Properties of bright squeezed vacuum at increasing brightness

A bright squeezed vacuum (BSV) is a nonclassical macroscopic state of light, which is generated through high-gain parametric down-conversion or four-wave mixing. Although the BSV is an important tool in quantum optics and has a lot of applications, its theoretical description is still not complete. In particular, the existing description in terms of Schmidt modes with gain-independent shapes fails to explain the spectral broadening observed in the experiment as the mean number of photons increases. Meanwhile, the semiclassical description accounting for the broadening does not allow us to decouple the intermodal photon-number correlations. In this work, we present a new generalized theoretical approach to describe the spatial properties of a multimode BSV. In the multimode case, one has to take into account the complicated interplay between all involved modes: each plane-wave mode interacts with all other modes, which complicates the problem significantly. The developed approach is based on exchanging the (k, t ) and (ω, z) representations and solving a system of integrodifferential equations. Our approach predicts correctly the dynamics of the Schmidt modes and the broadening of the angular distribution with the increase in the BSV mean photon number due to a stronger pumping. Moreover, the model correctly describes various properties of a widely used experimental configuration with two crystals and an air gap between them, namely, an SU(1,1) interferometer. In particular, it predicts the narrowing of the intensity distribution, the reduction and shift of the side lobes, and the decline in the interference visibility as the mean photon number increases due to stronger pumping. The presented experimental results confirm the validity of the new approach. The model can be easily extended to the case of the frequency spectrum, frequency Schmidt modes, and other experimental configurations

Diffusion at constant speed in a model phase space

We reconsider the problem of diffusion of particles at constant speed and present a generalization of the Telegrapher process to higher dimensional stochastic media ($d>1$), where the particle can move along $2^d$ directions. We derive the equations for the probability density function using the ``formulae of differentiation'' of Shapiro and Loginov. The model is an advancement over similiar models of photon migration in multiply scattering media in that it results in a true diffusion at constant speed in the limit of large dimensions.Comment: Final corrected version RevTeX, 6 pages, 1 figur

Stressed backbone and elasticity of random central-force systems

We use a new algorithm to find the stress-carrying backbone of ``generic'' site-diluted triangular lattices of up to 10^6 sites. Generic lattices can be made by randomly displacing the sites of a regular lattice. The percolation threshold is Pc=0.6975 +/- 0.0003, the correlation length exponent \nu =1.16 +/- 0.03 and the fractal dimension of the backbone Db=1.78 +/- 0.02. The number of ``critical bonds'' (if you remove them rigidity is lost) on the backbone scales as L^{x}, with x=0.85 +/- 0.05. The Young's modulus is also calculated.Comment: 5 pages, 5 figures, uses epsfi

Topological transitions in carbon nanotube networks via nanoscale confinement

Efforts aimed at large-scale integration of nanoelectronic devices that exploit the superior electronic and mechanical properties of single-walled carbon nanotubes (SWCNTs) remain limited by the difficulties associated with manipulation and packaging of individual SWNTs. Alternative approaches based on ultra-thin carbon nanotube networks (CNNs) have enjoyed success of late with the realization of several scalable device applications. However, precise control over the network electronic transport is challenging due to i) an often uncontrollable interplay between network coverage and its topology and ii) the inherent electrical heterogeneity of the constituent SWNTs. In this letter, we use template-assisted fluidic assembly of SWCNT networks to explore the effect of geometric confinement on the network topology. Heterogeneous SWCNT networks dip-coated onto sub-micron wide ultra-thin polymer channels exhibit a topology that becomes increasingly aligned with decreasing channel width and thickness. Experimental scale coarse-grained computations of interacting SWCNTs show that the effect is a reflection of an aligned topology that is no longer dependent on the network density, which in turn emerges as a robust knob that can induce semiconductor-to-metallic transitions in the network response. Our study demonstrates the effectiveness of directed assembly on channels with varying degrees of confinement as a simple tool to tailor the conductance of the otherwise heterogeneous network, opening up the possibility of robust large-scale CNN-based devices.Comment: 4 pages, 3 figure

fMRI-Based Effective Connectivity in Surgical Remediable Epilepsies: A Pilot Study

Simultaneous EEG-fMRI can contribute to identify the epileptogenic zone (EZ) in focal epilepsies. However, fMRI maps related to Interictal Epileptiform Discharges (IED) commonly show multiple regions of signal change rather than focal ones. Dynamic causal modeling (DCM) can estimate effective connectivity, i.e. the causal effects exerted by one brain region over another, based on fMRI data. Here, we employed DCM on fMRI data in 10 focal epilepsy patients with multiple IED-related regions of BOLD signal change, to test whether this approach can help the localization process of EZ. For each subject, a family of competing deterministic, plausible DCM models were constructed using IED as autonomous input at each node, one at time. The DCM findings were compared to the presurgical evaluation results and classified as: "Concordant" if the node identified by DCM matches the presumed focus, "Discordant" if the node is distant from the presumed focus, or "Inconclusive" (no statistically significant result). Furthermore, patients who subsequently underwent intracranial EEG recordings or surgery were considered as having an independent validation of DCM results. The effective connectivity focus identified using DCM was Concordant in 7 patients, Discordant in two cases and Inconclusive in one. In four of the 6 patients operated, the DCM findings were validated. Notably, the two Discordant and Invalidated results were found in patients with poor surgical outcome. Our findings provide preliminary evidence to support the applicability of DCM on fMRI data to investigate the epileptic networks in focal epilepsy and, particularly, to identify the EZ in complex cases

Importance Sampling and Stratification for Copula Models

An importance sampling approach for sampling from copula models is introduced. The proposed algorithm improves Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of its components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is particularly easy to implement for Archimedean copulas. We also show how the proposal distribution of our algorithm can be optimized by making a connection with stratified sampling. In a case study inspired by a typical insurance application, we obtain variance reduction factors sometimes larger than 1000 in comparison to standard Monte Carlo estimators when both importance sampling and quasi-Monte Carlo methods are used.NSERC, Grant 238959 NSERC, Grant 501