Jose M. Cervero

General solutions for a cosmological Robertsonwalker metric in the Brans-Dicke theory

The general vacuum solutions of the Brans-Dicke theory in a cosmological Robertson-Walker-type metric are explicitly given. Several families of solutions have properties which essentially differ from the conventional Einstein theory. The geometry is not uniquely determined by the equations of motion, raising doubts about the “Machian” character of the Brans-Dicke theory. The role of the cosmological constant is emphasized, in agreement with modern ideas of fundamental particle interactions.

SO(2,1)-invariant systems and the Berry phase

The general quadratic time-dependent quantum Hamiltonian is analysed using a time-dependent realisation of its SO(2,1) invariance Lie algebra. Several interesting features of this procedure are pointed out. As an example, the authors easily calculate dynamical and geometrical (Berry) phases using only an algebraic procedure. An incorrect result previously published by another author is also pointed out.

Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrödinger equation to 2+1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Absorption in atomic wires

The transfer matrix formalism is implemented in the form of the multiple collision technique to account for dissipative transmission processes by using complex potentials in several models of atomic chains. The absorption term is rigorously treated to recover unitarity for the non-Hermitian Hamiltonians. In contrast to other models of parametrized scatterers we assemble explicit potentials profiles in the form of delta arrays, Poeschl-Teller holes, and complex Scarf potentials. The techniques developed provide analytical expressions for the scattering and absorption probabilities of arbitrarily long wires. The approach presented is suitable for modeling molecular aggregate potentials and also supports new models of continuous disordered systems. The results obtained also suggest the possibility of using these complex potentials within disordered wires to study the loss of coherence in the electronic localization regime due to phase-breaking inelastic processes.

Contact symmetries and integrable non-linear dynamical systems

The authors present a systematic method of classifying and constructing invariants for Lagrangians containing arbitrary polynomial non-linear potentials. It is based on the assumption that these Lagrangians are invariant under contact groups of transformations. For a finite number of degrees of freedom they can prove integrability for a large class of polynomial potentials. The method can be extended in several directions.

The band spectrum of periodic potentials with Script PScript T-symmetry

A real band condition is shown to exist for one-dimensional periodic complex non-Hermitian potentials exhibiting -symmetry. We use an exactly solvable ultralocal periodic potential to obtain the band structure and discuss some spectral features of the model, specially those concerning the role of the imaginary parameters of the couplings. Analytical results as well as some numerical examples are provided.

Simple model for a quantum wire II. Statistically correlated disorder

In a previous paper (Eur. Phys. J. B 30, 239-251 (2002)) we have presented the main features and properties of a simple model which -in spite of its simplicity- describes quite accurately the qualitative behaviour of a quantum wire. The model was composed of N distinct deltas each one carrying a different coupling. We were able to diagonalize the Hamiltonian in the periodic case and yield a complete and analytic description of the subsequent band structure. Furthermore the random case was also analyzed and we were able to describe Anderson localization and fractal structure of the conductance. In the present paper we go one step further and show how to introduce correlations among the sites of the wire. The presence of a correlated disorder manifests itself by altering the distribution of states and the localization of the electrons within the system

Infinite chain of different deltas: A simple model for a quantum wire

Abstract:We present the exact diagonalization of the Schrödinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced.

Contact Transformations and Conformal Group. II. Non-Relativistic Theory

We find and identify the contact group of plane hyperbolic conformal geometry as a step to a better understanding of conformal invariance in physics.

Induced gravity and cosmology

Abstract We propose a fully conformal invariant theory describing gravity as a spontaneously broken theory. Newtons constant is automatically generated. We find through the study of classical solutions of the equations of motion that the breakdown of conformal symmetry can take place at the tree approximation without introducing arbitrary forms for the scalar potential. Using cosmological metrics, which we find natural from the physical point of view, some conclusions can be drawn regarding the nature of those metrics. The case of constant scalar curvature is particularly interesting, and gives rise to a gravitational version of the Goldstone theorem.