1,613 research outputs found
Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters
We investigate the influence of random errors in external control parameters
on the stability of holonomic quantum computation in the case of arbitrary
loops and adiabatic connections. A simple expression is obtained for the case
of small random uncorrelated errors. Due to universality of mathematical
description our results are valid for any physical system which can be
described in terms of holonomies. Theoretical results are confirmed by
numerical simulations.Comment: 7 pages, 3 figure
Transient rectification of Brownian diffusion with asymmetric initial distribution
In an ensemble of non-interacting Brownian particles, a finite systematic
average velocity may temporarily develop, even if it is zero initially. The
effect originates from a small nonlinear correction to the dissipative force,
causing the equation for the first moment of velocity to couple to moments of
higher order. The effect may be relevant when a complex system dissociates in a
viscous medium with conservation of momentum
Avoiding dark states in open quantum systems by tailored initial correlations
We study the transport of excitations on a V-shaped network of three coupled
two-level systems that are subjected to an environment that induces incoherent
hopping between the nodes. Two of the nodes are coupled to a source while the
third node is coupled to a drain. A common feature of these networks is the
existence of a dark-state that blocks the transport to the drain. Here we
propose a means to avoid this state by a suitable choice of initial
correlations, induced by a source that is common to both coupled nodes.Comment: 5 pages, 3 figure
Is transport in time-dependent random potentials universal ?
The growth of the average kinetic energy of classical particles is studied
for potentials that are random both in space and time. Such potentials are
relevant for recent experiments in optics and in atom optics. It is found that
for small velocities uniform acceleration takes place, and at a later stage
fluctuations of the potential are encountered, resulting in a regime of
anomalous diffusion. This regime was studied in the framework of the
Fokker-Planck approximation. The diffusion coefficient in velocity was
expressed in terms of the average power spectral density, which is the Fourier
transform of the potential correlation function. This enabled to establish a
scaling form for the Fokker-Planck equation and to compute the large and small
velocity limits of the diffusion coefficient. A classification of the random
potentials into universality classes, characterized by the form of the
diffusion coefficient in the limit of large and small velocity, was performed.
It was shown that one dimensional systems exhibit a large variety of novel
universality classes, contrary to systems in higher dimensions, where only one
universality class is possible. The relation to Chirikov resonances, that are
central in the theory of Chaos, was demonstrated. The general theory was
applied and numerically tested for specific physically relevant examples.Comment: 5 pages, 3 figure
Generalized Fokker-Planck equation, Brownian motion, and ergodicity
Microscopic theory of Brownian motion of a particle of mass in a bath of
molecules of mass is considered beyond lowest order in the mass ratio
. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Stochastic dynamics beyond the weak coupling limit: thermalization
We discuss the structure and asymptotic long-time properties of coupled
equations for the moments of a Brownian particle's momentum derived
microscopically beyond the lowest approximation in the weak coupling parameter.
Generalized fluctuation-dissipation relations are derived and shown to ensure
convergence to thermal equilibrium at any order of perturbation theory.Comment: 6+ page
Positive Feedback Regulation Results in Spatial Clustering and Fast Spreading of Active Signaling Molecules on a Cell Membrane
Positive feedback regulation is ubiquitous in cell signaling networks, often
leading to binary outcomes in response to graded stimuli. However, the role of
such feedbacks in clustering, and in spatial spreading of activated molecules,
has come to be appreciated only recently. We focus on the latter, using a
simple model developed in the context of Ras activation with competing negative
and positive feedback mechanisms. We find that positive feedback, in the
presence of slow diffusion, results in clustering of activated molecules on the
plasma membrane, and rapid spatial spreading as the front of the cluster
propagates with a constant velocity (dependent on the feedback strength). The
advancing fronts of the clusters of the activated species are rough, with
scaling consistent with the Kardar-Parisi-Zhang (KPZ) equation in one
dimension. Our minimal model is general enough to describe signal transduction
in a wide variety of biological networks where activity in the
membrane-proximal region is subject to feedback regulation.Comment: 37 pages, 8 figures. Journal of Chemical Physics (in press
The matter distribution in the local Universe as derived from galaxy groups in SDSS DR12 and 2MRS
Context. Friends-of-friends algorithms are a common tool to detect galaxy
groups and clusters in large survey data. In order to be as precise as
possible, they have to be carefully calibrated using mock catalogues.
Aims. We create an accurate and robust description of the matter distribution
in the local Universe using the most up-to-date available data. This will
provide the input for a specific cosmological test planned as follow-up to this
work, and will be useful for general extragalactic and cosmological research.
Methods. We created a set of galaxy group catalogues based on the 2MRS and
SDSS DR12 galaxy samples using a friends-of-friends based group finder
algorithm. The algorithm was carefully calibrated and optimised on a new set of
wide-angle mock catalogues from the Millennium simulation, in order to provide
accurate total mass estimates of the galaxy groups taking into account the
relevant observational biases in 2MRS and SDSS.
Results. We provide four different catalogues (i) a 2MRS based group
catalogue; (ii) an SDSS DR12 based group catalogue reaching out to a redshift z
= 0.11 with stellar mass estimates for 70% of the galaxies; (iii) a catalogue
providing additional fundamental plane distances for all groups of the SDSS
catalogue that host elliptical galaxies; (iv) a catalogue of the mass
distribution in the local Universe based on a combination of our 2MRS and SDSS
catalogues.
Conclusions. While motivated by a specific cosmological test, three of the
four catalogues that we produced are well suited to act as reference databases
for a variety of extragalactic and cosmological science cases. Our catalogue of
fundamental plane distances for SDSS groups provides further added value to
this paper.Comment: 31 pages, 25 figures, accepted for publication in A&
Fluctuating noise drives Brownian transport
The transport properties of Brownian ratchet was studied in the presence of
stochastic intensity noise (SIN) in both overdamped and underdamped regimes. In
the overdamped case, analytical solution using the matrix continued fraction
method revealed the existence of a maximum current when the noise intensity
fluctuates on intermediate time scale regions. Similar effects were observed
for the underdamped case by Monte Carlo simulations. The optimal
time-correlation for the Brownian transport coincided with the experimentally
observed time-correlation of the extrinsic noise in Esherichia coli gene
expression and implied the importance of environmental noise for molecular
mechanisms.Comment: 22 pages, 8 figure
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