The Quantum Arnold Transformation and its applications

The Quantum Arnold Transformation, a unitary operator mapping the solutions of the Schr¨odinger equation for time-dependent quadratic Hamiltonians into free-particle solutions, is revisited. Possible applications and extensions are also outlined: the analytic construction of harmonic states for the free particle, the Quantum Arnold-Ermakov-Pinney transformation and the description of the Release & Recapture method

Zero-temperature spin-glass freezing in self-organized arrays of Co nanoparticles

We study, by means of magnetic susceptibility and magnetic aging experiments, the nature of the glassy magnetic dynamics in arrays of Co nanoparticles, self-organized in N layers from N=1 (two-dimensional limit) up to N=20 (three-dimensional limit). We find no qualitative differences between the magnetic responses measured in these two limits, in spite of the fact that no spin-glass phase is expected above T=0 in two dimensions. More specifically, all the phenomena (critical slowing down, flattening of the field-cooled magnetization below the blocking temperature and the magnetic memory induced by aging) that are usually associated with this phase look qualitatively the same for two-dimensional and three-dimensional arrays. The activated scaling law that is typical of systems undergoing a phase transition at zero temperature accounts well for the critical slowing down of the dc and ac susceptibilities of all samples. Our data show also that dynamical magnetic correlations achieved by aging a nanoparticle array below its superparamagnetic blocking temperature extend mainly to nearest neighbors. Our experiments suggest that the glassy magnetic dynamics of these nanoparticle arrays is associated with a zero-temperature spin-glass transition.Comment: 6 pages 6 figure

Coherent States for infinite homogeneous waveguide arrays

Perelomov coherent states for equally spaced, infinite homogeneous waveguide arrays with Euclidean E(2) symmetry are defined, and new resolutions of the identity are constructed in Cartesian and polar coordinates. The key point to construct these resolutions of the identity is the fact that coherent states satisfy Helmholtz equation (in coherent states labels) an thus a non-local scalar product with a convolution kernel can be introduced which is invariant under the Euclidean group. It is also shown that these coherent states for the Eucliean E(2) group have a simple and natural physical realization in these waveguide arrays.Spanish MICINN through the project PGC2018-097831-B-I00 and Junta de Andalucı́a through the project FEDER/UJA-1381026

Harmonic states for the free particle

Different families of states, which are solutions of the time-dependent free Schr\"odinger equation, are imported from the harmonic oscillator using the Quantum Arnold Transformation introduced in a previous paper. Among them, infinite series of states are given that are normalizable, expand the whole space of solutions, are spatially multi-localized and are eigenstates of a suitably defined number operator. Associated with these states new sets of coherent and squeezed states for the free particle are defined representing traveling, squeezed, multi-localized wave packets. These states are also constructed in higher dimensions, leading to the quantum mechanical version of the Hermite-Gauss and Laguerre-Gauss states of paraxial wave optics. Some applications of these new families of states and procedures to experimentally realize and manipulate them are outlined.Comment: 21 pages, 3 figures. Title changed, content added, references adde

Performance of malolactic fermentation by inoculation of selected Lactobacillus plantarum and Oenococcus oeni strains isolated from Rioja red wines

Malolactic fermentations (MLF) of wines inoculated with selected lactic acid bacteria strains of the species Oenococcus oeni and Lactobacillus plantarum were studied and compared with spontaneous MLF. Bacterial populations were monitored along the whole process of MLF and bacteria identifications were carried out at species and strain level. Macrorestriction analysis with SfiI endonuclease and subsequent PFGE was carried out in order to identify O. oeni individual strains. L. plantarum active lyophila did not survive competing with the indigenous microbiota in a wine with 15.3 % (vol/vol) alcohol, whereas the selected O. oeni strains carried out wine MLF. The highest production of histamine took place during MLF in those wines that underwent spontaneous MLF with a mixed population of indigenous strains. The lowest levels of histamine were obtained with the selected commercial O. oeni strain that succeeded 100 % over the indigenous microbiota. Results indicate that development of MLF leaded by selected O. oeni active lyophila provides negligible histamine levels in red wines of quality that can be submitted to subsequent ageing in wood.