176 research outputs found
Lyapunov Mode Dynamics in Hard-Disk Systems
The tangent dynamics of the Lyapunov modes and their dynamics as generated
numerically - {\it the numerical dynamics} - is considered. We present a new
phenomenological description of the numerical dynamical structure that
accurately reproduces the experimental data for the quasi-one-dimensional
hard-disk system, and shows that the Lyapunov mode numerical dynamics is linear
and separate from the rest of the tangent space. Moreover, we propose a new,
detailed structure for the Lyapunov mode tangent dynamics, which implies that
the Lyapunov modes have well-defined (in)stability in either direction of time.
We test this tangent dynamics and its derivative properties numerically with
partial success. The phenomenological description involves a time-modal linear
combination of all other Lyapunov modes on the same polarization branch and our
proposed Lyapunov mode tangent dynamics is based upon the form of the tangent
dynamics for the zero modes
Breaking conjugate pairing in thermostatted billiards by magnetic field
We demonstrate that in the thermostatted three-dimensional Lorentz gas the
symmetry of the Lyapunov spectrum can be broken by adding to the system an
external magnetic field not perpendicular to the electric field. For
perpendicular field vectors, there is a Hamiltonian reformulation of the
dynamics and the conjugate pairing rule still holds. This indicates that
symmetric Lyapunov spectra has nothing to do with time reversal symmetry or
reversibility; instead, it seems to be related to the existence of a
Hamiltonian connection.Comment: 4 pages, 3 figure
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
First and second order clustering transitions for a system with infinite-range attractive interaction
We consider a Hamiltonian system made of classical particles moving in
two dimensions, coupled via an {\it infinite-range interaction} gauged by a
parameter . This system shows a low energy phase with most of the particles
trapped in a unique cluster. At higher energy it exhibits a transition towards
a homogenous phase. For sufficiently strong coupling an intermediate phase
characterized by two clusters appears. Depending on the value of the
observed transitions can be either second or first order in the canonical
ensemble. In the latter case microcanonical results differ dramatically from
canonical ones. However, a canonical analysis, extended to metastable and
unstable states, is able to describe the microcanonical equilibrium phase. In
particular, a microcanonical negative specific heat regime is observed in the
proximity of the transition whenever it is canonically discontinuous. In this
regime, {\it microcanonically stable} states are shown to correspond to {\it
saddles} of the Helmholtz free energy, located inside the spinodal region.Comment: 4 pages, Latex - 3 EPS Figs - Submitted to Phys. Rev.
A vortex description of the first-order phase transition in type-I superconductors
Using both analytical arguments and detailed numerical evidence we show that
the first order transition in the type-I 2D Abelian Higgs model can be
understood in terms of the statistical mechanics of vortices, which behave in
this regime as an ensemble of attractive particles. The well-known
instabilities of such ensembles are shown to be connected to the process of
phase nucleation. By characterizing the equation of state for the vortex
ensemble we show that the temperature for the onset of a clustering instability
is in qualitative agreement with the critical temperature. Below this point the
vortex ensemble collapses to a single cluster, which is a non-extensive phase,
and disappears in the absence of net topological charge. The vortex description
provides a detailed mechanism for the first order transition, which applies at
arbitrarily weak type-I and is gauge invariant unlike the usual field-theoretic
considerations, which rely on asymptotically large gauge coupling.Comment: 4 pages, 6 figures, uses RevTex. Additional references added, some
small corrections to the tex
Long Range Magnetic Order and the Darwin Lagrangian
We simulate a finite system of confined electrons with inclusion of the
Darwin magnetic interaction in two- and three-dimensions. The lowest energy
states are located using the steepest descent quenching adapted for velocity
dependent potentials. Below a critical density the ground state is a static
Wigner lattice. For supercritical density the ground state has a non-zero
kinetic energy. The critical density decreases with for exponential
confinement but not for harmonic confinement. The lowest energy state also
depends on the confinement and dimension: an antiferromagnetic cluster forms
for harmonic confinement in two dimensions.Comment: 5 figure
On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems
We discuss the transient and steady state fluctuation relation for a
mechanical system in contact with two deterministic thermostats at different
temperatures. The system is a modified Lorentz gas in which the fixed
