Estudios previos y propuesta de intervención en las pinturas murales, esculturas y ornamentos de la Real Parroquia de los Santos Juanes de Valencia

Throughout this article, the most representative aspects of the previous studies and the intervention proposal, carried out for the restoration of the paintings, sculptures and ornaments of the Royal Parish of the Santos Juanes in Valencia, are exposed. A project of this magnitude involves the effort and dedication of a great team, resulting in one-year work with exhaustive and constant research with the purpose of safeguarding the heritage assets of the church. With this article we want to make known the importance that these previous studies acquire. Been essential since they are the starting point and the basis for the execution of the restoration works that will be carried out during fo…

On the existence of the exponential solution of linear differential systems

The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.

A family of complex potentials with real spectrum

We consider a two-parameter non-Hermitian quantum mechanical Hamiltonian operator that is invariant under the combined effects of parity and time reversal transformations. Numerical investigation shows that for some values of the potential parameters the Hamiltonian operator supports real eigenvalues and localized eigenfunctions. In contrast with other parity times time reversal symmetric models which require special integration paths in the complex plane, our model is integrable along a line parallel to the real axis.

High-order Runge–Kutta–Nyström geometric methods with processing

Abstract We present new families of sixth- and eighth-order Runge–Kutta–Nystrom geometric integrators with processing for ordinary differential equations. Both the processor and the kernel are composed of explicitly computable flows associated with non trivial elements belonging to the Lie algebra involved in the problem. Their efficiency is found to be superior to other previously known algorithms of equivalent order, in some case up to four orders of magnitude.

Iterative approach to the exponential representation of the time–displacement operator

An iterative method due to Voslamber is reconsidered. It provides successive approximations for the logarithm of the time–displacement operator in quantum mechanics. The procedure may be interpreted, a posteriori, as an infinite re-summation of terms in the so-called Magnus expansion. A recursive generator for higher terms is obtained. From two illustrative examples, a detailed comparative study is carried out between the results of the iterative method and those of the Magnus expansion.

Unitary transformations depending on a small parameter

We formulate a unitary perturbation theory for quantum mechanics inspired by the LieDeprit formulation of canonical transformations. The original Hamiltonian is converted into a solvable one by a transformation obtained through a Magnus expansion. This ensures unitarity at every order in a small parameter. A comparison with the standard perturbation theory is provided. We work out the scheme up to order ten with some simple examples.

New Families of Symplectic Runge-Kutta-Nyström Integration Methods

We present new 6-th and 8-th order explicit symplectic Runge-Kutta-Nystrom methods for Hamiltonian systems which are more efficient than other previously known algorithms. The methods use the processing technique and non-trivial flows associated with different elements of the Lie algebra involved in the problem. Both the processor and the kernel are compositions of explicitly computable maps.

Geometric factors in the adiabatic evolution of classical systems

Abstract The adiabatic evolution of the classical time-dependent generalized harmonic oscillator in one dimension is analyzed in detail. In particular, we define the adiabatic approximation, obtain a new derivation of Hannay's angle requiring no averaging principle and point out the existence of a geometric factor accompanying changes in the adiabatic invariant.

Computer algebra and large scale perturbation theory

This work presents a brief resume of our applications of computer algebra to the study of large-scale perturbation theory in quantum mechanical systems, both in the small and in the strong coupling regimes.

The Magnus expansion and some of its applications

Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of prese…

Bifurcations in the Lozi map

We study the presence in the Lozi map of a type of abrupt order-to-order and order-to-chaos transitions which are mediated by an attractor made of a continuum of neutrally stable limit cycles, all with the same period.

Lyapunov exponent and topological entropy plateaus in piecewise linear maps

We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory.

Contextualización iconográfica e intervención en las pinturas murales de la Capilla de la Comunión de la iglesia parroquial de san Nicolás de Bari y de san Pedro mártir en la ciudad de Valencia

Floquet theory: exponential perturbative treatment

We develop a Magnus expansion well suited for Floquet theory of linear ordinary differential equations with periodic coefficients. We build up a recursive scheme to obtain the terms in the new expansion and give an explicit sufficient condition for its convergence. The method and formulae are applied to an illustrative example from quantum mechanics.

Non-Adiabatic Aspects of Time-Dependent Hamiltonian Systems

Extreme adiabatic behavior furnishes great simplification in the treatment of linear time-dependent Hamiltonian systems. But the actual time variation of the parameters is only finitely, rather than infinitely, slow. Then one is forced to consider corrections to the adiabatic limit.

Comments on `A new efficient method for calculating perturbation energies using functions which are not quadratically integrable'

The recently proposed method of calculating perturbation energies using a non-normalizable wavefunction by Skala and Cizek is analysed and rigorously proved.

Strong-coupling expansions for the -symmetric oscillators

We study the traditional problem of convergence of perturbation expansions when the hermiticity of the Hamiltonian is relaxed to a weaker symmetry. An elementary and quite exceptional cubic anharmonic oscillator is chosen as an illustrative example of such models. We describe its perturbative features paying particular attention to the strong-coupling regime. Efficient numerical perturbation theory proves suitable for such a purpose.

Magnus and Fer expansions for matrix differential equations: the convergence problem

Approximate solutions of matrix linear differential equations by matrix exponentials are considered. In particular, the convergence issue of Magnus and Fer expansions is treated. Upper bounds for the convergence radius in terms of the norm of the defining matrix of the system are obtained. The very few previously published bounds are improved. Bounds to the error of approximate solutions are also reported. All results are based just on algebraic manipulations of the recursive relation of the expansion generators.