Mean-field description of pairing effects, BKT physics, and superfluidity in 2D Bose gases

We derive a mean-field description for two-dimensional (2D) interacting Bose gases at arbitrary temperatures. We find that genuine Bose-Einstein condensation with long-range coherence only survives at zero temperature. At finite temperatures, many-body pairing effects included in our mean-field theory introduce a finite amplitude for the pairing density, which results in a finite superfluid density. We incorporate Berezinskii-Kosterlitz-Thouless (BKT) physics into our model by considering the phase fluctuations of our pairing field. This then leads to the result that the superfluid phase is only stable below the BKT temperature due to these phase fluctuations. In the weakly interacting regime at low temperature we compare our theory to previous results from perturbative calculations, renormalization group calculations as well as Monte Carlo simulations. We present a finite-temperature phase diagram of 2D Bose gases. One signature of the finite amplitude of the pairing density field is a two-peak structure in the single-particle spectral function, resembling that of the pseudogap phase in 2D attractive Fermi gases. © 2014 Elsevier Inc

Synthetic-Neuroscore: Using A Neuro-AI Interface for Evaluating Generative Adversarial Networks

Generative adversarial networks (GANs) are increasingly attracting attention in the computer vision, natural language processing, speech synthesis and similar domains. Arguably the most striking results have been in the area of image synthesis. However, evaluating the performance of GANs is still an open and challenging problem. Existing evaluation metrics primarily measure the dissimilarity between real and generated images using automated statistical methods. They often require large sample sizes for evaluation and do not directly reflect human perception of image quality. In this work, we describe an evaluation metric we call Neuroscore, for evaluating the performance of GANs, that more directly reflects psychoperceptual image quality through the utilization of brain signals. Our results show that Neuroscore has superior performance to the current evaluation metrics in that: (1) It is more consistent with human judgment; (2) The evaluation process needs much smaller numbers of samples; and (3) It is able to rank the quality of images on a per GAN basis. A convolutional neural network (CNN) based neuro-AI interface is proposed to predict Neuroscore from GAN-generated images directly without the need for neural responses. Importantly, we show that including neural responses during the training phase of the network can significantly improve the prediction capability of the proposed model. Materials related to this work are provided at https://github.com/villawang/Neuro-AI-Interface

Pacifying the Fermi-liquid: battling the devious fermion signs

The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics are self consistently translated into a geometrical constraint structure (the {\em nodal hypersurface}) acting on an effective bosonic dynamics. As an illustrative example we use this formalism to study 1+1-dimensional systems, where statistics are irrelevant, and hence the sign problem can be circumvented. In this low-dimensional example, the structure of the nodal constraints leads to a lucid picture of the entropic interaction essential to one-dimensional physics. Working with the path integral in momentum space, we then show that the Fermi gas can be understood by analogy to a Mott insulator in a harmonic trap. Going back to real space, we discuss the topological properties of the nodal cells, and suggest a new holographic conjecture relating Fermi liquids in higher dimensions to soft-core bosons in one dimension. We also discuss some possible connections between mixed Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure

Developed turbulence: From full simulations to full mode reductions

Developed Navier-Stokes turbulence is simulated with varying wavevector mode reductions. The flatness and the skewness of the velocity derivative depend on the degree of mode reduction. They show a crossover towards the value of the full numerical simulation when the viscous subrange starts to be resolved. The intermittency corrections of the scaling exponents of the pth order velocity structure functions seem to depend mainly on the proper resolution of the inertial subrange. Universal scaling properties (i.e., independent of the degree of mode reduction) are found for the relative scaling exponents rho which were recently defined by Benzi et al.Comment: 4 pages, 5 eps-figures, replaces version from August 5th, 199

Coincident extremely large sporadic sodium and sporadic E layers observed in the lower thermosphere over Colorado and Utah

International audienceOn the night of 2 June 2002, the sodium lidar in Fort Collins, CO (40.6 N, 105 W) measured an extremely strong sporadic sodium layer lasting from 03:30 to 05:00 UT with several weaker layers later in the night at 06:00 and 09:00 UT. There is a double layer structure with peaks at 101 and 104 km. The peak sodium density was 21 000 atoms/cm3 with a column abundance of up to twice that of the normal sodium layer. The peak density was 500 times greater than the typical density at that altitude. The sporadic layer abundance and strength factor were higher than any reported in the literature. The two lidar beams, separated by 70 km at this altitude, both measured 0.6 h periodicities in the abundance, but out of phase with each other by 0.3 h. There is also evidence for strong wave activity in the lidar temperatures and winds. The NOAA ionosonde in Boulder, CO (40.0 N, 105 W) measured a critical frequency (foEs) of 14.3 MHz at 03:00 UT on this night, the highest value anytime during 2002. The high values of total ion density inferred means that Na+ fraction must have been only a few percent to explain the neutral Na layer abundances. The Bear Lake, Utah (41.9 N, 111.4 W) dynasonde also measured intense Es between 02:00 and 05:00 UT and again from 06:00 to 08:00 UT about 700 km west of the lidar, with most of the ionograms during these intervals measuring Es up to 12 MHz, the limit of the ionosonde sweep. Other ionosondes around North America on the NGDC database measured normal foEs values that night, so it was a localized event within North America. The peak of Es activity observed in Europe during the summer of 2002 occurred on 4 June. The observations are consistent with the current theories where a combination of wind shears and long period waves form and push downward a concentrated layer of ions, which then chemically react and form a narrow layer of sodium atoms

A new scaling property of turbulent flows

We discuss a possible theoretical interpretation of the self scaling property of turbulent flows (Extended Self Similarity). Our interpretation predicts that, even in cases when ESS is not observed, a generalized self scaling, must be observed. This prediction is checked on a number of laboratory experiments and direct numerical simulations.Comment: Plain Latex, 1 figure available upon request to [email protected]

Polarization anisotropy in the optical properties of silicon ellipsoids

A new real space quantum mechanical approach with local field effects included is applied to the calculation of the optical properties of silicon nanocrystals. Silicon ellipsoids are studied and the role of surface polarization is discussed in details. In particular, surface polarization is shown to be responsible for a strong optical anisotropy in silicon ellipsoids, much more pronounced with respect to the case in which only quantum confinement effects are considered. The static dielectric constant and the absorption spectra are calculated, showing that the perpendicular and parallel components have a very different dependence on the ellipsoid aspect ratio. Then, a comparison with the classical dielectric model is performed, showing that the model only works for large and regular structures, but it fails for thin elongated ellipsoids.Comment: 5 pages, 4 figures, International Conference on NANO-Structures Self-Assemblin