69 research outputs found
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
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