Spin tunneling in magnetic molecules: Quantitative estimates for Fe8 clusters

Spin tunneling in the particular case of the magnetic molecular cluster octanuclear iron(III), Fe8, is treated by an effective Hamiltonian that allows for an angle-based description of the process. The presence of an external magnetic field along the easy axis is also taken into account in this description. Analytic expressions for the energy levels and barriers are obtained from a harmonic approximation of the potential function which give results in good agreement with the experimental results. The energy splittings due to spin tunneling is treated in an adapted WKB approach and it is shown that the present description can give results to a reliable degree of accuracy.Comment: 17 pages, 2 figures, preprint submitted to Physica

Urban vehicular traffic: fitting the data using a hybrid stochastic model. Part II

In this second part of our research we used the models presented in \emph{Modeling a vehicular traffic network. Part I} \cite{ogm1} to perform an analysis of the urban traffic as recorded by cameras distributed in a chosen sector of Tigre, a city in the province of Buenos Aires, Argentina. We found that the circulation of vehicles -- the traffic dynamics --, along a whole day, can be described by a hybrid model that is an adapted blend of model 2, for an open linear system, with model 3, which is nonlinear, developed in Part I. The objectives of this work were, firstly, to verify whether the vehicular flux can be modeled as an $n$-step stochastic process for its evolution, $n$ for the time. Secondly, to find out if the model, with its parameters fixed to describe the traffic of a single day, may adequately describe the traffic in other days. Thirdly, to propose changes in the already established set of the urban traffic rules in order to optimize the vehicular flow and to diminish the average time that a vehicle stays idle at the semaphores. We estimate that the goals were achieved satisfactorily within the margins of the experimental errors of the gathered data.Comment: 12 pages, 11 figure

On the q-deformation of the NJL model

Using a q-deformed fermionic algebra we perform explicitly a deformation of the Nambu-Jona-Lasinio (NJL) Hamiltonian. In the Bogoliubov-Valatin approach we obtain the deformed version of the functional for the total energy, which is minimized to obtain the corresponding gap equation. The breaking of chiral symmetry and its restoration in the limit $q \to 0$ are then discussed.Comment: 5 eps figure

A new description of spin tunneling in magnetic molecules

A new approach is used that allows to describe the magnetic molecules main properties in a direct and simple way. Results obtained for the Fe8 cluster show good agreement with the experimental data.Comment: 7 pages, 2 figure