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

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

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

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

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

Magnetic impurity resonance states and symmetry of the superconducting order parameter in iron-based superconductors

We investigate the effect of magnetic impurities on the local quasiparticle density of states (LDOS) in iron-based superconductors. Employing the two-orbital model where 3$d$ electron and hole conduction bands are hybridizing with the localized $f$-orbital of the impurity spin, we investigate how various symmetries of the superconducting gap and its nodal structure influence the quasiparticle excitations and impurity bound states. We show that the bound states behave qualitatively different for each symmetry. Most importantly we find that the impurity-induced bound states can be used to identify the nodal structure of the extended s-wave symmetry ($S^{\pm}$) that is actively discussed in ferropnictides.Comment: 7 pages, 5 figures, theory part is extended, figures are replace

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 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

Fractionation of sulfur isotopes during heterogeneous oxidation of SO₂ on sea salt aerosol: a new tool to investigate non-sea salt sulfate production in the marine boundary layer

The oxidation of SO₂ to sulfate on sea salt aerosols in the marine environment is highly important because of its effect on the size distribution of sulfate and the potential for new particle nucleation from H₂SO₄ (g). However, models of the sulfur cycle are not currently able to account for the complex relationship between particle size, alkalinity, oxidation pathway and rate – which is critical as SO₂ oxidation by O₃ and Cl catalysis are limited by aerosol alkalinity, whereas oxidation by hypohalous acids and transition metal ions can continue at low pH once alkalinity is titrated. We have measured ³⁴S/³²S fractionation factors for SO₂ oxidation in sea salt, pure water and NaOCl aerosol, as well as the pH dependency of fractionation. <br><br> Oxidation of SO₂ by NaOCl aerosol was extremely efficient, with a reactive uptake coefficient of ≈0.5, and produced sulfate that was enriched in ³²S with &alpha;_OCl = 0.9882±0.0036 at 19 °C. Oxidation on sea salt aerosol was much less efficient than on NaOCl aerosol, suggesting alkalinity was already exhausted on the short timescale of the experiments. Measurements at pH = 2.1 and 7.2 were used to calculate fractionation factors for each step from SO₂(g) → multiple steps → SO_OCl^2&minus;. Oxidation on sea salt aerosol resulted in a lower fractionation factor than expected for oxidation of SO₃^2&minus; by O₃ (&alpha;_seasalt = 1.0124±0.0017 at 19 °C). Comparison of the lower fractionation during oxidation on sea salt aerosol to the fractionation factor for high pH oxidation shows HOCl contributed 29% of S(IV) oxidation on sea salt in the short experimental timescale, highlighting the potential importance of hypohalous acids in the marine environment. <br><br> The sulfur isotope fractionation factors measured in this study allow differentiation between the alkalinity-limited pathways – oxidation by O₃ and by Cl catalysis (&alpha;₃₄ = 1.0163&plusmn;0.0018 at 19 °C in pure water or 1.0199&plusmn;0.0024 at pH = 7.2) – which favour the heavy isotope, and the alkalinity non-limited pathways – oxidation by transition metal catalysis (&alpha;₃₄ = 0.9905±0.0031 at 19 °C, Harris et al., 2012a) and by hypohalites (&alpha;₃₄ = 0.9882±0.0036 at 19 °C) – which favour the light isotope. In combination with field measurements of the oxygen and sulfur isotopic composition of SO₂ and sulfate, the fractionation factors presented in this paper may be capable of constraining the relative importance of different oxidation pathways in the marine boundary layer