313 research outputs found
Slow relaxation, confinement, and solitons
Millisecond crystal relaxation has been used to explain anomalous decay in
doped alkali halides. We attribute this slowness to Fermi-Pasta-Ulam solitons.
Our model exhibits confinement of mechanical energy released by excitation.
Extending the model to long times is justified by its relation to solitons,
excitations previously proposed to occur in alkali halides. Soliton damping and
observation are also discussed
Topological methods for searching barriers and reaction paths
We present a family of algorithms for the fast determination of reaction
paths and barriers in phase space and the computation of the corresponding
rates. The method requires the reaction times be large compared to the
microscopic time, irrespective of the origin - energetic, entropic, cooperative
- of the timescale separation. It lends itself to temperature cycling as in
simulated annealing and to activation-relaxation routines. The dynamics is
ultimately based on supersymmetry methods used years ago to derive Morse
theory. Thus, the formalism automatically incorporates all relevant topological
information.Comment: 4 pages, 4 figures, RevTex
Efficiency of a thermodynamic motor at maximum power
Several recent theories address the efficiency of a macroscopic thermodynamic
motor at maximum power and question the so-called "Curzon-Ahlborn (CA)
efficiency." Considering the entropy exchanges and productions in an n-sources
motor, we study the maximization of its power and show that the controversies
are partly due to some imprecision in the maximization variables. When power is
maximized with respect to the system temperatures, these temperatures are
proportional to the square root of the corresponding source temperatures, which
leads to the CA formula for a bi-thermal motor. On the other hand, when power
is maximized with respect to the transitions durations, the Carnot efficiency
of a bi-thermal motor admits the CA efficiency as a lower bound, which is
attained if the duration of the adiabatic transitions can be neglected.
Additionally, we compute the energetic efficiency, or "sustainable efficiency,"
which can be defined for n sources, and we show that it has no other universal
upper bound than 1, but that in certain situations, favorable for power
production, it does not exceed 1/2
Exact solutions for a mean-field Abelian sandpile
We introduce a model for a sandpile, with N sites, critical height N and each
site connected to every other site. It is thus a mean-field model in the
spin-glass sense. We find an exact solution for the steady state probability
distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe
On-line motor control in patients with Parkinson's disease
Recent models based, in part on a study of Huntington's disease, suggest that the basal ganglia are involved in on-line movement guidance. Two experiments were conducted to investigate this idea. First, we studied advanced Parkinson's disease patients performing a reaching task known to depend on on-line guidance. The task was to ‘look and point' in the dark at visual targets displayed in the peripheral visual field. In some trials, the target location was slightly modified during saccadic gaze displacement (when vision is suppressed). In both patient and control groups, the target jump induced a gradual modification of the movement which diverged smoothly from its original path to reach the new target location. No deficit was found in the patients, except for an increased latency to respond to the target jump (Parkinson's disease: 243 ms; controls: 166 ms). A computational simulation indicated that this response slowing was likely to be a by-product of bradykinesia. The unexpected inconsistency between this result and previous reports was investigated in a second experiment. We hypothesized that the relevant factor was the characteristics of the corrections to be performed. To test this prediction, we investigated a task requiring corrections of the same type as investigated in Huntington's disease, namely large, consciously detected errors induced by large target jumps at hand movement onset. In contrast with the smooth adjustments observed in the first experiment, the subjects responded to the target jump by generating a discrete corrective sub-movement. While this iterative response was relatively rapid in the control subjects (220 ms), Parkinson's disease patients exhibited either dramatically late (>730 ms) or totally absent on-line corrections. When on-line corrections were absent, the initial motor response was completed before a second corrective response was initiated (the latency of the corrective response was the same as the latency of the initial response). Considered together, these results suggest that basal ganglia dependent circuits are not critical for feedback loops involving a smooth modulation of the ongoing command. These circuits may rather contribute to the generation of discrete corrective sub-movements. This deficit is in line with the general impairment of sequential and simultaneous actions in patients with basal ganglia disorder
