Parametric oscillator in a Kerr medium: evolution of coherent states

We study the temporal evolution of a coherent state under the action of a parametric oscillator and a nonlinear Kerr-like medium. We make use of the interaction picture representation and use an exact time evolution operator for the time independent part of the Hamiltonian. We approximate the interaction picture Hamiltonian in such a way as to make it a member of a Lie algebra. The corresponding time evolution operator behaves like a squeezing operator due to the temporal dependence of the oscillator's frequency. We analyze the probability amplitude and the auto correlation function for different Hamiltonian parameters and we find a very good agreement between our approximate results and converged numerical calculations.Comment: 11 pages, 3 figure

Corrections to scaling for diffusion in disordered media

We study the diffusion of a particle in a d-dimensional lattice where disorder arises from a random distribution of waiting times associated with each site of the lattice. Using scaling arguments we derive, in addition to the leading asymptotic behaviour, the correction-to-scaling terms for the mean square displacement. We also perform detailed Monte Carlo simulations for one, two and three dimensions which give results in substantial agreement with the scaling argument predictions

Ga+, In+ and Tl+ Impurities in Alkali Halide Crystals: Distortion Trends

A computational study of the doping of alkali halide crystals (AX: A = Na, K; X = Cl, Br) by ns2 cations (Ga+, In+ and Tl+) is presented. Active clusters of increasing size (from 33 to 177 ions) are considered in order to deal with the large scale distortions induced by the substitutional impurities. Those clusters are embedded in accurate quantum environments representing the surrounding crystalline lattice. The convergence of the distortion results with the size of the active cluster is analyced for some selected impurity systems. The most important conclusion from this study is that distortions along the (100) and (110) crystallographic directions are not independent. Once a reliable cluster model is found, distortion trends as a function of impurity, alkali cation and halide anion are identified and discussed. These trends may be useful when analycing other cation impurities in similar host lattices.Comment: LaTeX file. 7 pages and 2 pictures. Accepted for publication in J. Chem. Phy

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Pressure management and residential consumption reduction

[EN] The benefits of applying pressure management in urban water supply networks are well known for more than 10 years. Apart from reducing leakage, it also reduces burst frequency and consumption. However, the reduction of consumption with pressure is an objective that has only been considered a priority in water scarcity scenarios and suffers from a lack of systematic or conclusive studies. This paper analyses the relationship between pressure and consumption in a water distribution network equipped with remote water meter reading. Based on end use breakdowns, the paper estimates the percentage of pressure-dependent consumption. It establishes three different scenarios and assesses the relationship between pressure and consumption by means of the N3 coefficient.Garmendia, M.; Almandoz Berrondo, J.; Arrizabalaga, A.; Arregui De La Cruz, F. (2018). Pressure management and residential consumption reduction. Water Science & Technology: Water Supply. 19(1):236-244. https://doi.org/10.2166/ws.2018.071S23624419

The determination of the apsidal angles and Bertrand's theorem

We derive an expression for the determination of the apsidal angles that holds good for arbitrary central potentials. Then we discuss under what conditions the apsidal angles remain independent of the mechanical energy and angular momentum in the central force problem. As a consequence, an alternative and non-perturbative proof of Bertrand's theorem is obtained.Comment: Latex file, one figure; submitted for publicatio

Relativistic quantum mechanics of a Dirac oscillator

The Dirac oscillator is an exactly soluble model recently introduced in the context of many particle models in relativistic quantum mechanics. The model has been also considered as an interaction term for modelling quark confinement in quantum chromodynamics. These considerations should be enough for demonstrating that the Dirac oscillator can be an excellent example in relativistic quantum mechanics. In this paper we offer a solution to the problem and discuss some of its properties. We also discuss a physical picture for the Dirac oscillator's non-standard interaction, showing how it arises on describing the behaviour of a neutral particle carrying an anomalous magnetic moment and moving inside an uniformly charged sphere.Comment: 19 pages, 1 figur