184 research outputs found
Dynamics of Triangulations
We study a few problems related to Markov processes of flipping
triangulations of the sphere. We show that these processes are ergodic and
mixing, but find a natural example which does not satisfy detailed balance. In
this example, the expected distribution of the degrees of the nodes seems to
follow the power law
Brownian Motors driven by Particle Exchange
We extend the Langevin dynamics so that particles can be exchanged with a
particle reservoir. We show that grand canonical ensembles are realized at
equilibrium and derive the relations of thermodynamics for processes between
equilibrium states. As an application of the proposed evolution rule, we devise
a simple model of Brownian motors driven by particle exchange. KEYWORDS:
Langevin Dynamics, Thermodynamics, Open SystemsComment: 5 pages, late
Feynman's ratchet and pawl: an exactly solvable model
We introduce a simple, discrete model of Feynman's ratchet and pawl,
operating between two heat reservoirs. We solve exactly for the steady-state
directed motion and heat flows produced, first in the absence and then in the
presence of an external load. We show that the model can act both as a heat
engine and as a refrigerator. We finally investigate the behavior of the system
near equilibrium, and use our model to confirm general predictions based on
linear response theory.Comment: 19 pages + 10 figures; somewhat tighter presentatio
Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean field approach
We address a recently introduced model describing a system of periodically
coupled nonlinear phase oscillators submitted to multiplicative white noises,
wherein a ratchet-like transport mechanism arises through a symmetry-breaking
noise-induced nonequilibrium phase transition. Numerical simulations of this
system reveal amazing novel features such as negative zero-bias conductance and
anomalous hysteresis, explained resorting to a strong-coupling analysis in the
thermodynamic limit. Using an explicit mean-field approximation we explore the
whole ordered phase finding a transition from anomalous to normal hysteresis
inside this phase, estimating its locus and identifying (within this scheme) a
mechanism whereby it takes place.Comment: RevTex, 21 pgs, 15 figures. Submited to Physical Review E (2000
Quantum Ratchets
The concept of thermal ratchets is extended to the system governed by quantum
mechanics. We study a tight-binding model with an asymmetric periodic potential
contacting with a heat bath under an external oscillating field as a specific
example of quantum ratchet. Dynamics of a density operator of this system is
studied numerically by using the quantum Liouville equation. Finite net current
is found in the non-equilibrium steady state. The direction of the current
varies with parameters, in contrast with the classical thermal ratchets.Comment: 7 pages, Latex, 4 ps figures; No change in the text by this
replacement. only the figures are replaced with higher quality ones (but
smaller size
Strong friction limit in quantum mechanics: the Quantum Smoluchowski equation
For a quantum system coupled to a heat bath environment the strong friction
limit is studied starting from the exact path integral formulation.
Generalizing the classical Smoluchowski limit to low temperatures a time
evolution equation for the position distribution is derived and the strong role
of quantum fluctuations in this limit is revealed.Comment: 4 pages, PRL in pres
Dissipation Enhanced Asymmetric Transport in Quantum Ratchets
Quantum mechanical motion of a particle in a periodic asymmetric potential is
studied theoretically at zero temperature. It is shown based on semi-classical
approximation that the tunneling probability from one local minimum to the next
becomes asymmetric in the presence of weak oscillating field, even though there
is no macroscopic field gradient in average. Dissipation enhances this
asymmetry, and leads to a steady unidirectional current, resulting in a quantum
ratchet system.Comment: 12 pages, 2 Figures, submitted to J. Phys. Soc. Jp
In search of multipolar order on the Penrose tiling
Based on Monte Carlo calculations, multipolar ordering on the Penrose tiling,
relevant for two-dimensional molecular adsorbates on quasicrystalline surfaces
and for nanomagnetic arrays, has been analyzed. These initial investigations
are restricted to multipolar rotors of rank one through four - described by
spherical harmonics Ylm with l=1...4 and restricted to m=0 - positioned on the
vertices of the rhombic Penrose tiling. At first sight, the ground states of
odd-parity multipoles seem to exhibit long-range multipolar order, indicated by
the appearance of a superstructure in the form of the decagonal
Hexagon-Boat-Star tiling, in agreement with previous investigations of dipolar
systems. Yet careful analysis establishes that long-range multipolar order is
absent in all cases investigated here, and only short-range order exists. This
result should be taken as a warning for any future analysis of order in either
real or simulated arrangements of multipoles on quasiperiodic templates
Energetics of Forced Thermal Ratchet
Molecular motors are known to have the high efficiency of energy
transformation in the presence of thermal fluctuation.
Motivated by the surprising fact, recent studies of thermal ratchet models
are showing how and when work should be extracted from non-equilibrium
fluctuations.
One of the important finding was brought by Magnasco where he studied the
temperature dependence on the fluctuation-induced current in a ratchet
(multistable) system and showed that the current can generically be maximized
in a finite temperature.
The interesting finding has been interpreted that thermal fluctuation is not
harmful for the fluctuation-induced work and even facilitates its efficiency.
We show, however, this interpretation turns out to be incorrect as soon as we
go into the realm of the energetics
[Sekimoto,J.Phys.Soc.Jpn.66,1234-1237(1997)]: the efficiency of energy
transformation is not maximized at finite temperature, even in the same system
that Magnasco considered. The maximum efficiency is realized in the absence of
thermal fluctuation. The result presents an open problem whether thermal
fluctuation could facilitate the efficiency of energetic transformation from
force-fluctuation into work.Comment: 3pages, 4sets of figure
Asymmetric motion in a double-well under the action of zero-mean Gaussian white noise and periodic forcing
Residence times of a particle in both the wells of a double-well system,
under the action of zero-mean Gaussian white noise and zero-averaged but
temporally asymmetric periodic forcings, are recorded in a numerical
simulation. The difference between the relative mean residence times in the two
wells shows monotonic variation as a function of asymmetry in the periodic
forcing and for a given asymmetry the difference becomes largest at an optimum
value of the noise strength. Moreover, the passages from one well to the other
become less synchronous at small noise strength as the asymmetry parameter
(defined below) differs from zero, but at relatively larger noise strengths the
passages become more synchronous with asymmetry in the field sweep. We propose
that asymmetric periodic forcing (with zero mean) could provide a simple but
sensible physical model for unidirectional motion in a symmetric periodic
system aided by a symmetric Gaussian white noise.Comment: Appeared in PRE March 1997, figures available on reques
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