scatterers exchange energy with the gas of particles, and the thermostats are
modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the
system. The transient fluctuation relation, which holds only for a precise
choice of the initial ensemble, is verified at all times, as expected. Times
longer than the mesoscopic scale, needed for local equilibrium to be settled,
are required if a different initial ensemble is considered. This shows how the
transient fluctuation relation asymptotically leads to the steady state
relation when, as explicitly checked in our systems, the condition found in
[D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity
of the steady state fluctuation relation, is verified. For the steady state
fluctuations of the phase space contraction rate \zL and of the dissipation
function \zW, a similar relaxation regime at shorter averaging times is
found. The quantity \zW satisfies with good accuracy the fluctuation relation
for times larger than the mesoscopic time scale; the quantity \zL appears to
begin a monotonic convergence after such times. This is consistent with the
fact that \zW and \zL differ by a total time derivative, and that the tails
of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of
Statistical Physic
Master equation approach to the conjugate pairing rule of Lyapunov spectra for many-particle thermostatted systems
The master equation approach to Lyapunov spectra for many-particle systems is
applied to non-equilibrium thermostatted systems to discuss the conjugate
pairing rule. We consider iso-kinetic thermostatted systems with a shear flow
sustained by an external restriction, in which particle interactions are
expressed as a Gaussian white randomness. Positive Lyapunov exponents are
calculated by using the Fokker-Planck equation to describe the tangent vector
dynamics. We introduce another Fokker-Planck equation to describe the
time-reversed tangent vector dynamics, which allows us to calculate the
negative Lyapunov exponents. Using the Lyapunov exponents provided by these two
Fokker-Planck equations we show the conjugate pairing rule is satisfied for
thermostatted systems with a shear flow in the thermodynamic limit. We also
give an explicit form to connect the Lyapunov exponents with the
time-correlation of the interaction matrix in a thermostatted system with a
color field.Comment: 10 page
Equilibrium and dynamical properties of two dimensional self-gravitating systems
A system of N classical particles in a 2D periodic cell interacting via
long-range attractive potential is studied. For low energy density a
collapsed phase is identified, while in the high energy limit the particles are
homogeneously distributed. A phase transition from the collapsed to the
homogeneous state occurs at critical energy U_c. A theoretical analysis within
the canonical ensemble identifies such a transition as first order. But
microcanonical simulations reveal a negative specific heat regime near .
The dynamical behaviour of the system is affected by this transition : below
U_c anomalous diffusion is observed, while for U > U_c the motion of the
particles is almost ballistic. In the collapsed phase, finite -effects act
like a noise source of variance O(1/N), that restores normal diffusion on a
time scale diverging with N. As a consequence, the asymptotic diffusion
coefficient will also diverge algebraically with N and superdiffusion will be
observable at any time in the limit N \to \infty. A Lyapunov analysis reveals
that for U > U_c the maximal exponent \lambda decreases proportionally to
N^{-1/3} and vanishes in the mean-field limit. For sufficiently small energy,
in spite of a clear non ergodicity of the system, a common scaling law \lambda
\propto U^{1/2} is observed for any initial conditions.Comment: 17 pages, Revtex - 15 PS Figs - Subimitted to Physical Review E - Two
column version with included figures : less paper waste
Measurement of the polarisation of W bosons produced with large transverse momentum in pp collisions at sqrt(s) = 7 TeV with the ATLAS experiment
This paper describes an analysis of the angular distribution of W->enu and
W->munu decays, using data from pp collisions at sqrt(s) = 7 TeV recorded with
the ATLAS detector at the LHC in 2010, corresponding to an integrated
luminosity of about 35 pb^-1. Using the decay lepton transverse momentum and
the missing transverse energy, the W decay angular distribution projected onto
the transverse plane is obtained and analysed in terms of helicity fractions
f0, fL and fR over two ranges of W transverse momentum (ptw): 35 < ptw < 50 GeV
and ptw > 50 GeV. Good agreement is found with theoretical predictions. For ptw
> 50 GeV, the values of f0 and fL-fR, averaged over charge and lepton flavour,
are measured to be : f0 = 0.127 +/- 0.030 +/- 0.108 and fL-fR = 0.252 +/- 0.017
+/- 0.030, where the first uncertainties are statistical, and the second
include all systematic effects.Comment: 19 pages plus author list (34 pages total), 9 figures, 11 tables,
revised author list, matches European Journal of Physics C versio
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