^{4}x$ and $\Phi d^{4}x$, where $\Phi$ is a metric independent density, used as an additional measure of integration. Also curvature, curvature square terms and for scale invariance a dilaton field $\phi$ are considered in the action. The first order formalism is applied. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of scale invariance (S.I.). After S.S.B. of S.I., it is found that a non trivial potential for the dilaton is generated. In the Einstein frame we also add a cosmological term that parametrizes the zero point fluctuations. The resulting effective potential for the dilaton contains two flat regions, for $\phi \rightarrow \infty$ relevant for the non singular origin of the Universe, followed by an inflationary phase and $\phi \rightarrow -\infty$, describing our present Universe. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emergent universe solutions, which exists for a parameter range of values of the vacuum energy in $\phi \rightarrow -\infty$, which must be positive but not very big, avoiding the extreme fine tuning required to keep the vacuum energy density of the present universe small. Zero vacuum energy density for the present universe defines the threshold for the creation of the universe.Comment: 28 pages, short version of this paper awarded an honorable mention by the Gravity Research Foundation, 2011, accepted for publication in International Journal of Modern Physics

Gravity on a parallelizable manifold. Exact solutions

The wave type field equation \square \vt^a=\la \vt^a, where \vt^a is a coframe field on a space-time, was recently proposed to describe the gravity field. This equation has a unique static, spherical-symmetric, asymptotically-flat solution, which leads to the viable Yilmaz-Rosen metric. We show that the wave type field equation is satisfied by the pseudo-conformal frame if the conformal factor is determined by a scalar 3D-harmonic function. This function can be related to the Newtonian potential of classical gravity. So we obtain a direct relation between the non-relativistic gravity and the relativistic model: every classical exact solution leads to a solution of the field equation. With this result we obtain a wide class of exact, static metrics. We show that the theory of Yilmaz relates to the pseudo-conformal sector of our construction. We derive also a unique cosmological (time dependent) solution of the described type.Comment: Latex, 17 page

Volume elements of spacetime and a quartet of scalar fields

Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density \sigma. Whereas conventionally \sqrt{|\det g_{ij}|} is used for that purpose, with g_{ij} as the components of the metric, we point out other possibilities, namely \sigma as a `dilaton' field or as a derived quantity from either a linear connection or a quartet of scalar fields, as suggested by Guendelman and Kaganovich.Comment: 7 pages RevTEX, submitted to Phys. Rev.

Torsion and the Gravitational Interaction

By using a nonholonomous-frame formulation of the general covariance principle, seen as an active version of the strong equivalence principle, an analysis of the gravitational coupling prescription in the presence of curvature and torsion is made. The coupling prescription implied by this principle is found to be always equivalent with that of general relativity, a result that reinforces the completeness of this theory, as well as the teleparallel point of view according to which torsion does not represent additional degrees of freedom for gravity, but simply an alternative way of representing the gravitational field.Comment: Version 2: minor presentation changes, a reference added, 11 pages (IOP style

Observation of anomalously strong penetration of terahertz electric field through terahertz-opaque gold films into a GaAs/AlGaAs quantum well

We observe an anomalously high electric field of terahertz (THz) radiation acting on a two-dimensional electron gas (2DEG) placed beneath a thin gold film, which, however, is supposed to be opaque at THz frequencies. We show that the anomalously strong penetration of the THz electric field through a very high conductive gold film emerges if two conditions are fulfilled simultaneously: (i) the film's thickness is less than the skin depth and (ii) the THz electric field is measured beneath the film at distances substantially smaller than the radiation wavelength. We demonstrate that under these conditions the strength of the field acting on a 2DEG is almost the same as it would be in the absence of the gold film. The effect is detected for macroscopically homogeneous perforation-free gold films illuminated by THz-laser radiation with a spot smaller than the film area. This eliminates the near-field of the edge diffraction as a possible cause of the anomalous penetration. The microscopic origin of the effect remains unexplained in its details, yet. The observed effect can be used for the development of THz devices based on two-dimensional materials requiring robust highly conducting top gates placed at less than nanometer distance from the electron gas location

Wave propagation in axion electrodynamics

In this paper, the axion contribution to the electromagnetic wave propagation is studied. First we show how the axion electrodynamics model can be embedded into a premetric formalism of Maxwell electrodynamics. In this formalism, the axion field is not an arbitrary added Chern-Simon term of the Lagrangian, but emerges in a natural way as an irreducible part of a general constitutive tensor.We show that in order to represent the axion contribution to the wave propagation it is necessary to go beyond the geometric approximation, which is usually used in the premetric formalism. We derive a covariant dispersion relation for the axion modified electrodynamics. The wave propagation in this model is studied for an axion field with timelike, spacelike and null derivative covectors. The birefringence effect emerges in all these classes as a signal of Lorentz violation. This effect is however completely different from the ordinary birefringence appearing in classical optics and in premetric electrodynamics. The axion field does not simple double the ordinary light cone structure. In fact, it modifies the global topological structure of light cones surfaces. In CFJ-electrodynamics, such a modification results in violation of causality. In addition, the optical metrics in axion electrodynamics are not pseudo-Riemannian. In fact, for all types of the axion field, they are even non-Finslerian

Emerging Universe from Scale Invariance

We consider a scale invariant model which includes a $R^{2}$ term in action and show that a stable "emerging universe" scenario is possible. The model belongs to the general class of theories, where an integration measure independent of the metric is introduced. To implement scale invariance (S.I.), a dilaton field is introduced. The integration of the equations of motion associated with the new measure gives rise to the spontaneous symmetry breaking (S.S.B) of S.I. After S.S.B. of S.I. in the model with the $R^{2}$ term (and first order formalism applied), it is found that a non trivial potential for the dilaton is generated. The dynamics of the scalar field becomes non linear and these non linearities are instrumental in the stability of some of the emerging universe solutions, which exists for a parameter range of the theory.Comment: 21 pages, 4 figures. Accepted for publication in JCA