The replica symmetric behavior of the analogical neural network

In this paper we continue our investigation of the analogical neural network, paying interest to its replica symmetric behavior in the absence of external fields of any type. Bridging the neural network to a bipartite spin-glass, we introduce and apply a new interpolation scheme to its free energy that naturally extends the interpolation via cavity fields or stochastic perturbations to these models. As a result we obtain the free energy of the system as a sum rule, which, at least at the replica symmetric level, can be solved exactly. As a next step we study its related self-consistent equations for the order parameters and their rescaled fluctuations, found to diverge on the same critical line of the standard Amit-Gutfreund-Sompolinsky theory.Comment: 17 page

Self-Similar blow-up for a diffusion-attraction problem

In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the assumptions of radial symmetry, it is known that this system has at least two stable mechanisms of singularity formation (see e.g. M.P. Brenner et al.1999, Nonlinearity, 12, 1071-1098); one type is self-similar, and may be viewed as a trade-off between diffusion and attraction, while in the other type the attraction prevails over the diffusion and a non-self-similar shock wave results. Our main result identifies a class of initial data for which the blow-up behaviour is of the former, self-similar type. The blow-up profile is characterized as belonging to a subset of stationary solutions of the associated ordinary differential equation.Comment: 28 pages, 1 figure with 2 picture

Wigner representation for polarization-momentum hyperentanglement generated in parametric down conversion, and its application to complete Bell-state measurement

We apply the Wigner function formalism to the study of two-photon polarization-momentum hyperentanglement generated in parametric down conversion. It is shown that the consideration of a higher number of degrees of freedom is directly related to the extraction of additional uncorrelated sets of zeropoint modes at the source. We present a general expression for the description of the quantum correlations corresponding to the sixteen Bell base states, in terms of four beams whose amplitudes are correlated through the stochastic properties of the zeropoint field. A detailed analysis of the two experiments on complete Bell-state measurement included in [Walborn et al., Phys. Rev. A 68, 042313 (2003)] is made, emphasizing the role of the zeropoint field. Finally, we investigate the relationship between the zeropoint inputs at the source and the analysers, and the limits on optimal Bell-state measurement.Comment: 28 pages, 4 figure

Photoexcitation of lasers and chemical reactions for NASA missions: A theoretical study

The possibility of obtaining CW laser oscillation by optical pumping in the infrared at an elevated gas pressure is reviewed. A specific example utilizing a mixture of CO and NO gases is included. The gas pressures considered are in excess of several atmospheres. Laser frequency tuning over a broad region becomes possible at such elevated gas pressures due to collisional broadening of the amplifying transitions. The prior-rate and surprisal analysis are applied to obtain detailed VV and VT rates for CO and NO molecules and the transfer rates in a CO-NO gas mixture. The analysis is capable of giving temperature dependence of the rate constants. Computer estimates of the rates are presented for vibrational levels up to v = 50. The results show that in the high-lying vibrational states the VV transfer rates with Delta nu = 2 become appreciable

Partial Bell-state analysis with parametric down conversion in the Wigner function formalism

We apply the Wigner function formalism to partial Bell-state analysis using polarization entanglement produced in parametric down conversion. Two-photon statistics at a beam-splitter are reproduced by a wavelike description with zeropoint fluctuations of the electromagnetic field. In particular, the fermionic behaviour of two photons in the singlet state is explained from the invariance on the correlation properties of two light beams going through a balanced beam-splitter. Moreover, we show that a Bell-state measurement introduces some fundamental noise at the idle channels of the analyzers. As a consequence, the consideration of more independent sets of vacuum modes entering the crystal appears as a need for a complete Bell-state analysis