The socle of a Leavitt path algebra

In this paper we characterize the minimal left ideals of a Leavitt path algebra as those ones which are isomorphic to principal left ideals generated by line point vertices, that is, by vertices whose trees do not contain neither bifurcations nor closed paths. Moreover, we show that the socle of a Leavitt path algebra is the two-sided ideal generated by these line point vertices. This characterization allows us to compute the socle of some algebras that arise as the Leavitt path algebra of some row-finite graphs. A complete description of the socle of a Leavitt path algebra is given: it is a locally matricial algebra.Comment: 13 pg

Long-range correlations and trends in Colombian seismic time series

We study long-range correlations and trends in time series extracted from the data of seismic events occurred from 1973 to 2011 in a rectangular region that contains mainly all the continental part of Colombia. The long-range correlations are detected by the calculation of the Hurst exponents for the time series of interevent intervals, separation distances, depth differences and magnitude differences. By using a modification of the classical $R/S$ method that has been developed to detect short-range correlations in time series, we find the existence of persistence for all the time series considered except for magnitude differences. We find also, by using the $DFA$ until the third order, that the studied time series are not influenced by trends. Additionally, an analysis of the Hurst exponent as a function of the number of events in the time and the maximum window size is presented.Comment: 21 pages, 6 figures, 2 figures added, types corrected, accepted to be published in Physica

Frequency shift on the potential-dependent surface-enhanced Raman scattering of pyridine: simplified models for metal and solvent effects

The electronic structure of adsorbates is altered when it interacts with a surface, modifying the properties of both entities and giving rise to interesting phenomena related to heterogeneous catalysis or molecular electronics. If such surface is a metallic substrate, the electrode potential can be used to tune this interaction. Potential-dependent Surface-Enhanced Raman Scattering (SERS) is a particularly useful technique to study the induced effects on the molecule when the metal-adsorbate surface complex is formed, as the observed frequency shifts of the vibrational modes can provide information about it. However, from the computational point of view, these systems are difficult to model, because the macroscopic metal cannot be modelled easily using quantum mechanics. As an approach, we propose a simple model using silver atomic wires with different size and charge bonded to the molecule (AgnPyq, n = 2,3,5,7 and q = 0 and ±1 for n even and odd, respectively) which has been developed by the group and provides a good description of the effect of the electrode potential on the chemical enhancement mechanism of SERS.1-3 Electronic calculations were performed using Density Functional Theory (DFT). In order to study the frequency shifts, solvent effects have been taken into account by using the Polarizable Continuum Model (PCM). We have used three different functionals (B3LYP, PW91 and M06HF) and two basis sets (LANL2DZ for all atoms and LANL2DZ for Ag and 6-31G(d) for C,N,H) and, in all cases, a good agreement is achieved in terms of amplitude and trend of the frequency shift for most of the vibrational modes, especially when solvent interactions are included. The method was extended to other metals and solvents giving results in agreement with the available experimental data.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Charge Transfer mechanism in the Surface Enhanced Raman Scattering of 2,2'-bipyridine recorded on a silver electrode

Nowadays, Surface Enhanced Raman Spectroscopy (SERS) has become a powerful technique to investigate the electronic structure of surface-molecule hybrid systems due to the huge enhancement of the Raman signal. It is established that the origin of this enhancement has two main contributions; the electromagnetic (EM), related to surface plasmons, and the chemical mechanism, due to resonant charge transfer (CT) processes between the adsorbate and the metal. With the aim to investigate the SERS-CT of bipyridine and to identify charge transfer process, the spectra were recorded on silver electrode by using three different wavelengths (473, 532 and 785 nm) in a range from 0.0 up to -1.4 V electrode potential. The electrode potential was modelled in the calculations with atomic silver wires of different size and charge attached to the BPy molecule (AgnBPyq, with q = 0 for n = 2 and q = ±1 for n = 3, 5, 7) and were computed with Density Functional Theory (DFT). Although BPy shows a trans conformation in solution, a cis conformation was chosen for its chelating properties. The results indicate that the intensification of the ~1550 cm-1 band at negative potentials is due the Franck-Condon factors related to the resonant CT process from the metal to the BPy molecule.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

An MS-CASPT2 Study of the Photodecomposition of 4- Methoxyphenyl Azide. Role of Internal Conversion and Intersystem Crossing

Aryl azides photochemistry is strongly dependent on the substituent relative position, as has been studied by time resolved resonant Raman (TR3) spectroscopy for 4-methoxyphenyl azide and its isomer 3-methoxyphenyl azide. When irradiated at 266 nm, the former results in 4,4’-dimethoxyazobenzene whereas the latter forms 1,2-didehydroazepine. It is proposed that the key step of the reactions is the formation of a nitrene derivative. Recently, it has been proposed by us that nitrenes might have a relevant role in the Surface-Enhanced Raman Scattering (SERS) of p-aminothiophenol, however, the molecular mechanism is not well known in neither of these cases. Therefore, we studied the photodecomposition of 4-methoxyphenyl azide using multiconfigurational self-consistent field methods (MC-SCF) with the CAS-SCF and MS-CASPT2 approximations and calculated the resonant Raman spectra of the relevant species using a multi-state version of Albrecht’s vibronic theory. The results propose that the reaction follows a two steps sequence after irradiation at 266 nm: an intersystem crossing 21A’/23A’’ which decays through a 21A’/21A’’ conical intersection producing molecular nitrogen and triplet 4-methoxyphenyl nitrene in its ground state.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states

This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and twocontrols. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about "(x,u)-flatness" of these systems, with much more elementary techniques

A deterministic detector for vector vortex states

Encoding information in high-dimensional degrees of freedom of photons has led to new avenues in various quantum protocols such as communication and information processing. Yet to fully benefit from the increase in dimension requires a deterministic detection system, e.g., to reduce dimension dependent photon loss in quantum key distribution. Recently, there has been a growing interest in using vector vortex modes, spatial modes of light with entangled degrees of freedom, as a basis for encoding information. However, there is at present no method to detect these non-separable states in a deterministic manner, negating the benefit of the larger state space. Here we present a method to deterministically detect single photon states in a four dimensional space spanned by vector vortex modes with entangled polarisation and orbital angular momentum degrees of freedom. We demonstrate our detection system with vector vortex modes from the |[Formula: see text]| = 1 and |[Formula: see text]| = 10 subspaces using classical and weak coherent states and find excellent detection fidelities for both pure and superposition vector states. This work opens the possibility to increase the dimensionality of the state-space used for encoding information while maintaining deterministic detection and will be invaluable for long distance classical and quantum communication