1.- Energetics and Dynamics of Small Molecular Clusters

            To attain accurate description of their properties and an understanding of the nanoscopic behavior of atomic and
             molecular clusters (and, ultimately, of the condensed phase of materials) requires a correspondingly accurate and
             realistic knowledge of their intermolecular forces. In particular, ensembles of variable size which are made up of
             fairly simple components such as the neutral, identical rare gases have been for a long time the preferred testing
             ground for a broad variety of theoretical and computational analysis of such intermolecular forces.

             Small clusters of Helium (in particular, dimers and trimers) present a series of unusual quantum properties of
             fundamental interest. These properties can play a role not only in connection with the statistical  behavior  of
             collective modes of Helium gas at low temperatures, but also with the Bose-Einstein condensation as well as with
             the appearance of the so-called Efimov states in three body interaction. The recent years have brought  to  the
             forefront of both applied and fundamental research the importance of knowing the mechanism for, in general,
             three body recombination dynamics when only very weakly interacting species are involved and when such events
             are forced to happen at very low temperatures of the gaseous thermal bath,  preluding to the occurrence of
             mesoscopic effects such as the Bose-Einstein condensation induced by photo-absorption, radiative cooling or other
             laser-induced processes.

   2.- Quantum and Classical Trajectories. Classical and Quantum Chaos

            From its beginning Quantum Mechanics has revealed as a very successful and powerful theory to describe  nature.
            However, the standard formalism in terms of probabilities is often unable to provide a satisfactory intuitive insight
            into the underlying physical processes, as it is the case for the corresponding classical description. The situation   is
            even worse if one takes into account that there must be some kind of correspondence between the predictions of both
            mechanics in the appropriate limits. Some alternative formalisms of Quantum Mechanics have been proposed in the
            literature such as, for example, Feynman path integrals, Madelung hydrodynamical formulation, Semiclassical-IVR 
            approach and Bohm formalism. Bohm developed, in particular, a formalism in which the initial and final states of a
            physical process are connected causally by the so-called quantum trajectories. Bohmian Mechanics combines both the
            prediction of Quantum Mechanics and the capability of providing an intuitive interpretation of the physical processes                 involved.

            Particle diffraction experiements have played a key role in the development of Quantum theory since its inception. In
            words of Feynman, the double-slit experiment has in it the heart of Quantum Mechanics. Our work is running along
            this line. We have tackled the diffraction of atoms from surfaces with different degrees of corrugation and in presence
            or not of single adsorbates as well as the selective adsorption  and threshold resonances in elastic scattering.  Our aim
            now is to extent this  type of analysis to inelastic scattering and see the role played by  the temperature of the surface.
            Due to the fact we are mainly interested in interpretative aspects, we are  obliged to analyze the  physical  problems
            aboved mentioned in terms of classical, semiclassical and standard quantum methods. The physical processes studied
            are complex and non-linear showing that the underlying dynamics display chaos and catastrophes.

   3.- Helium Atom Scattering. Diffraction, Diffusion and Adsorbate

            Low-energy incident beams of light neutral particles are able to probe, in a non-destructive way, the outermost layer
            of metallic, insulator and semiconductor surfaces. In particular, experiments with Helium atoms have been extensively
            carried out and, due to the small value of the mass, the scattering is predominantly elastic and diffraction dominates.
            This has led to the obtaining of a wealth of data and a lot of experimental information about the orientation  and size
            of the surface unit cells, surface corrugations, particle-surface physisorption interaction potentials, surface diffusion,
            condensation and growth phenomena. Inelastic processes can also be studied and phonon dispersion curves are obtained
            by combining pulsed beams and time-of-flight techniques. The role played by the surface temperature as well as the
            coverage of adsorbates on the surface in most of the elementary processes ocurring at surfaces is our main goal in this
            topic. In particular, we are currently investigating how the interaction between adsorbates is affecting diffusion and
            their low-energy modes.

   4.- Quantum Dissipative Systems. Stochastic Processes         

            Quantum dynamics of open systems is an interdiciplinary branch of Physics where exchange of ideas and methods of
            very broad fields  of interest meet together, processes which are ubiquitous in Biology, Chemistry, Economy, etc. In
            a very broad sense, all real physical systems are open systems since the interaction with their environment can never
            be totally neglected. Interaction with an environment generally causes systems to become mixed;  the whole is in  a
            definite state whereas the parts are not (entanglement). Quantum interference is an example and if the system and
            the environment or bath are entangled and then stop interacting, the entanglement remains. Usually we are interested
            in the system since the bath is an extended system and it is too difficult to deal with. The coupling between the bath
            and the system acts as a continuous measuring apparatus leading to an incessant destruction of phase correlations

            Damping occurs because a system interacts with the bath and the energy of the system is dissipated onto the bath.
            However, noise arise also since the bath distributes some of its energy back to the system. In presence of noise, we
            have to speak of fluctuation which is a stochastic variable with zero mean. The paradigm of a dissipative system is
            the Brownian motion which can be regarded as stochastic because detailed information is lost for molecules in the
            medium. Similarly, if a large number of degrees of freedom of a many-particle system is masked from observation,
            the motion of the remaining degrees of freedom is described as a stochastic process.

            In our recent work on atom-surface scattering, we have considered the surface as a heat bath and some of the most
            elementary processes such as diffraction at surfaces with the presence or not of single adsorbates,  selective adsorption
            resonances, diffusion and low-energy vibrational relaxation are being currently analyzed. 

            Finally, some extension to Econophysics is being developed. In particular, the Pricing Theory of Black-Scholes-Merton
            to warrants and interest rates are also subjects of our actual interest.