1,013 research outputs found
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
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
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
On Nonlinear Diffusion with Multiplicative Noise
Nonlinear diffusion is studied in the presence of multiplicative noise. The
nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing
field. A dynamic phase transition occurs when the system ``unbinds'' from the
wall. Two different universality classes, corresponding to the cases of an
``upper'' and a ``lower'' wall, are identified and their critical properties
are characterized. While the lower wall problem can be understood by applying
the knowledge of linear diffusion with multiplicative noise, the upper wall
problem exhibits an anomaly due to nontrivial dynamics in the vicinity of the
wall. Broad power-law distribution is obtained throughout the bound phase.Comment: 4 pages, LaTeX, text and figures also available at
http://matisse.ucsd.edu/~hw
Demographic growth and the distribution of language sizes
It is argued that the present log-normal distribution of language sizes is,
to a large extent, a consequence of demographic dynamics within the population
of speakers of each language. A two-parameter stochastic multiplicative process
is proposed as a model for the population dynamics of individual languages, and
applied over a period spanning the last ten centuries. The model disregards
language birth and death. A straightforward fitting of the two parameters,
which statistically characterize the population growth rate, predicts a
distribution of language sizes in excellent agreement with empirical data.
Numerical simulations, and the study of the size distribution within language
families, validate the assumptions at the basis of the model.Comment: To appear in Int. J. Mod. Phys. C (2008
Exact Distributions for Stochastic Gene Expression Models with Bursting and Feedback
Stochasticity in gene expression can give rise to fluctuations in protein
levels and lead to phenotypic variation across a population of genetically
identical cells. Recent experiments indicate that bursting and feedback
mechanisms play important roles in controlling noise in gene expression and
phenotypic variation. A quantitative understanding of the impact of these
factors requires analysis of the corresponding stochastic models. However, for
stochastic models of gene expression with feedback and bursting, exact
analytical results for protein distributions have not been obtained so far.
Here, we analyze a model of gene expression with bursting and feedback
regulation and obtain exact results for the corresponding protein steady-state
distribution. The results obtained provide new insights into the role of
bursting and feedback in noise regulation and optimization. Furthermore, for a
specific choice of parameters, the system studied maps on to a two-state
biochemical switch driven by a bursty input noise source. The analytical
results derived thus provide quantitative insights into diverse cellular
processes involving noise in gene expression and biochemical switching.Comment: Accepted in Phys. Rev. Let
A new method of quantization of classical solutions
Using stochastic quantization method we derive equations for correlators of
quantum fluctuations around the classical solution in the massless phi^4
theory. The obtained equations are then solved in the lowest orders of
perturbation theory, and the first correction to the free propagator of a
quantum fluctuation is calculated.Comment: 8 page
Spin-torque shot noise in magnetic tunnel junctions
Spin polarized current may transfer angular momentum to a ferromagnet,
resulting in a spin-torque phenomenon. At the same time the shot noise,
associated with the current, leads to a non-equilibrium stochastic force acting
on the ferromagnet. We derive stochastic version of Landau-Lifshitz-Gilbert
equation for a magnetization of a ''free'' ferromagnetic layer in contact with
a ''fixed'' ferromagnet. We solve the corresponding Fokker-Planck equation and
show that the non-equilibrium noise yields to a non-monotonous dependence of
the precession spectrum linewidth on the current.Comment: 5 pages, 2 figure
- …