Comment on "Canonical and Mircocanonical Calculations for Fermi Systems"

In the context of nuclear physics Pratt recently investigated noninteracting Fermi systems described by the microcanonical and canonical ensemble. As will be shown his discussion of the model of equally spaced levels contains a flaw and a statement which is at least confusing.Comment: Comment on S. Pratt, Phys. Rev. Lett. 84, 4255 (2000) and nucl-th/990505

Order-disorder transition in nanoscopic semiconductor quantum rings

Using the path integral Monte Carlo technique we show that semiconductor quantum rings with up to six electrons exhibit a temperature, ring diameter, and particle number dependent transition between spin ordered and disordered Wigner crystals. Due to the small number of particles the transition extends over a broad temperature range and is clearly identifiable from the electron pair correlation functions.Comment: 4 pages, 5 figures, For recent information on physics of small systems see http://www.smallsystems.d

Classification of phase transitions in small systems

We present a classification scheme for phase transitions in finite systems like atomic and molecular clusters based on the Lee-Yang zeros in the complex temperature plane. In the limit of infinite particle numbers the scheme reduces to the Ehrenfest definition of phase transitions and gives the right critical indices. We apply this classification scheme to Bose-Einstein condensates in a harmonic trap as an example of a higher order phase transitions in a finite system and to small Ar clusters.Comment: 12 pages, 4 figures, accepted for publication in Phys. Rev. Let

Fluorescence from a few electrons

Systems containing few Fermions (e.g., electrons) are of great current interest. Fluorescence occurs when electrons drop from one level to another without changing spin. Only electron gases in a state of equilibrium are considered. When the system may exchange electrons with a large reservoir, the electron-gas fluorescence is easily obtained from the well-known Fermi-Dirac distribution. But this is not so when the number of electrons in the system is prevented from varying, as is the case for isolated systems and for systems that are in thermal contact with electrical insulators such as diamond. Our accurate expressions rest on the assumption that single-electron energy levels are evenly spaced, and that energy coupling and spin coupling between electrons are small. These assumptions are shown to be realistic for many systems. Fluorescence from short, nearly isolated, quantum wires is predicted to drop abruptly in the visible, a result not predicted by the Fermi-Dirac distribution. Our exact formulas are based on restricted and unrestricted partitions of integers. The method is considerably simpler than the ones proposed earlier, which are based on second quantization and contour integration.Comment: 10 pages, 3 figures, RevTe

Heterogeneous freezing of single sulfuric acid solution droplets: laboratory experiments utilizing an acoustic levitator

International audienceThe heterogeneous freezing temperatures of single binary sulfuric acid solution droplets were measured in dependency of acid concentration down to temperatures as low as -50°C. In order to avoid influence of supporting substrates on the freezing characteristics, a new technique has been developed to suspend the droplet by means of an acoustic levitator. The droplets contained immersed particles of graphite, kaolin or montmorillonite in order to study the influence of the presence of such contamination on the freezing temperature. The radii of the suspended droplets spanned the range between 0.4 and 1.1mm and the concentration of the sulfuric acid solution varied between 5 and 14 weight percent. The presence of the particles in the solution raises the freezing temperature with respect to homogeneous freezing of these solution droplets. The pure solution droplets can be supercooled up to 40 degrees below the ice-acid solution thermodynamic equilibrium curve. Depending on the concentration of sulfuric acid and the nature of the impurity the polluted droplets froze between -11°C and -35°C. The new experimental set-up, combining a deep freezer with a movable ultrasonic levitator and suitable optics, proved to be a useful approach for such investigations on individual droplets

Classification of the Nuclear Multifragmentation Phase Transition

Using a recently proposed classification scheme for phase transitions in finite systems [Phys.Rev.Lett.{\bf 84},3511 (2000)] we show that within the statistical standard model of nuclear multifragmentation the predicted phase transition is of first order.Comment: 5 pages, 4 eps figures, accepted for publication in Phys.Rev.C (in press

Deceptive signals of phase transitions in small magnetic clusters

We present an analysis of the thermodynamic properties of small transition metal clusters and show how the commonly used indicators of phase transitions like peaks in the specific heat or magnetic susceptibility can lead to deceptive interpretations of the underlying physics. The analysis of the distribution of zeros of the canonical partition function in the whole complex temperature plane reveals the nature of the transition. We show that signals in the magnetic susceptibility at positive temperatures have their origin at zeros lying at negative temperatures.Comment: 4 pages, 5 figures, revtex4, for further information see http://www.smallsystems.d

Towards predicting Pedestrian Evacuation Time and Density from Floorplans using a Vision Transformer

Conventional pedestrian simulators are inevitable tools in the design process of a building, as they enable project engineers to prevent overcrowding situations and plan escape routes for evacuation. However, simulation runtime and the multiple cumbersome steps in generating simulation results are potential bottlenecks during the building design process. Data-driven approaches have demonstrated their capability to outperform conventional methods in speed while delivering similar or even better results across many disciplines. In this work, we present a deep learning-based approach based on a Vision Transformer to predict density heatmaps over time and total evacuation time from a given floorplan. Specifically, due to limited availability of public datasets, we implement a parametric data generation pipeline including a conventional simulator. This enables us to build a large synthetic dataset that we use to train our architecture. Furthermore, we seamlessly integrate our model into a BIM-authoring tool to generate simulation results instantly and automatically

The interplay between shell effects and electron correlations in quantum dots

We use the Path Integral Monte Carlo method to investigate the interplay between shell effects and electron correlations in single quantum dots with up to 12 electrons. By use of an energy estimator based on the hypervirial theorem of Hirschfelder we study the energy contributions of different interaction terms in detail. We discuss under which conditions the total spin of the electrons is given by Hund's rule, and the temperature dependence of the crystallization effects.Comment: 6 pages, 4 figure

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de