Localization of thermal packets and metastable states in Sinai model
We consider the Sinai model describing a particle diffusing in a 1D random
force field. As shown by Golosov, this model exhibits a strong localization
phenomenon for the thermal packet: the disorder average of the thermal
distribution of the relative distance y=x-m(t), with respect to the
(disorder-dependent) most probable position m(t), converges in the limit of
infinite time towards a distribution P(y). In this paper, we revisit this
question of the localization of the thermal packet. We first generalize the
result of Golosov by computing explicitly the joint asymptotic distribution of
relative position y=x(t)-m(t) and relative energy u=U(x(t))-U(m(t)) for the
thermal packet. Next, we compute in the infinite-time limit the localization
parameters Y_k, representing the disorder-averaged probabilities that k
particles of the thermal packet are at the same place, and the correlation
function C(l) representing the disorder-averaged probability that two particles
of the thermal packet are at a distance l from each other. We moreover prove
that our results for Y_k and C(l) exactly coincide with the thermodynamic limit
of the analog quantities computed for independent particles at equilibrium in a
finite sample of length L. Finally, we discuss the properties of the
finite-time metastable states that are responsible for the localization
phenomenon and compare with the general theory of metastable states in glassy
systems, in particular as a test of the Edwards conjecture.Comment: 17 page
Influence of the Barrier Shape on Resonant Activation
The escape of a Brownian particle over a dichotomously fluctuating barrier is
investigated for various shapes of the barrier. The problem of resonant
activation is revisited with the attention on the effect of the barrier shape
on optimal value of the mean escape time in the system. The characteristic
features of resonant behavior are analyzed for barriers switching either
between different heights, or "on" and "off" positions. PACS number(s):
05.10-a, 02.50.-r, 82.20.-wj.Comment: 7 pages, 8 figures, RevTex4. Manuscript has been revised and
enhanced. Pictures have been made more clear and some of them have been
cancelled. Additional references have been added. The paper has been
submitted to Phys. Rev.
Algebraic Aspects of Abelian Sandpile Models
The abelian sandpile models feature a finite abelian group G generated by the
operators corresponding to particle addition at various sites. We study the
canonical decomposition of G as a product of cyclic groups G = Z_{d_1} X
Z_{d_2} X Z_{d_3}...X Z_{d_g}, where g is the least number of generators of G,
and d_i is a multiple of d_{i+1}. The structure of G is determined in terms of
toppling matrix. We construct scalar functions, linear in height variables of
the pile, that are invariant toppling at any site. These invariants provide
convenient coordinates to label the recurrent configurations of the sandpile.
For an L X L square lattice, we show that g = L. In this case, we observe that
the system has nontrivial symmetries coming from the action of the cyclotomic
Galois group of the (2L+2)th roots of unity which operates on the set of
eigenvalues of the toppling matrix. These eigenvalues are algebraic integers,
whose product is the order |G|. With the help of this Galois group, we obtain
an explicit factorizaration of |G|. We also use it to define other simpler,
though under-complete, sets of toppling invariants.Comment: 39 pages, TIFR/TH/94-3
Temporal behavior and quantum Zeno time of an excited state of the hydrogen atom
The quantum "Zeno" time of the 2P-1S transition of the hydrogen atom is
computed and found to be approximately 3.59 10^{-15}s (the lifetime is
approximately 1.595 10^{-9}s). The temporal behavior of this system is analyzed
in a purely quantum field theoretical framework and is compared to the
exponential decay law.Comment: 11 page
Proper incorporation of self-adjoint extension method to Green's function formalism : one-dimensional -function potential case
One-dimensional -function potential is discussed in the framework
of Green's function formalism without invoking perturbation expansion. It is
shown that the energy-dependent Green's function for this case is crucially
dependent on the boundary conditions which are provided by self-adjoint
extension method. The most general Green's function which contains four real
self-adjoint extension parameters is constructed. Also the relation between the
bare coupling constant and self-adjoint extension parameter is derived.Comment: LATEX, 13 page
- …