Boosting Monte Carlo simulations of spin glasses using autoregressive neural networks

The autoregressive neural networks are emerging as a powerful computational tool to solve relevant problems in classical and quantum mechanics. One of their appealing functionalities is that, after they have learned a probability distribution from a dataset, they allow exact and efficient sampling of typical system configurations. Here we employ a neural autoregressive distribution estimator (NADE) to boost Markov chain Monte Carlo (MCMC) simulations of a paradigmatic classical model of spin-glass theory, namely the two-dimensional Edwards-Anderson Hamiltonian. We show that a NADE can be trained to accurately mimic the Boltzmann distribution using unsupervised learning from system configurations generated using standard MCMC algorithms. The trained NADE is then employed as smart proposal distribution for the Metropolis-Hastings algorithm. This allows us to perform efficient MCMC simulations, which provide unbiased results even if the expectation value corresponding to the probability distribution learned by the NADE is not exact. Notably, we implement a sequential tempering procedure, whereby a NADE trained at a higher temperature is iteratively employed as proposal distribution in a MCMC simulation run at a slightly lower temperature. This allows one to efficiently simulate the spin-glass model even in the low-temperature regime, avoiding the divergent correlation times that plague MCMC simulations driven by local-update algorithms. Furthermore, we show that the NADE-driven simulations quickly sample ground-state configurations, paving the way to their future utilization to tackle binary optimization problems.Comment: 13 pages, 14 figure

Critical temperature of interacting Bose gases in two and three dimensions

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale Path Integral Monte Carlo simulations (with up to $N=10^5$ particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter $na^3 \lesssim 10^{-4}$. This value is different from the estimate $na^3 \lesssim 10^{-6}$ for the validity of the asymptotic expansion in the limit of vanishing $na^3$. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice $|\psi|^4$ model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.Comment: 4 pages, 5 figure

Incidence of mild cognitive impairment and dementia in Parkinson's disease: The Parkinson's disease cognitive impairment study

Background: Cognitive impairment in Parkinson's disease (PD) includes a spectrum varying from Mild Cognitive Impairment (PD-MCI) to PD Dementia (PDD). The main aim of the present study is to evaluate the incidence of PD-MCI, its rate of progression to dementia, and to identify demographic and clinical characteristics which predict cognitive impairment in PD patients. Methods: PD patients from a large hospital-based cohort who underwent at least two comprehensive neuropsychological evaluations were retrospectively enrolled in the study. PD-MCI and PDD were diagnosed according to the Movement Disorder Society criteria. Incidence rates of PD-MCI and PDD were estimated. Clinical and demographic factors predicting PD-MCI and dementia were evaluated using Cox proportional hazard model. Results: Out of 139 enrolled PD patients, 84 were classified with normal cognition (PD-NC), while 55 (39.6%) fulfilled the diagnosis of PD-MCI at baseline. At follow-up (mean follow-up 23.5 ± 10.3 months) 28 (33.3%) of the 84 PD-NC at baseline developed MCI and 4 (4.8%) converted to PDD. The incidence rate of PD-MCI was 184.0/1000 pyar (95% CI 124.7-262.3). At multivariate analysis a negative association between education and MCI development at follow-up was observed (HR 0.37, 95% CI 0.15-0.89; p = 0.03). The incidence rate of dementia was 24.3/1000 pyar (95% CI 7.7-58.5). Out of 55 PD-MCI patients at baseline, 14 (25.4%) converted to PDD, giving an incidence rate of 123.5/1000 pyar (95% CI 70.3-202.2). A five time increased risk of PDD was found in PD patients with MCI at baseline (RR 5.09, 95% CI 1.60-21.4). Conclusion: Our study supports the relevant role of PD-MCI in predicting PDD and underlines the importance of education in reducing the risk of cognitive impairment

Slave boson model for two-dimensional trapped Bose-Einstein condensate

A system of N bosons in a two-dimensional harmonic trap is considered. The system is treated in term of the slave boson representation for hard-core bosons which is valid in the arbitrary density regimes. I discuss the consequences of higher order interactions on the density profiles by mapping the slave boson equation to the known Kohn-Sham type equation within the density functional scheme.Comment: 12 pages, 3 figures. Submitted to J. Phys. B : At. mol. opt. phy

Solving the Hamilton-Jacobi Equation for General Relativity

We demonstrate a systematic method for solving the Hamilton-Jacobi equation for general relativity with the inclusion of matter fields. The generating functional is expanded in a series of spatial gradients. Each term is manifestly invariant under reparameterizations of the spatial coordinates (``gauge-invariant''). At each order we solve the Hamiltonian constraint using a conformal transformation of the 3-metric as well as a line integral in superspace. This gives a recursion relation for the generating functional which then may be solved to arbitrary order simply by functionally differentiating previous orders. At fourth order in spatial gradients, we demonstrate solutions for irrotational dust as well as for a scalar field. We explicitly evolve the 3-metric to the same order. This method can be used to derive the Zel'dovich approximation for general relativity.Comment: 13 pages, RevTeX, DAMTP-R93/2

Is there a problem with quantum wormhole states in N=1 Supergravity?

