Bose-Einstein condensation under external conditions

We discuss the phenomenon of Bose-Einstein condensation under general external conditions using connections between partition sums and the heat-equation. Thermodynamical quantities like the critical temperature are given in terms of the heat-kernel coefficients of the associated Schr\"odinger equation. The general approach is applied to situations where the gas is confined by arbitrary potentials or by boxes of arbitrary shape.Comment: 11 pages, LaTeX, to appear in Phys. Lett.

Density of states for Bose-Einstein condensation in harmonic oscillator potentials

We discuss how it is possible to obtain a reliable approximation for the density of states for a system of particles in an anisotropic harmonic oscillator potential. A direct application of the result to study Bose-Einstein condensation of atomic gases in a potential trap can be given. In contrast to a previous study, our method involves only analytic calculations.Comment: 7 pages, LaTeX2e, no figure

Investigations on finite ideal quantum gases

Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional harmonic oscillator potential, for the three-dimensional harmonic oscillator approximations are tested. Applications to excited nuclei and Bose-Einstein condensation are discussed.Comment: 13 pages, 7 postscript figures, uses 'epsfig.sty'. Submitted to Physica A. More information available at http://obelix.physik.uni-osnabrueck.de/~schnack

Bose-Einstein condensation in arbitrarily shaped cavities

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical temperature of the system, is considered. We use two main methods which are shown to be equivalent. The first deals with the partition function as a sum over energy levels and uses a Mellin-Barnes integral representation to extract an asymptotic formula. The second method converts the sum over the energy levels to an integral with a suitable density of states factor obtained from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review

Smoking and High-Sensitivity Troponin I Levels in Young and Healthy Adults from the General Population

Lower troponin concentrations measured in smokers in a healthy population raise the question of whether a lower troponin threshold should be considered for tobacco users. We aim to evaluate differences in troponin levels according to the smoking status in healthy young adults. Participants aged 25–41 years were enrolled in a population-based observational study. The smoking status was self-assessed, and participants were classified as never-, past-, and current smokers. Pack-years of smoking were calculated. High-sensitivity cardiac troponin I (hs-cTnI) concentrations were measured from thawed blood samples, and associations were assessed using multivariable linear regression analyses. We included 2155 subjects in this analysis. The mean (SD) age was 35.4 ± 5.22 years; 53% were women. The median hs-cTnI levels across smoking status categories were 0.70 (interquartile range 0.43–1.23) ng/L in never smokers (n = 1174), 0.69 (interquartile range 0.43–1.28) ng/L in past smokers (n = 503), and 0.67 (interquartile range 0.41–1.04) ng/L in current smokers (n = 478), p = 0.04. The troponin levels remained significantly lower in current smokers after adjustment for potential confounders (β-coefficient [95%CI] of −0.08 [−0.25; −0.08], p < 0.001). Our results confirm that current smokers have lower hs-cTnI levels than past or never smokers, with a significant dose–response relationship among current smokers. The absolute differences in hs-cTnI levels were small

Bose-Einstein Condensation in a Harmonic Potential

We examine several features of Bose-Einstein condensation (BEC) in an external harmonic potential well. In the thermodynamic limit, there is a phase transition to a spatial Bose-Einstein condensed state for dimension D greater than or equal to 2. The thermodynamic limit requires maintaining constant average density by weakening the potential while increasing the particle number N to infinity, while of course in real experiments the potential is fixed and N stays finite. For such finite ideal harmonic systems we show that a BEC still occurs, although without a true phase transition, below a certain ``pseudo-critical'' temperature, even for D=1. We study the momentum-space condensate fraction and find that it vanishes as 1/N^(1/2) in any number of dimensions in the thermodynamic limit. In D less than or equal to 2 the lack of a momentum condensation is in accord with the Hohenberg theorem, but must be reconciled with the existence of a spatial BEC in D=2. For finite systems we derive the N-dependence of the spatial and momentum condensate fractions and the transition temperatures, features that may be experimentally testable. We show that the N-dependence of the 2D ideal-gas transition temperature for a finite system cannot persist in the interacting case because it violates a theorem due to Chester, Penrose, and Onsager.Comment: 34 pages, LaTeX, 6 Postscript figures, Submitted to Jour. Low Temp. Phy

Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions

For a fermion gas with equally spaced energy levels, the density and the pair correlation function are obtained. The derivation is based on the path integral approach for identical particles and the inversion of the generating functions for both static responses. The density and the pair correlation function are evaluated explicitly in the ground state of a confined fermion system with a number of particles ranging from 1 to 220 and filling the Fermi level completely.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in Phys. Rev. E, Vol. 58 (August 1, 1998

Blood Omega-3 Fatty Acids Are Inversely Associated With Albumin-Creatinine Ratio in Young and Healthy Adults (The Omega-Kid Study).

