Javier Garcia

A comparative QSAR on 1,2,5-thiadiazolidin-3-one 1,1-dioxide compounds as selective inhibitors of human serine proteinases.

Selective inhibitors of target serine proteinases have a potential therapeutic role for the treatment of various inflammatory and related diseases. We develop a comparative quantitative structure-activity relationships based analysis on compounds embodying the 1,2,5-thiadiazolidin-3-one 1,1-dioxide scaffold. By means of classical Molecular Dynamics we obtain the conformation of each lowest-energy molecular structure from which we derive more than a thousand of structural descriptors necessary for building predictive QSAR models. We resort to two different modeling approaches with the purpose of testing the consistency of our results: (a) multivariable linear regressions based on the replacement method and forward stepwise regression, and (b) the calculation of flexible descriptors with the CORAL program. All the models are properly validated by means of standard procedures. The resulting QSAR models are supposed to be of great utility for the rational search and design (including synthesis and/or in vitro biochemical studies) of new effective non-peptidyl inhibitors of serine proteinases.

Quantitative Structure–Activity Relationships of Mosquito Larvicidal Chalcone Derivatives

The mosquito larvicidal activities of a series of chalcones and some derivatives were subjected to a quantitative structure-activity relationship (QSAR) study, using more than a thousand constitutional, topological, geometrical, and electronic molecular descriptors calculated with Dragon software. The larvicidal activity values for 28 active compounds of the series were predicted, showing in general a good approximation to the experimental values found in the literature. Chalcones having one or both electron-rich rings showed high toxicity. However, the activity of chalcones was reduced by electron-withdrawing groups, and this was roughly diminished by derivatization of the carbonyl group. A set of six chalcones being structurally similar to some of the active ones, with a still unknown larvicidal activity, were prepared. Their activity values were predicted by applying the developed QSAR models, showing that two chalcones of such set, both 32 and 34, were expected to be highly active.

Non-Hermitian Hamiltonians with unitary and antiunitary symmetries

Abstract We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C 2 v exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry.

Is space-time symmetry a suitable generalization of parity-time symmetry?

Abstract We discuss space-time symmetric Hamiltonian operators of the form H = H 0 + i g H ′ , where H 0 is Hermitian and g real. H 0 is invariant under the unitary operations of a point group G while H ′ is invariant under transformation by elements of a subgroup G ′ of G . If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g . In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 g g c , where g c is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H may exhibit real or complex eigenvalues for g > 0 . We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.

Non-Hermitian oscillators with Td symmetry

Abstract We analyse some PT-symmetric oscillators with T d symmetry that depend on a potential parameter g . We calculate the eigenvalues and eigenfunctions for each irreducible representation and for a range of values of g . Pairs of eigenvalues coalesce at exceptional points g c ; their magnitude roughly decreasing with the magnitude of the eigenvalues. It is difficult to estimate whether there is a phase transition at a nonzero value of g as conjectured in earlier papers. Group theory and perturbation theory enable one to predict whether a given space–time symmetry leads to real eigenvalues for sufficiently small nonzero values of g .

Critical parameters for non-hermitian Hamiltonians

PT-symmetric Hamiltonians exhibit real eigenvalues.Real eigenvalues appear when PT-symmetry is unbroken.The range of real eigenvalues is determined by exceptional points or critical parameters.The diagonalization method is suitable for the calculation of critical parameters.Degenerate eigenvalues require a more general definition of unbroken symmetry. We calculate accurate critical parameters for a class of non-hermitian Hamiltonians by means of the diagonalization method. We study three one-dimensional models and two perturbed rigid rotors with PT symmetry. One of the latter models illustrates the necessity of a more general condition for the appearance of real eigenvalues that we also discuss here.

Eigenvalues and eigenfunctions of the anharmonic oscillator V(x, y) = x 2 y 2

We obtain sufficiently accurate eigenvalues and eigenfunctions for the anharmonic oscillator with potential V(x, y) = x2y2 by means of three different methods. Our results strongly suggest that the spectrum of this oscillator is discrete in agreement with early rigorous mathematical proofs and against a recent statement that cast doubts about it

Comment on ?A simple analytical expression for bound state energies for an attractive Gaussian confining potential?

We discuss in this paper a recently proposed analytical formula for the eigenvalues of the Gaussian well and compare it with the analytical expression provided by the variational method with the simplest trial function. The latter yields considerably more accurate results than the former for the energies and critical parameters.

Highly accurate calculation of the resonances in the Stark effect in hydrogen

We obtained accurate resonances for the Stark effect in hydrogen by means of three independent methods. Two of them are based on complex rotation of the coordinates and diagonalization of the Hamiltonian matrix (CRLM and CRCH). The other one is based on the Riccati equations for the logarithmic derivatives of factors of the wavefunction (RPM). The latter approach enabled us to obtain the most accurate results and extremely sharp resonances.

Ad Hoc Physical Hilbert Spaces in Quantum Mechanics

The overall principles of what is now widely known as PT-symmetric quantum mechanics are listed, explained and illustrated via a few examples. In particular, models based on an elementary local interaction V(x) are discussed as motivated by the naturally emergent possibility of an efficient regularization of an otherwise unacceptable presence of a strongly singular repulsive core in the origin. The emphasis is put on the constructive aspects of the models. Besides the overall outline of the formalism we show how the low-lying energies of bound states may be found in closed form in certain dynamical regimes. Finally, once these energies are found real we explain that in spite of a manifest non-Hermiticity of the Hamiltonian the time-evolution of the system becomes unitary in a properly amended physical Hilbert space.