The issue concerning the existence of wormhole states in locally supersymmetric minisuperspace models with matter is addressed. Wormhole states are apparently absent in models obtained from the more general theory of N=1 supergravity with supermatter. A Hartle-Hawking type solution can be found, even though some terms (which are scalar field dependent) cannot be determined in a satisfactory way. A possible cause is investigated here. As far as the wormhole situation is concerned, we argue here that the type of Lagrange multipliers and fermionic derivative ordering used can make a difference. A proposal is made for supersymmetric quantum wormholes to also be invested with a Hilbert space structure, associated with a maximal analytical extension of the corresponding minisuperspace.is concerned, we argue here that the type of Lagrange multipliers and fermionic derivative ordering used can make a difference. A proposal is made for supersymmetric quantum wormholes to also be invested with a Hilbert space structure, associated with a maximal analytical extension of the corresponding minisuperspace.Comment: 22 pages, TeX (some font problems may occur, just press Return), Based on a essay submitted to the 1995 ravity Research Foundation Awards, accepted in G.R.

Breakdown of the semiclassical approximation at the black hole horizon

The definition of matter states on spacelike hypersurfaces of a 1+1 dimensional black hole spacetime is considered. The effect of small quantum fluctuations of the mass of the black hole due to the quantum nature of the infalling matter is taken into account. It is then shown that the usual approximation of treating the gravitational field as a classical background on which matter is quantized, breaks down near the black hole horizon. Specifically, on any hypersurface that captures both infalling matter near the horizon and Hawking radiation, quantum fluctuations in the background geometry become important, and a semiclassical calculation is inconsistent. An estimate of the size of correlations between the matter and gravity states shows that they are so strong that a fluctuation in the black hole mass of order exp[-M/M_{Planck}] produces a macroscopic change in the matter state.Comment: Latex, 31 pages + 5 uuencoded figure

Fluorine-induced J-aggregation enhances emissive properties of a new NLO push-pull chromophore

A new fluorinated push-pull chromophore with good second-order NLO properties even in concentrated solution shows solid state intermolecular aryl-fluoroaryl interactions leading to J-aggregates with intense solid state luminescence. This journal is \ua9 the Partner Organisations 2014

Strongly Correlated Quantum Fluids: Ultracold Quantum Gases, Quantum Chromodynamic Plasmas, and Holographic Duality

Strongly correlated quantum fluids are phases of matter that are intrinsically quantum mechanical, and that do not have a simple description in terms of weakly interacting quasi-particles. Two systems that have recently attracted a great deal of interest are the quark-gluon plasma, a plasma of strongly interacting quarks and gluons produced in relativistic heavy ion collisions, and ultracold atomic Fermi gases, very dilute clouds of atomic gases confined in optical or magnetic traps. These systems differ by more than 20 orders of magnitude in temperature, but they were shown to exhibit very similar hydrodynamic flow. In particular, both fluids exhibit a robustly low shear viscosity to entropy density ratio which is characteristic of quantum fluids described by holographic duality, a mapping from strongly correlated quantum field theories to weakly curved higher dimensional classical gravity. This review explores the connection between these fields, and it also serves as an introduction to the Focus Issue of New Journal of Physics on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas. The presentation is made accessible to the general physics reader and includes discussions of the latest research developments in all three areas.Comment: 138 pages, 25 figures, review associated with New Journal of Physics special issue "Focus on Strongly Correlated Quantum Fluids: from Ultracold Quantum Gases to QCD Plasmas" (http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Strongly%20Correlated%20Quantum%20Fluids%20-%20from%20Ultracold%20Quantum%20Gases%20to%20QCD%20Plasmas

Basics of Bose-Einstein Condensation

The review is devoted to the elucidation of the basic problems arising in the theoretical investigation of systems with Bose-Einstein condensate. Understanding these challenging problems is necessary for the correct description of Bose-condensed systems. The principal problems considered in the review are as follows: (i) What is the relation between Bose-Einstein condensation and global gauge symmetry breaking? (ii) How to resolve the Hohenberg-Martin dilemma of conserving versus gapless theories? (iii) How to describe Bose-condensed systems in strong spatially random potentials? (iv) Whether thermodynamically anomalous fluctuations in Bose systems are admissible? (v) How to create nonground-state condensates? Detailed answers to these questions are given in the review. As examples of nonequilibrium condensates, three cases are described: coherent modes, turbulent superfluids, and heterophase fluids.Comment: Review articl