Involutive constrained systems and Hamilton-Jacobi formalism

In this paper, we study singular systems with complete sets of involutive constraints. The aim is to establish, within the Hamilton-Jacobi theory, the relationship between the Frobenius' theorem, the infinitesimal canonical transformations generated by constraints in involution with the Poisson brackets, and the lagrangian point (gauge) transformations of physical systems

Spontaneous symmetry breaking as a resource for noncritically squeezed light

In the last years we have proposed the use of the mechanism of spontaneous symmetry breaking with the purpose of generating perfect quadrature squeezing. Here we review previous work dealing with spatial (translational and rotational) symmetries, both on optical parametric oscillators and four-wave mixing cavities, as well as present new results. We then extend the phenomenon to the polarization state of the signal field, hence introducing spontaneous polarization symmetry breaking. Finally we propose a Jaynes-Cummings model in which the phenomenon can be investigated at the single-photon-pair level in a non-dissipative case, with the purpose of understanding it from a most fundamental point of view.Comment: Review for the proceedings of SPIE Photonics Europe. 11 pages, 5 figures

Hamilton-Jacobi formalism for Linearized Gravity

In this work we study the theory of linearized gravity via the Hamilton-Jacobi formalism. We make a brief review of this theory and its Lagrangian description, as well as a review of the Hamilton-Jacobi approach for singular systems. Then we apply this formalism to analyze the constraint structure of the linearized gravity in instant and front-form dynamics.Comment: To be published in Classical and Quantum Gravit

Variability of early autumn planktonic assemblages in the strait of Gibraltar: a regionalization analysis

The Strait of Gibraltar (SG) is the only connection of the Mediterranean Sea with the global circulation. The SG is an outstanding marine region to explore physical-biological coupling of pelagic communities due to its hydrodynamic complexity, including strong tidal forcing and marked spatial gradients and fronts. The authors have unravelled the role of the fortnightly tidal scale (spring and neap tides) and local processes (upwelling and tidal-topographic mixing) that shape planktonic assemblages in the Strait. To do so, an oceanographic cruise was taken in early autumn 2008 with a high-resolution grid sampling and spring/neap tidal conditions. The planktonic features were captured using different automatic and semi-automatic techniques of plankton analyses (flow cytometry, FlowCAM, LOPC and Ecotaxa) that allowed covering a wide range of sizes of the community from pico- to mesoplankton. The SG was sectorized into two clusters based on the biogeochemical and main water column properties. Cluster 1 (CL1) covered shallow productive areas around Cape Trafalgar (CT). CL1 presented higher concentrations of chlorophyll and nutrients, and phytoplankton was mostly represented by Synechococcus and coastal diatoms while zooplankton had the highest percentage of meroplankton (31%). In contrast, cluster 2 (CL2) covered open ocean waters and presented more oligotrophic features, i.e. nitrogen-depleted waters with lower chlorophyll concentrations and a picoplankton community dominated by Prochlorococcus and holoplankton predominance in mesozooplankton. Under early autumn conditions with overall nutrient-depleted and stratified waters, the CT area emerges as an ecosystem where the constant tidal mixing and nutrients supply is coupled with an active production also being favored by high residence times and finally shaping a plankton community with unique features in the area.En prensa0,56

Theory of quantum fluctuations of optical dissipative structures and its application to the squeezing properties of bright cavity solitons

We present a method for the study of quantum fluctuations of dissipative structures forming in nonlinear optical cavities, which we illustrate in the case of a degenerate, type I optical parametric oscillator. The method consists in (i) taking into account explicitly, through a collective variable description, the drift of the dissipative structure caused by the quantum noise, and (ii) expanding the remaining -internal- fluctuations in the biorthonormal basis associated to the linear operator governing the evolution of fluctuations in the linearized Langevin equations. We obtain general expressions for the squeezing and intensity fluctuations spectra. Then we theoretically study the squeezing properties of a special dissipative structure, namely, the bright cavity soliton. After reviewing our previous result that in the linear approximation there is a perfectly squeezed mode irrespectively of the values of the system parameters, we consider squeezing at the bifurcation points, and the squeezing detection with a plane--wave local oscillator field, taking also into account the effect of the detector size on the level of detectable squeezing.Comment: 10 figure

Quantum squeezing of optical dissipative structures

We show that any optical dissipative structure supported by degenerate optical parametric oscillators contains a special transverse mode that is free from quantum fluctuations when measured in a balanced homodyne detection experiment. The phenomenon is not critical as it is independent of the system parameters and, in particular, of the existence of bifurcations. This result is a consequence of the spatial symmetry breaking introduced by the dissipative structure. Effects that could degrade the squeezing level are considered.Comment: 4 pages and a half, 1 fugure. Version to appear in Europhysics Letter

Hamilton-Jacobi formalism for Podolsky’s electromagnetic theory on the null-plane

We develop the Hamilton-Jacobi formalism for Podolsky’s electromagnetic theory on the null-plane. The main goal is to build the complete set of Hamiltonian generators of the system, as well as to study the canonical and gauge transformations of the theory