2,998 research outputs found
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 for different values of 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]
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 Taylor-Reynolds number
up to , employing a reduced wave
vector set method (introduced earlier) to approximately solve the Navier-Stokes
equation. First, also for these extremely high Reynolds numbers ,
the energy spectra as well as the higher moments -- when scaled by the spectral
intensity at the wave number of peak dissipation -- can be described by
{\it one universal} function of for all . Second, the ISR
scaling exponents of this universal function are in agreement with
the 1941 Kolmogorov theory (the better, the large is), as is the
dependence of . Only around 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.
Fractal dimension crossovers in turbulent passive scalar signals
The fractal dimension of turbulent passive scalar signals is
calculated from the fluid dynamical equation. depends on the
scale. For small Prandtl (or Schmidt) number one gets two ranges,
for small scale r and =5/3 for large r, both
as expected. But for large one gets a third, intermediate range in
which the signal is extremely wrinkled and has . In that
range the passive scalar structure function has a plateau. We
calculate the -dependence of the crossovers. Comparison with a numerical
reduced wave vector set calculation gives good agreement with our predictions.Comment: 7 pages, Revtex, 3 figures (postscript file on request
Spectropolarimetric observations of the Ca II 8498 A and 8542 A lines in the quiet Sun
The Ca II infrared triplet is one of the few magnetically sensitive
chromospheric lines available for ground-based observations. We present
spectropolarimetric observations of the 8498 A and 8542 A lines in a quiet Sun
region near a decaying active region and compare the results with a simulation
of the lines in a high plasma-beta regime. Cluster analysis of Stokes V profile
pairs shows that the two lines, despite arguably being formed fairly close,
often do not have similar shapes. In the network, the local magnetic topology
is more important in determining the shapes of the Stokes V profiles than the
phase of the wave, contrary to what our simulations show. We also find that
Stokes V asymmetries are very common in the network, and the histograms of the
observed amplitude and area asymmetries differ significantly from the
simulation. Both the network and internetwork show oscillatory behavior in the
Ca II lines. It is stronger in the network, where shocking waves, similar to
those in the high-beta simulation, are seen and large self-reversals in the
intensity profiles are common.Comment: 23 pages, 17 figures, accepted to ApJ some figures are low-res, for
high-res email [email protected]
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
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
Dynamics of an electron in finite and infinite one dimensional systems in presence of electric field
We study,numerically, the dynamical behavior of an electron in a two site
nonlinear system driven by dc and ac electric field separately. We also study,
numerically, the effect of electric field on single static impurity and
antidimeric dynamical impurity in an infinite 1D chain to find the strength of
the impurities. Analytical arguments for this system have also been given.Comment: File Latex, 8 Figures available on reques
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
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