Dynamics and non-equilibrium steady state in a system of coupled harmonic oscillators

A system of two coupled oscillators, each of them coupled to an independent reservoir, is analysed. The analytical solution of the non-rotating wave master equation is obtained in the high-temperature and weak coupling limits. No thermal entanglement is found in the high-temperature limit. In the weak coupling limit the system converges to an entangled non-equilibrium steady state. A critical temperature for the appearance of quantum correlations is found.     

The Thermodynamic Limit in Mean Field Spin Glass Models

 We present a simple strategy in order to show the existence and uniqueness of the infinite volume limit of thermodynamic quantities, for a large class of mean field disordered models, as for example the Sherrington-Kirkpatrick model, and the Derrida p-spin model. The main argument is based on a smooth interpolation between a large system, made of N spin sites, and two similar but independent subsystems, made of N ₁ and N ₂ sites, respectively, with N ₁ +N ₂ =N. The quenched average of the free energy turns out to be subadditive with respect to the size of the system. This gives immediately convergence of the free energy per site, in the infinite volume limit. Moreover, a simple argument, based on concentration of measure, gives the almost sure convergence, with respect to the external noise. Similar results hold also for the ground state energy per site. Received: 19 April 2002 / Accepted: 22 April 2002 Published online: 6 August 2002     

A heterodyne interferometric polarimeter for the detection of jones and stokes polarization vectors

A heterodyne interferometric polarimeter for detection of the Jones components and Stokes parameters is demonstrated. The measurement of both sets of quantities for various polarization states is achieved with excellent precision. The details of the corresponding Lissajous picture (ellipse) can be visualized in real time. Finally, the polarization data collected at the output of a highly birefringent fiber have been used for submillimetric beat-Length measurements.     

A complete treatment of a steady-state four-level model for the interpretation of OH laser-induced fluorescence measurements in atmospheric pressure flames

In order to obtain OH concentration measurements in atmospheric pressure flames from saturated fluorescence signal, we have developed a stationary four-level model. A general relationship between the measured upper state population and the total number density has been derived. The effects of the imbalance between the rotational transfer rates in the upper and ground states is analyzed. We show that in the case of comparable rotational rates, the results of our treatment are similar to the ones obtained with the balanced cross rate model. A set of complementary data which should facilitate absolute OH concentration measurements is also pointed out.     

Long Term Stability of Proper Rotations of the Perturbed Euler Rigid Body

We study the long term stability of the proper rotations of the perturbed Euler rigid body, in the framework of Nekhoroshev theory. For simplicity we treat here in detail only the kinetically symmetric case (the potential needs not to be symmetric), but we indicate how to extend the results to the triaxial case. We show that the proper rotations around the symmetry axis are Nekhoroshev stable: more precisely, if the initial datum is sufficiently close to a proper rotation, then for a very long time it remains such, and the tip of the unit vector parallel to the angular momentum precesses, up to a small noise, along the level curves of a regular function on the unit sphere. If the proper rotations are resonant, chaotic motions with positive Lyapunov exponents are possible, but chaos (unlike the case of ordinary motions, that is motions not close to proper rotations) is always localized, and does not affect in an essential way the motion of the angular momentum in space. Preliminary numerical results indicate that the theory is, in many aspects, optimal, although in some points it can still be improved.     

Mean-field gauge interactions in five dimensions II. The orbifold

We study Gauge–Higgs Unification in five dimensions on the lattice by means of the mean-field expansion. We formulate it for the case of an SU(2)$\mathit{SU}(2)$ pure gauge theory and orbifold boundary conditions along the extra dimension, which explicitly break the gauge symmetry to U(1)$U(1)$ on the boundaries. Our main result is that the gauge boson mass computed from the static potential along four-dimensional hyperplanes is non-zero implying spontaneous symmetry breaking. This observation supports earlier data from Monte Carlo simulations in Irges and Knechtli (2007) [12].     

Amplification phenomena of Casimir force fluctuations on close scatterers coupled via a coherent fermionic fluid

We study the mechanical actions affecting close scatterers immersed in a coherent fermionic fluid. Using a scattering field theory, we theoretically analyse the single-scatterer and the two-scatterer case. Concerning the single-scatterer case, we find that a net force affects the scatterer dynamics only in non-equilibrium condition, i.e. imposing the presence of a non-vanishing particle current flowing through the system. The force fluctuation (variance) is instead not negligible both in equilibrium and in non-equilibrium conditions. Concerning the two-scatterer case, an attractive fluid-mediated Casimir force is experienced by the scatterers at small spatial separation, while a decaying attractive/repulsive behavior as a function of the scatterer separation is found. Furthermore, the Casimir force fluctuations acting on a given scatterer in close vicinity of the other present an oscillating behavior reaching a long distance limit comparable to the noise level of the single-scatterer case. The relevance of these findings is discussed in connection with fluctuation phenomena in low-dimensional nanostructures and cold atoms systems.