1,208 research outputs found
Viscosity in the escape-rate formalism
We apply the escape-rate formalism to compute the shear viscosity in terms of
the chaotic properties of the underlying microscopic dynamics. A first passage
problem is set up for the escape of the Helfand moment associated with
viscosity out of an interval delimited by absorbing boundaries. At the
microscopic level of description, the absorbing boundaries generate a fractal
repeller. The fractal dimensions of this repeller are directly related to the
shear viscosity and the Lyapunov exponent, which allows us to compute its
values. We apply this method to the Bunimovich-Spohn minimal model of viscosity
which is composed of two hard disks in elastic collision on a torus. These
values are in excellent agreement with the values obtained by other methods
such as the Green-Kubo and Einstein-Helfand formulas.Comment: 16 pages, 16 figures (accepted in Phys. Rev. E; October 2003
Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
In systems with few degrees of freedom modern quantum calculations are, in
general, numerically more efficient than semiclassical methods. However, this
situation can be reversed with increasing dimension of the problem. For a
three-dimensional system, viz. the hyperbolic four-sphere scattering system, we
demonstrate the superiority of semiclassical versus quantum calculations.
Semiclassical resonances can easily be obtained even in energy regions which
are unattainable with the currently available quantum techniques.Comment: 10 pages, 1 figure, submitted to Phys. Lett.
Quantum fingerprints of classical Ruelle-Pollicot resonances
N-disk microwave billiards, which are representative of open quantum systems,
are studied experimentally. The transmission spectrum yields the quantum
resonances which are consistent with semiclassical calculations. The spectral
autocorrelation of the quantum spectrum is shown to be determined by the
classical Ruelle-Pollicot resonances, arising from the complex eigenvalues of
the Perron-Frobenius operator. This work establishes a fundamental connection
between quantum and classical correlations in open systems.Comment: 6 pages, 2 eps figures included, submitted to PR
Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal Conductivity
The thermal conductivity is calculated with the Helfand-moment method in the
Lennard-Jones fluid near the triple point. The Helfand moment of thermal
conductivity is here derived for molecular dynamics with periodic boundary
conditions. Thermal conductivity is given by a generalized Einstein relation
with this Helfand moment. We compute thermal conductivity by this new method
and compare it with our own values obtained by the standard Green-Kubo method.
The agreement is excellent.Comment: Submitted to the Journal of Chemical Physic
Thermodynamic time asymmetry in nonequilibrium fluctuations
We here present the complete analysis of experiments on driven Brownian
motion and electric noise in a circuit, showing that thermodynamic entropy
production can be related to the breaking of time-reversal symmetry in the
statistical description of these nonequilibrium systems. The symmetry breaking
can be expressed in terms of dynamical entropies per unit time, one for the
forward process and the other for the time-reversed process. These entropies
per unit time characterize dynamical randomness, i.e., temporal disorder, in
time series of the nonequilibrium fluctuations. Their difference gives the
well-known thermodynamic entropy production, which thus finds its origin in the
time asymmetry of dynamical randomness, alias temporal disorder, in systems
driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and
experimen
Spectral Characterization of Anomalous Diffusion of a Periodic Piecewise Linear Intermittent Map
For a piecewise linear version of the periodic map with anomalous diffusion,
the evolution of statistical averages of a class of observables with respect to
piecewise constant initial densities is investigated and generalized
eigenfunctions of the Frobenius-Perron operator are explicitly derived. The
evolution of the averages is controlled by real eigenvalues as well as
continuous spectra terminating at the unit circle. Appropriate scaling limits
are shown to give a normal diffusion if the reduced map is in the stationary
regime with normal fluctuations, a L\'evy flight if the reduced map is in the
stationary regime with L\'evy-type fluctuations and a transport of ballistic
type if the reduced map is in the non-stationary regime.Comment: submitted to Physica D (CHAOTRAN conference proceedings
A Herschel PACS survey of the dust and gas in Upper Scorpius disks
We present results of far-infrared photometric observations with Herschel
PACS of a sample of Upper Scorpius stars, with a detection rate of previously
known disk-bearing K and M stars at 70, 100, and 160 micron of 71%, 56%, and
50%, respectively. We fit power-law disk models to the spectral energy
distributions of K & M stars with infrared excesses, and have found that while
many disks extend in to the sublimation radius, the dust has settled to lower
scale heights than in disks of the less evolved Taurus-Auriga population, and
have much reduced dust masses. We also conducted Herschel PACS observations for
far-infrared line emission and JCMT observations for millimeter CO lines. Among
B and A stars, 0 of 5 debris disk hosts exhibit gas line emission, and among K
and M stars, only 2 of 14 dusty disk hosts are detected. The OI 63 micron and
CII 157 micron lines are detected toward [PZ99] J160421.7-213028 and [PBB2002]
J161420.3-190648, which were found in millimeter photometry to host two of the
most massive dust disks remaining in the region. Comparison of the OI line
emission and 63 micron continuum to that of Taurus sources suggests the
emission in the former source is dominated by the disk, while in the other
there is a significant contribution from a jet. The low dust masses found by
disk modeling and low number of gas line detections suggest that few stars in
Upper Scorpius retain sufficient quantities of material for giant planet
formation. By the age of Upper Scorpius, giant planet formation is essentially
complete.Comment: 48 pages, 14 figures, accepted A&
Microwave study of quantum n-disk scattering
We describe a wave-mechanical implementation of classically chaotic n-disk
scattering based on thin 2-D microwave cavities. Two, three, and four-disk
scattering are investigated in detail. The experiments, which are able to probe
the stationary Green's function of the system, yield both frequencies and
widths of the low-lying quantum resonances. The observed spectra are found to
be in good agreement with calculations based on semiclassical periodic orbit
theory. Wave-vector autocorrelation functions are analyzed for various
scattering geometries, the small wave-vector behavior allowing one to extract
the escape rate from the quantum repeller. Quantitative agreement is found with
the value predicted from classical scattering theory. For intermediate
energies, non-universal oscillations are detected in the autocorrelation
function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include
Transport and Helfand moments in the Lennard-Jones fluid. I. Shear viscosity
We propose a new method, the Helfand-moment method, to compute the shear
viscosity by equilibrium molecular dynamics in periodic systems. In this
method, the shear viscosity is written as an Einstein-like relation in terms of
the variance of the so-called Helfand moment. This quantity, is modified in
order to satisfy systems with periodic boundary conditions usually considered
in molecular dynamics. We calculate the shear viscosity in the Lennard-Jones
fluid near the triple point thanks to this new technique. We show that the
results of the Helfand-moment method are in excellent agreement with the
results of the standard Green-Kubo method.Comment: Submitted to the Journal of Chemical Physic
A multibaker map for shear flow and viscous heating
A consistent description of shear flow and the accompanied viscous heating as
well the associated entropy balance is given in the framework of a
deterministic dynamical system. A laminar shear flow is modeled by a
Hamiltonian multibaker map which drives velocity and temperature fields. In an
appropriate macroscopic limit one recovers the Navier-Stokes and heat
conduction equations along with the associated entropy balance. This indicates
that results of nonequilibrium thermodynamics can be described by means of an
abstract, sufficiently chaotic and mixing dynamics. A thermostating algorithm
can also be incorporated into this framework.Comment: 11 pages; RevTex with multicol+graphicx packages; eps-figure
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