577 research outputs found
The Boltzmann Entropy for Dense Fluids Not in Local Equilibrium
We investigate, via computer simulations, the time evolution of the
(Boltzmann) entropy of a dense fluid not in local equilibrium. The
macrovariables describing the system are the (empirical) particle density
f=\{f(\un{x},\un{v})\} and the total energy . We find that is
monotone increasing in time even when its kinetic part is decreasing. We argue
that for isolated Hamiltonian systems monotonicity of
should hold generally for ``typical'' (the overwhelming majority of) initial
microstates (phase-points) belonging to the initial macrostate ,
satisfying . This is a direct consequence of Liouville's theorem
when evolves autonomously.Comment: 8 pages, 5 figures. Submitted to PR
Sampling rare fluctuations of height in the Oslo ricepile model
We have studied large deviations of the height of the pile from its mean
value in the Oslo ricepile model. We sampled these very rare events with
probabilities of order by Monte Carlo simulations using importance
sampling. These simulations check our qualitative arguement [Phys. Rev. E, {\bf
73}, 021303, 2006] that in steady state of the Oslo ricepile model, the
probability of large negative height fluctuations about
the mean varies as as with
held fixed, and .Comment: 7 pages, 8 figure
Expanding direction of the period doubling operator
We prove that the period doubling operator has an expanding direction at the
fixed point. We use the induced operator, a ``Perron-Frobenius type operator'',
to study the linearization of the period doubling operator at its fixed point.
We then use a sequence of linear operators with finite ranks to study this
induced operator. The proof is constructive. One can calculate the expanding
direction and the rate of expansion of the period doubling operator at the
fixed point
Hydrogen-induced ferromagnetism in ZnO single crystals investigated by Magnetotransport
We investigated the electrical and magnetic properties of low-energy
hydrogen-implanted ZnO single crystals with hydrogen concentrations up to 3
at.% in the first 20 nm surface layer between 10 K and 300 K. All samples
showed clear ferromagnetic hysteresis loops at 300 K with a saturation
magnetization up to 4 emu/g. The measured anomalous Hall effect agrees with the
hysteresis loops measured by superconducting quantum interferometer device
magnetometry. All the H-treated ZnO crystals exhibited a negative
magnetoresistance up to the room temperature. The relative magnitude of the
anisotropic magnetoresistance reaches 0.4 % at 250 K and 2 % at 10 K,
exhibiting an anomalous, non-monotonous behavior and a change of sign below 100
K. All the experimental data indicate that hydrogen atoms alone in a few
percent range trigger a magnetic order in a ZnO crystalline state. Hydrogen
implantation turns out to be a simpler and effective method to generate a
magnetic order in ZnO, which provides interesting possibilities for future
applications due to the strong reduction of the electrical resistance
Chaotic properties of quantum many-body systems in the thermodynamic limit
By using numerical simulations, we investigate the dynamics of a quantum
system of interacting bosons. We find an increase of properly defined mixing
properties when the number of particles increases at constant density or the
interaction strength drives the system away from integrability. A
correspondence with the dynamical chaoticity of an associated -number system
is then used to infer properties of the quantum system in the thermodynamic
limit.Comment: 4 pages RevTeX, 4 postscript figures included with psfig; Completely
restructured version with new results on mixing properties added
On the dynamical behavior of the ABC model
We consider the ABC dynamics, with equal density of the three species, on the
discrete ring with sites. In this case, the process is reversible with
respect to a Gibbs measure with a mean field interaction that undergoes a
second order phase transition. We analyze the relaxation time of the dynamics
and show that at high temperature it grows at most as while it grows at
least as at low temperature
Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
We consider the electromagnetic field in a cavity with a periodically
oscillating perfectly reflecting boundary and show that the mathematical theory
of circle maps leads to several physical predictions. Notably, well-known
results in the theory of circle maps (which we review briefly) imply that there
are intervals of parameters where the waves in the cavity get concentrated in
wave packets whose energy grows exponentially. Even if these intervals are
dense for typical motions of the reflecting boundary, in the complement there
is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i,
42.60.Da, 42.65.Y
Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients
The foundations of the chaotic scattering theory for transport and
reaction-rate coefficients for classical many-body systems are considered here
in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is
employed to obtain an expression for the escape-rate for a phase space
trajectory to leave a finite open region of phase space for the first time.
This expression relates the escape rate to the difference between the sum of
the positive Lyapunov exponents and the K-S entropy for the fractal set of
trajectories which are trapped forever in the open region. This result is well
known for systems of a few degrees of freedom and is here extended to systems
of many degrees of freedom. The formalism is applied to smooth hyperbolic
systems, to cellular-automata lattice gases, and to hard sphere sytems. In the
latter case, the goemetric constructions of Sinai {\it et al} for billiard
systems are used to describe the relevant chaotic scattering phenomena. Some
applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file.
Figures are available on request from [email protected]
A dynamical classification of the range of pair interactions
We formalize a classification of pair interactions based on the convergence
properties of the {\it forces} acting on particles as a function of system
size. We do so by considering the behavior of the probability distribution
function (PDF) P(F) of the force field F in a particle distribution in the
limit that the size of the system is taken to infinity at constant particle
density, i.e., in the "usual" thermodynamic limit. For a pair interaction
potential V(r) with V(r) \rightarrow \infty) \sim 1/r^a defining a {\it
bounded} pair force, we show that P(F) converges continuously to a well-defined
and rapidly decreasing PDF if and only if the {\it pair force} is absolutely
integrable, i.e., for a > d-1, where d is the spatial dimension. We refer to
this case as {\it dynamically short-range}, because the dominant contribution
to the force on a typical particle in this limit arises from particles in a
finite neighborhood around it. For the {\it dynamically long-range} case, i.e.,
a \leq d-1, on the other hand, the dominant contribution to the force comes
from the mean field due to the bulk, which becomes undefined in this limit. We
discuss also how, for a \leq d-1 (and notably, for the case of gravity, a=d-2)
P(F) may, in some cases, be defined in a weaker sense. This involves a
regularization of the force summation which is generalization of the procedure
employed to define gravitational forces in an infinite static homogeneous
universe. We explain that the relevant classification in this context is,
however, that which divides pair forces with a > d-2 (or a < d-2), for which
the PDF of the {\it difference in forces} is defined (or not defined) in the
infinite system limit, without any regularization. In the former case dynamics
can, as for the (marginal) case of gravity, be defined consistently in an
infinite uniform system.Comment: 12 pages, 1 figure; significantly shortened and focussed, additional
references, version to appear in J. Stat. Phy
Fluctuations in Stationary non Equilibrium States
In this paper we formulate a dynamical fluctuation theory for stationary non
equilibrium states (SNS) which covers situations in a nonlinear hydrodynamic
regime and is verified explicitly in stochastic models of interacting
particles. In our theory a crucial role is played by the time reversed
dynamics. Our results include the modification of the Onsager-Machlup theory in
the SNS, a general Hamilton-Jacobi equation for the macroscopic entropy and a
non equilibrium, non linear fluctuation dissipation relation valid for a wide
class of systems
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