Background: Omega-3 fatty acids are associated with a lower risk of cardiovascular disease (CVD) and with beneficial effects on CV risk factors. The albumin-creatinine ratio (ACR) is a risk factor for CVD, all-cause mortality and accelerated glomerular filtration rate (GFR) decline in the general population. We aimed to investigate the association between n-3 PUFAS and ACR in heathy individuals with preserved GFR. Design and Methods: The present cross-sectional analysis is part of the GAPP study, a population-based cohort of healthy adults aged 25-41 years. Individuals with known CVD, diabetes, or a BMI >35 kg/m2 were excluded. eGFR was calculated according to the combined Creatinine/Cystatin C CKD-EPI formula. ACR was obtained from a fasting morning urine sample. The Omega-3 Index (relative amount of EPA and DHA of total fatty acids in %) was obtained from whole blood aliquots. Results: Overall, 2001 participants (median age 37 years IQR 31; 40, 53% female) were included in this analysis. Median Omega-3 Index was 4.59 (IQR 4.06; 5.25) and median eGFR 111 ml/min/1.73 m2 (IQR 103; 118). Median ACR was 0.14 mg/mmol (IQR 0; 0.43). We found a significant inverse association of the Omega-3 Index with ACR (ratio 0.84, 95%CI 0.73-0.96; p = 0.011) which remained after comprehensive adjustment (ratio 0.86, 95%CI 0.74-1.00; p = 0.048). No association of the Omega-3 Index with eGFR was found. The adjusted difference in eGFR per 1-unit increase in Omega3-Index was -0.21 (95%CI -0.76; 0.35; p = 0.47). Conclusions: A higher Omega-3 Index was significantly associated with lower ACR in this young and healthy population with preserved eGFR. Omega-3 fatty acids may exhibit cardio- and nephroprotective effects in healthy individuals through modulation of ACR

Bose-Einstein condensation of atomic gases in a harmonic oscillator confining potential trap

We present a model which predicts the temperature of Bose-Einstein condensation in atomic alkali gases and find excellent agreement with recent experimental observations. A system of bosons confined by a harmonic oscillator potential is not characterized by a critical temperature in the same way as an identical system which is not confined. We discuss the problem of Bose-Einstein condensation in an isotropic harmonic oscillator potential analytically and numerically for a range of parameters of relevance to the study of low temperature gases of alkali metals.Comment: 11 pages latex with two postscript figure

Concentrations of Serum Brain Injury Biomarkers Following SARS-CoV-2 Infection in Individuals with and without Long-COVID-Results from the Prospective Population-Based COVI-GAPP Study.

It is unknown whether neurological symptoms are associated with brain injury after SARS-CoV-2 infections and whether brain injury and related symptoms also emerge in Long-COVID patients. Biomarkers such as serum neurofilament light chain (sNfL) and glial fibrillary acidic protein (sGFAP) can be used to elucidate neuro-axonal and astroglial injuries. We investigated whether these biomarkers are associated with COVID-19 infection status, associated symptoms and Long-COVID. From 146 individuals of the general population with a post-acute, mild-to-moderate SARS-CoV-2 infection, sNfL and sGFAP were measured before, during and after (five and ten months) the infection. Individual symptoms and Long-COVID status were assessed using questionnaires. Neurological associated symptoms were described for individuals after a mild and moderate COVID-19 infection; however, sNfL (p = 0.74) and sGFAP (p = 0.24) did not change and were not associated with headache (p = 0.51), fatigue (p = 0.93), anosmia (p = 0.77) or ageusia (p = 0.47). In Long-COVID patients, sGFAP (p = 0.038), but not sNfL (p = 0.58), significantly increased but was not associated with neurological associated symptoms. Long-COVID status, but not post-acute SARS-CoV-2 infections, may be associated with astroglial injury/activation, even if neurological associated symptoms were not correlated