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

Towards spatial reasoning on building information models

The paper presents a conceptual study on the application of spatial reasoning on building information models. In many cases, building regulations and client demands imply traints on the building design with inherent spatial semantics. If we are able to represent these spatial constraints in a computerinterpretable way, the building design can be checked for fulfilling them. In this context, spatial reasoning technology can be applied in two different ways. First, we can check the consistency of the spatial constraints in effect, i.e. find out whether there are contradictions between them. Second, we can check whether a concrete building design is compliant with these constraints. The paper gives a detailed overview on the currently available spatial calculi and introduces two possible implementation pproaches

Thermodynamic fermion-boson symmetry in harmonic oscillator potentials

A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to negative temperatures, and vice versa.Comment: 7 pages, no figures, submitted to PHYSICA A. More information available at http://www.physik.uni-osnabrueck.de/makrosysteme

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

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

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

Observations of meteoric material and implications for aerosol nucleation in the winter Arctic lower stratosphere derived from in situ particle measurements

Number concentrations of total and non-volatile aerosol particles with size diameters >0.01 μm as well as particle size distributions (0.4–23 μm diameter) were measured in situ in the Arctic lower stratosphere (10–20.5 km altitude). The measurements were obtained during the campaigns European Polar Stratospheric Cloud and Lee Wave Experiment (EUPLEX) and Envisat-Arctic-Validation (EAV). The campaigns were based in Kiruna, Sweden, and took place from January to March 2003. Measurements were conducted onboard the Russian high-altitude research aircraft Geophysica using the low-pressure Condensation Nucleus Counter COPAS (COndensation PArticle Counter System) and a modified FSSP 300 (Forward Scattering Spectrometer Probe). Around 18–20 km altitude typical total particle number concentrations nt range at 10–20 cm−3 (ambient conditions). Correlations with the trace gases nitrous oxide (N2O) and trichlorofluoromethane (CFC-11) are discussed. Inside the polar vortex the total number of particles >0.01 μm increases with potential temperature while N2O is decreasing which indicates a source of particles in the above polar stratosphere or mesosphere. A separate channel of the COPAS instrument measures the fraction of aerosol particles non-volatile at 250°C. Inside the polar vortex a much higher fraction of particles contained non-volatile residues than outside the vortex (~67% inside vortex, ~24% outside vortex). This is most likely due to a strongly increased fraction of meteoric material in the particles which is transported downward from the mesosphere inside the polar vortex. The high fraction of non-volatile residual particles gives therefore experimental evidence for downward transport of mesospheric air inside the polar vortex. It is also shown that the fraction of non-volatile residual particles serves directly as a suitable experimental vortex tracer. Nanometer-sized meteoric smoke particles may also serve as nuclei for the condensation of gaseous sulfuric acid and water in the polar vortex and these additional particles may be responsible for the increase in the observed particle concentration at low N2O. The number concentrations of particles >0.4 μm measured with the FSSP decrease markedly inside the polar vortex with increasing potential temperature, also a consequence of subsidence of air from higher altitudes inside the vortex. Another focus of the analysis was put on the particle measurements in the lowermost stratosphere. For the total particle density relatively high number concentrations of several hundred particles per cm3 at altitudes below ~14 km were observed in several flights. To investigate the origin of these high number concentrations we conducted air mass trajectory calculations and compared the particle measurements with other trace gas observations. The high number concentrations of total particles in the lowermost stratosphere are probably caused by transport of originally tropospheric air from lower latitudes and are potentially influenced by recent particle nucleation

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

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

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