330 research outputs found
Galerkin Method in the Gravitational Collapse: a Dynamical System Approach
We study the general dynamics of the spherically symmetric gravitational
collapse of a massless scalar field. We apply the Galerkin projection method to
transform a system of partial differential equations into a set of ordinary
differential equations for modal coefficients, after a convenient truncation
procedure, largely applied to problems of turbulence. In the present case, we
have generated a finite dynamical system that reproduces the essential features
of the dynamics of the gravitational collapse, even for a lower order of
truncation. Each initial condition in the space of modal coefficients
corresponds to a well definite spatial distribution of scalar field. Numerical
experiments with the dynamical system show that depending on the strength of
the scalar field packet, the formation of black-holes or the dispersion of the
scalar field leaving behind flat spacetime are the two main outcomes. We also
found numerical evidence that between both asymptotic states, there is a
critical solution represented by a limit cycle in the modal space with period
.Comment: 9 pages, revtex4, 10 ps figures; Phys. Rev. D, in pres
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Optical study of orbital excitations in transition-metal oxides
The orbital excitations of a series of transition-metal compounds are studied by means of optical spectroscopy. Our aim was to identify signatures of collective orbital excitations by comparison with experimental and theoretical results for predominantly local crystal-field excitations. To this end, we have studied TiOCl, RTiO3 (R = La, Sm and Y), LaMnO3, Y2BaNiO5, CaCu2O3 and K4Cu4OCl10, ranging from early to late transition-metal ions, from t2g to eg systems, and including systems in which the exchange coupling is predominantly three-dimensional, one-dimensional or zero-dimensional. With the exception of LaMnO3, we find orbital excitations in all compounds. We discuss the competition between orbital fluctuations (for dominant exchange coupling) and crystal-field splitting (for dominant coupling to the lattice). Comparison of our experimental results with configuration-interaction cluster calculations in general yields good agreement, demonstrating that the coupling to the lattice is important for a quantitative description of the orbital excitations in these compounds. However, detailed theoretical predictions for the contribution of collective orbital modes to the optical conductivity (e.g. the line shape or the polarization dependence) are required to decide on a possible contribution of orbital fluctuations at low energies, in particular, in case of the orbital excitations at ≈0.25 eV in RTiO3. Further calculations are called for which take into account the exchange interactions between the orbitals and the coupling to the lattice on an equal footing
Advances in ab-initio theory of Multiferroics. Materials and mechanisms: modelling and understanding
Within the broad class of multiferroics (compounds showing a coexistence of
magnetism and ferroelectricity), we focus on the subclass of "improper
electronic ferroelectrics", i.e. correlated materials where electronic degrees
of freedom (such as spin, charge or orbital) drive ferroelectricity. In
particular, in spin-induced ferroelectrics, there is not only a {\em
coexistence} of the two intriguing magnetic and dipolar orders; rather, there
is such an intimate link that one drives the other, suggesting a giant
magnetoelectric coupling. Via first-principles approaches based on density
functional theory, we review the microscopic mechanisms at the basis of
multiferroicity in several compounds, ranging from transition metal oxides to
organic multiferroics (MFs) to organic-inorganic hybrids (i.e. metal-organic
frameworks, MOFs)Comment: 22 pages, 9 figure
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