Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study

By using exact Path Integral Monte Carlo methods we calculate the equation of state of an interacting Bose gas as a function of temperature both below and above the superfluid transition. The universal character of the equation of state for dilute systems and low temperatures is investigated by modeling the interatomic interactions using different repulsive potentials corresponding to the same s-wave scattering length. The results obtained for the energy and the pressure are compared to the virial expansion for temperatures larger than the critical temperature. At very low temperatures we find agreement with the ground-state energy calculated using the diffusion Monte Carlo method.Comment: 7 pages, 6 figure

Condensate deformation and quantum depletion of Bose-Einstein condensates in external potentials

The one-body density matrix of weakly interacting, condensed bosons in external potentials is calculated using inhomogeneous Bogoliubov theory. We determine the condensate deformation caused by weak external potentials on the mean-field level. The momentum distribution of quantum fluctuations around the deformed ground state is obtained analytically, and finally the resulting quantum depletion is calculated. The depletion due to the external potential, or potential depletion for short, is a small correction to the homogeneous depletion, validating our inhomogeneous Bogoliubov theory. Analytical results are derived for weak lattices and spatially correlated random potentials, with simple, universal results in the Thomas-Fermi limit of very smooth potentials.Comment: 17 pages, 4 figures. v2: published version, minor change

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

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

Transcranial random noise stimulation over the primary motor cortex in PD-MCI patients: a crossover, randomized, sham-controlled study

Mild cognitive impairment (MCI) is a very common non-motor feature of Parkinson’s disease (PD) and the non-amnestic single-domain is the most frequent subtype. Transcranial random noise stimulation (tRNS) is a non-invasive technique, which is capable of enhancing cortical excitability. As the main contributor to voluntary movement control, the primary motor cortex (M1) has been recently reported to be involved in higher cognitive functioning. The aim of this study is to evaluate the effects of tRNS applied over M1 in PD-MCI patients in cognitive and motor tasks. Ten PD-MCI patients, diagnosed according to the Movement Disorder Society, Level II criteria for MCI, underwent active (real) and placebo (sham) tRNS single sessions, at least 1 week apart. Patients underwent cognitive (Digit Span Forward and Backward, Digit Symbol, Visual Search, Letter Fluency, Stroop Test) and motor assessments (Unified Parkinson’s Disease Rating Scale [UPDRS-ME], specific timed trials for bradykinesia, 10-m walk and Timed up and go tests) before and after each session. A significant improvement in motor ability (UPDRS-ME and lateralized scores, ps from 0.049 to 0.003) was observed after real versus sham tRNS. On the contrary, no significant differences were found in other motor tasks and cognitive assessment both after real and sham stimulations. These results confirm that tRNS is a safe and effective tool for improving motor functioning in PD-MCI. Future studies using a multisession tRNS applied over multitargeted brain areas (i.e., dorsolateral prefrontal cortex and M1) are required to clarify the role of tRNS regarding rehabilitative intervention in PD

Bose-Einstein Condensate in Weak 3d Isotropic Speckle Disorder

The effect of a weak three-dimensional (3d) isotropic laser speckle disorder on various thermodynamic properties of a dilute Bose gas is considered at zero temperature. First, we summarize the derivation of the autocorrelation function of laser speckles in 1d and 2d following the seminal work of Goodman. The goal of this discussion is to show that a Gaussian approximation of this function, proposed in some recent papers, is inconsistent with the general background of laser speckle theory. Then we propose a possible experimental realization for an isotropic 3d laser speckle potential and derive its corresponding autocorrelation function. Using a Fourier transform of that function, we calculate both condensate depletion and sound velocity of a Bose-Einstein condensate as disorder ensemble averages of such a weak laser speckle potential within a perturbative solution of the Gross-Pitaevskii equation. By doing so, we reproduce the expression of the normalfluid density obtained earlier within the treatment of Landau. This physically transparent derivation shows that condensate particles, which are scattered by disorder, form a gas of quasiparticles which is responsible for the normalfluid component

Transport regimes of cold gases in a two-dimensional anisotropic disorder

We numerically study the dynamics of cold atoms in a two-dimensional disordered potential. We consider an anisotropic speckle potential and focus on the classical regime, which is relevant to some recent experiments. First, we study the behavior of particles with a fixed energy and identify different transport regimes. For low energy, the particles are classically localized due to the absence of a percolating cluster. For high energy, the particles undergo normal diffusion and we show that the diffusion constants scale algebraically with the particle energy, with an anisotropy factor which significantly differs from that of the disordered potential. For intermediate energy, we find a transient sub-diffusive regime, which is relevant to the time scale of typical experiments. Second, we study the behavior of a cold-atomic gas with an arbitrary energy distribution, using the above results as a groundwork. We show that the density profile of the atomic cloud in the diffusion regime is strongly peaked and, in particular, that it is not Gaussian. Its behavior at large distances allows us to extract the energy-dependent diffusion constants from experimental density distributions. For a thermal cloud released into the disordered potential, we show that our numerical predictions are in agreement with experimental findings. Not only does this work give insights to recent experimental results, but it may also serve interpretation of future experiments searching for deviation from classical diffusion and traces of Anderson localization.Comment: 19 pages, 16 figure

Hydrogen and halogen bonding drive the orthogonal self-assembly of an organic framework possessing 2D channels

Orthogonal self-assembly of an open organic framework showing 2D channels has been obtained by combining hydrogen and halogen bonding. The framework is able to host various guest molecules with a diverse set of steric demands and substitution patterns, and survives single-crystal-to-single-crystal guest exchanges from liquid and gas phases