Realizations of Poincar group induced by second order differential systems. Non interaction theorem

A generalization of the predictive relativistic mechanics is studied where the initial conditions are taken on a general hypersurface of M4. The induced realizations of the Poincar group are obtained. The same procedure is used for the Galileo group. Noninteraction theorems are derived for both groups.

Generalized adiabatic invariance

In this paper we find the quantities that are adiabatic invariants of any desired order for a general slowly time-dependent Hamiltonian. In a preceding paper, we chose a quantity that was initially an adiabatic invariant to first order, and sought the conditions to be imposed upon the Hamiltonian so that the quantum mechanical adiabatic theorem would be valid to mth order. [We found that this occurs when the first (m - 1) time derivatives of the Hamiltonian at the initial and final time instants are equal to zero.] Here we look for a quantity that is an adiabatic invariant to mth order for any Hamiltonian that changes slowly in time, and that does not fulfill any special condition (its first time derivatives are not zero initially and finally).

General Interaction Picture from Action Principle for Mechanics

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.

Classical predictive electrodynamics of two charges with radiation: General framework. I.

Outgoing radiation is introduced in the framework of the classical predictive electrodynamics using LorentzDiracs equation as a subsidiary condition. In a perturbative scheme in the charges the first radiative self-terms of the accelerations, momentum and angular momentum of a two charge system without external field are calculated.

On the spinning axis representation

A new spinning axis representation is introduced. It allows us to calculate the evolution operator of a system with slowly varying time dependent Hamiltonian with the desired degree of approximation in the parameter used for describing its dynamical evolution. The procedure is compared with a previously existing one and applied to a simple example.

Contribuciones de Einstein a la teoría cuántica (1905-1925)

El mito Einstein se ha formado básicamente en torno a sus teorías relativistas que, entre otras implicaciones, conducían a una original concepción del espacio-tiempo e incluso a una nueva forma de descripción del mundo físico. No obstante, sus contribuciones a la teoría cuántica -aunque no tan divulgadas- son de tal envergadura que por sí solas constituyen un aporte más que suficiente para que su autor ocupara un destacadísimo lugar entre los grandes creadores científicos de todos los tiempos. En el presente trabajo nos proponemos justificar tan categórica afirmación, empleando los medios que la historiografía moderna ofrece e incluyendo también resultados de algunas investigaciones propias.

Strange nonchaotic attractors in Harper maps

We study the existence of strange nonchaotic attractors (SNA) in the family of Harper maps. We prove that for a set of parameters of positive measure, the map possesses a SNA. However, the set is nowhere dense. By changing the parameter arbitrarily small amounts, the attractor is a smooth curve and not a SNA.

Front propagation in spatially modulated media

A two-dimensional reaction-diffusion front which propagates in a modulated medium is studied. The modulation consists of a spatial variation of the local front velocity in the transverse direction to that of the front propagation. We study analytically and numerically the final steady-state velocity and shape of the front, resulting from a nontrivial interplay between the local curvature effects and the global competition process between different maxima of the control parameter. The transient dynamics of the process is also studied numerically and analytically by means of singular perturbation techniques.

Wave competition in excitable modulated media.

The propagation of an initially planar front is studied within the framework of the photosensitive Belousov-Zhabotinsky reaction modulated by a smooth spatial variation of the local front velocity in the direction perpendicular to front propagation. Under this modulation, the wave front develops several fingers corresponding to the local maxima of the modulation function. After a transient, the wave front achieves a stationary shape that does not necessarily coincide with the one externally imposed by the modulation. Theoretical predictions for the selection criteria of fingers and steady-state velocity are experimentally validated.

Percolation thresholds in chemical disordered excitable media

The behavior of chemical waves advancing through a disordered excitable medium is investigated in terms of percolation theory and autowave properties in the framework of the light-sensitive Belousov-Zhabotinsky reaction. By controlling the number of sites with a given illumination, different percolation thresholds for propagation are observed, which depend on the relative wave transmittances of the two-state medium considered.

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations.

External Fluctuations in Front Propagation

We study the effects of external noise in a one-dimensional model of front propagation. Noise is introduced through the fluctuations of a control parameter leading to a multiplicative stochastic partial differential equation. Analytical and numerical results for the front shape and velocity are presented. The linear-marginal-stability theory is found to increase its range of validity in the presence of external noise. As a consequence noise can stabilize fronts not allowed by the deterministic equation.

Space and momentum representation analysis of Hartman's effect in wave packet transmission

The Hartman effect is analyzed in both the position and momentum representations of the problem. The importance of Wigner tunneling and deep tunneling is singled out. It is shown quantitatively how the barrier acts as a filter for low momenta (quantum speed up) as the width increases, and a detailed mechanism is proposed. Superluminal transmission is also discussed.

Coisotropic regularization of singular Lagrangians

We present an alternative approach to the usual treatments of singular Lagrangians. It is based on a Hamiltonian regularization scheme inspired on the coisotropic embedding of presymplectic systems. A Lagrangian regularization of a singular Lagrangian is a regular Lagrangian defined on an extended velocity phase space that reproduces the original theory when restricted to the initial configuration space. A Lagrangian regularization does not always exists, but a family of singular Lagrangians is studied for which such a regularization can be described explicitly. These regularizations turn out to be essentially unique and provide an alternative setting to quantize the corresponding physical systems. These ideas can be applied both in classical mechanics and field theories. Several examples are discussed in detail. 1995 American Institute of Physics.

Silicon quantum dots embedded in a SiO2 matrix: From structural study to carrier transport properties

We study the details of electronic transport related to the atomistic structure of silicon quantum dots embedded in a silicon dioxide matrix using ab initio calculations of the density of states. Several structural and composition features of quantum dots (QDs), such as diameter and amorphization level, are studied and correlated with transport under transfer Hamiltonian formalism. The current is strongly dependent on the QD density of states and on the conduction gap, both dependent on the dot diameter. In particular, as size increases, the available states inside the QD increase, while the QD band gap decreases due to relaxation of quantum confinement. Both effects contribute to increasing the current with the dot size. Besides, valence band offset between the band edges of the QD and the silica, and conduction band offset in a minor grade, increases with the QD diameter up to the theoretical value corresponding to planar heterostructures, thus decreasing the tunneling transmission probability and hence the total current. We discuss the influence of these parameters on electron and hole transport, evidencing a correlation between the electron (hole) barrier value and the electron (hole) current, and obtaining a general enhancement of the electron (hole) transport for larger (smaller) QD. Finally, we show that crystalline and amorphous structures exhibit enhanced probability of hole and electron current, respectively.