3,993 research outputs found
Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss
The dissipation associated with nonequilibrium flow processes is reflected by
the formation of strange attractor distributions in phase space. The
information dimension of these attractors is less than that of the equilibrium
phase space, corresponding to the extreme rarity of nonequilibrium states. Here
we take advantage of a simple model for heat conduction to demonstrate that the
nonequilibrium dimensionality loss can definitely exceed the number of
phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte
Time-reversed symmetry and covariant Lyapunov vectors for simple particle models in and out of thermal equilibrium
Recently, a new algorithm for the computation of covariant Lyapunov vectors
and of corresponding local Lyapunov exponents has become available. Here we
study the properties of these still unfamiliar quantities for a number of
simple models, including an harmonic oscillator coupled to a thermal gradient
with a two-stage thermostat, which leaves the system ergodic and fully time
reversible. We explicitly demonstrate how time-reversal invariance affects the
perturbation vectors in tangent space and the associated local Lyapunov
exponents. We also find that the local covariant exponents vary discontinuously
along directions transverse to the phase flow.Comment: 13 pages, 11 figures submitted to Physical Review E, 201
INCORPORATION OF QUANTUM STATISTICAL FEATURES IN MOLECULAR DYNAMICS
We formulate a method for incorporating quantum fluctuations into molecular-
dynamics simulations of many-body systems, such as those employed for energetic
nuclear collision processes. Based on Fermi's Golden Rule, we allow spontaneous
transitions to occur between the wave packets which are not energy eigenstates.
The ensuing diffusive evolution in the space of the wave packet parameters
exhibits appealing physical properties, including relaxation towards quantum-
statistical equilibrium.Comment: 8 latex pages + 1 uuencoded ps figur
Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering
In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript
Ion dynamics in a linear radio-frequency trap with a single cooling laser
We analyse the possibility of cooling ions with a single laser beam, due to
the coupling between the three components of their motion induced by the
Coulomb interaction. For this purpose, we numerically study the dynamics of ion
clouds of up to 140 particles, trapped in a linear quadrupole potential and
cooled with a laser beam propagating in the radial plane. We use Molecular
Dynamics simulations and model the laser cooling by a stochastic process. For
each component of the motion, we systematically study the dependence of the
temperature with the anisotropy of the trapping potential. Results obtained
using the full radio-frequency (rf) potential are compared to those of the
corresponding pseudo-potential. In the rf case, the rotation symmetry of the
potential has to be broken to keep ions inside the trap. Then, as for the
pseudo-potential case, we show that the efficiency of the Coulomb coupling to
thermalize the components of motion depends on the geometrical configuration of
the cloud. Coulomb coupling appears to be not efficient when the ions organise
as a line or a pancake and the three components of motion reach the same
temperature only if the cloud extends in three dimensions
Macroscopic equations for the adiabatic piston
A simplified version of a classical problem in thermodynamics -- the
adiabatic piston -- is discussed in the framework of kinetic theory. We
consider the limit of gases whose relaxation time is extremely fast so that the
gases contained on the left and right chambers of the piston are always in
equilibrium (that is the molecules are uniformly distributed and their
velocities obey the Maxwell-Boltzmann distribution) after any collision with
the piston. Then by using kinetic theory we derive the collision statistics
from which we obtain a set of ordinary differential equations for the evolution
of the macroscopic observables (namely the piston average velocity and
position, the velocity variance and the temperatures of the two compartments).
The dynamics of these equations is compared with simulations of an ideal gas
and a microscopic model of gas settled to verify the assumptions used in the
derivation. We show that the equations predict an evolution for the macroscopic
variables which catches the basic features of the problem. The results here
presented recover those derived, using a different approach, by Gruber, Pache
and Lesne in J. Stat. Phys. 108, 669 (2002) and 112, 1177 (2003).Comment: 13 pages, 7 figures (revTeX4) The paper has been completely rewritten
with new derivation and results, supplementary information can be found at
http://denali.phys.uniroma1.it/~cencini/Papers/cppv07_supplements.pd
Lyapunov instability of fluids composed of rigid diatomic molecules
We study the Lyapunov instability of a two-dimensional fluid composed of
rigid diatomic molecules, with two interaction sites each, and interacting with
a WCA site-site potential. We compute full spectra of Lyapunov exponents for
such a molecular system. These exponents characterize the rate at which
neighboring trajectories diverge or converge exponentially in phase space.
Quam. These exponents characterize the rate at which neighboring trajectories
diverge or converge exponentially in phase space. Qualitative different degrees
of freedom -- such as rotation and translation -- affect the Lyapunov spectrum
differently. We study this phenomenon by systematically varying the molecular
shape and the density. We define and evaluate ``rotation numbers'' measuring
the time averaged modulus of the angular velocities for vectors connecting
perturbed satellite trajectories with an unperturbed reference trajectory in
phase space. For reasons of comparison, various time correlation functions for
translation and rotation are computed. The relative dynamics of perturbed
trajectories is also studied in certain subspaces of the phase space associated
with center-of-mass and orientational molecular motion.Comment: RevTeX 14 pages, 7 PostScript figures. Accepted for publication in
Phys. Rev.
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