Molecular hydrogen as baryonic dark matter

High-angular resolution CO observations of small-area molecular structures (SAMS) are presented. The feature-less structures seen in the single-dish measurements break up into several smaller clumps in the interferometer map. At an adopted distance of 100pc their sizes are of order a few hundred AU, some of which are still unresolved at an angular resolution of about 3". The clumps have a fractal structure with a fractal index between 1.7 and 2.0. Their kinetic temperature is between 7K and 18K. Adopting standard conversion factors masses are about 1/10 Jupiter-masses for individual clumps and densities are higher than 20000cm^{-3}. The clumps are highly overpressured and it is unknown what creates or maintains such structures.Comment: 8 pages, 1 figure, accepted by Astrophysical Journal Letter

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

Variational bound on energy dissipation in turbulent shear flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in plane Couette flow, bridging the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits structure, namely a pronounced minimum at intermediate Reynolds numbers, and recovers the Busse bound in the asymptotic regime. The most notable feature is a bifurcation of the minimizing wavenumbers, giving rise to simple scaling of the optimized variational parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz file from [email protected]

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

Modified semiclassical approximation for trapped Bose gases

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The results of the modified approach are shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. Effective thermodynamic limit is defined for any confining dimension. The behaviour of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.Comment: Revtex file, 13 page

Localization and entanglement of two interacting electrons in a quantum-dot molecule

The localization of two interacting electrons in a coupled-quantum-dots semiconductor structure is demonstrated through numerical calculations of the time evolution of the two-electron wave function including the Coulomb interaction between the electrons. The transition from the ground state to a localized state is induced by an external, time-dependent, uniform electric field. It is found that while an appropriate constant field can localize both electrons in one of the wells, oscillatory fields can induce roughly equal probabilities for both electrons to be localized in either well, generating an interesting type of localized and entangled state. We also show that shifting the field suddenly to an appropriate constant value can maintain in time both types of localization.Comment: 4 pages, 4 figure

On phases in weakly interacting finite Bose systems

We study precursors of thermal phase transitions in finite systems of interacting Bose gases. For weakly repulsive interactions there is a phase transition to the one-vortex state. The distribution of zeros of the partition function indicates that this transition is first order, and the precursors of the phase transition are already displayed in systems of a few dozen bosons. Systems of this size do not exhibit new phases as more vortices are added to the system.Comment: 7 pages, 2 figure

Transitions and Probes in Turbulent Helium

Previous analysis of a Paris turbulence experiment \cite{zoc94,tab95} shows a transition at the Taylor Reynolds number \rel \approx 700. Here correlation function data is analyzed which gives further evidence for this transition. It is seen in both the power spectrum and in structure function measurements. Two possible explanations may be offered for this observed transition: that it is intrinsic to the turbulence flow in this closed box experiment or that it is an effect of a change in the flow around the anemometer. We particularly examine a pair of ``probe effects''. The first is a thermal boundary layer which does exist about the probe and does limit the probe response, particularly at high frequencies. Arguments based on simulations of the response and upon observations of dissipation suggests that this effect is only crucial beyond \rel\approx 2000. The second effect is produced by vortex shedding behind the probe. This has been seen to produce a large modification in some of the power spectra for large \rel. It might also complicate the interpretation of the experimental results. However, there seems to be a remaining range of data for \rel < 1300 uncomplicated by these effects, and which are thus suggestive of an intrinsic transition.Comment: uuencoded .ps files. submitted to PRE. 12 figures are sent upon request to jane wang ([email protected]

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev.

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