446 research outputs found
Vlasov Equation In Magnetic Field
The linearized Vlasov equation for a plasma system in a uniform magnetic
field and the corresponding linear Vlasov operator are studied. The spectrum
and the corresponding eigenfunctions of the Vlasov operator are found. The
spectrum of this operator consists of two parts: one is continuous and real;
the other is discrete and complex. Interestingly, the real eigenvalues are
infinitely degenerate, which causes difficulty solving this initial value
problem by using the conventional eigenfunction expansion method. Finally, the
Vlasov equation is solved by the resolvent method.Comment: 15 page
Efficient Energy Transfer in Light-Harvesting Systems, II: Quantum-Classical Comparison, Flux Network, and Robustness Analysis
Following the calculation of optimal energy transfer in thermal environment
in our first paper (Wu et al., New J. Phys., 2010, 12, 105012), full quantum
dynamics and leading-order `classical' hopping kinetics are compared in the
seven-site Fenna-Matthews-Olson (FMO) protein complex. The difference between
these two dynamic descriptions is due to higher-order quantum corrections. Two
thermal bath models, classical white noise (the Haken-Strobl-Reineker model)
and quantum Debye model, are considered. In the seven-site FMO model, we
observe that higher-order corrections lead to negligible changes in the
trapping time or in energy transfer efficiency around the optimal and
physiological conditions (2% in the HSR model and 0.1% in the quantum Debye
model for the initial site at BChl 1). However, using the concept of integrated
flux, we can identify significant differences in branching probabilities of the
energy transfer network between hopping kinetics and quantum dynamics (26% in
the HSR model and 32% in the quantum Debye model for the initial site at BChl
1). This observation indicates that the quantum coherence can significantly
change the distribution of energy transfer pathways in the flux network with
the efficiency nearly the same. The quantum-classical comparison of the average
trapping time with the removal of the bottleneck site, BChl 4, demonstrates the
robustness of the efficient energy transfer by the mechanism of multi-site
quantum coherence. To reconcile with the latest eight-site FMO model, the
quantum-classical comparison with the flux network analysis is summarized in
the appendix. The eight-site FMO model yields similar trapping time and network
structure as the seven-site FMO model but leads to a more disperse distribution
of energy transfer pathways.Comment: submitted to Journal of Chemical Physic
Fluctuations in Gene Regulatory Networks as Gaussian Colored Noise
The study of fluctuations in gene regulatory networks is extended to the case
of Gaussian colored noise. Firstly, the solution of the corresponding Langevin
equation with colored noise is expressed in terms of an Ito integral. Then, two
important lemmas concerning the variance of an Ito integral and the covariance
of two Ito integrals are shown. Based on the lemmas, we give the general
formulae for the variances and covariance of molecular concentrations for a
regulatory network near a stable equilibrium explicitly. Two examples, the gene
auto-regulatory network and the toggle switch, are presented in details. In
general, it is found that the finite correlation time of noise reduces the
fluctuations and enhances the correlation between the fluctuations of the
molecular components.Comment: 10 pages, 4 figure
An exactly solvable nonlinear model: Constructive effects of correlations between Gaussian noises
A system with two correlated Gaussian white noises is analysed. This system
can describe both stochastic localization and long tails in the stationary
distribution. Correlations between the noises can lead to a nonmonotonic
behaviour of the variance as function of the intensity of one of the noises and
to a stochastic resonance. A method for improving the transmission of external
periodic signal by tuning parameters of the system discussed in this paper is
proposed
Exactly solvable nonlinear model with two multiplicative Gaussian colored noises
An overdamped system with a linear restoring force and two multiplicative
colored noises is considered. Noise amplitudes depend on the system state
as and . An exactly soluble model of a system is constructed
due to consideration of a specific relation between noises. Exact expressions
for the time-dependent univariate probability distribution function and the
fractional moments are derived. Their long-time asymptotic behavior is
investigated analytically. It is shown that anomalous diffusion and stochastic
localization of particles, not subjected to a restoring force, can occur.Comment: 15 page
Long Range Correlations in the Disordered Phase of a Simple Three State Lattice Gas
We investigate the dynamics of a three-state stochastic lattice gas,
consisting of holes and two oppositely "charged" species of particles, under
the influence of an "electric" field, at zero total charge. Interacting only
through an excluded volume constraint, particles can hop to nearest neighbour
empty sites. With increasing density and drive, the system orders into a
charge-segregated state. Using a combination of Langevin equations and Monte
Carlo simulations, we study the steady-state structure factors in the
disordered phase where homogeneous configurations are stable against small
harmonic perturbations. They show a discontinuity singularity at the origin
which in real space leads to an intricate crossover between power laws of
different kinds.Comment: 7 RevTeX pages, 1 postscript figure include
Anomalous diffusion for overdamped particles driven by cross-correlated white noise sources
We study the statistical properties of overdamped particles driven by two
cross-correlated multiplicative Gaussian white noises in a time-dependent
environment. Using the Langevin and Fokker-Planck approaches, we derive the
exact probability distribution function for the particle positions, calculate
its moments and find their corresponding long-time, asymptotic behaviors. The
generally anomalous diffusive regimes of the particles are classified, and
their dependence on the friction coefficient and the characteristics of the
noises is analyzed in detail. The asymptotic predictions are confirmed by exact
solutions for two examples.Comment: 15 page
Phase-dependent spectra in a driven two-level atom
We propose a method to observe phase-dependent spectra in resonance
fluorescence, employing a two-level atom driven by a strong coherent field and
a weak, amplitude-fluctuating field. The spectra are similar to those which
occur in a squeezed vacuum, but avoid the problem of achieving squeezing over a
solid angle. The system shows other interesting features, such as
pronounced gain without population inversion.Comment: 4 pages and 4 figures. Submitted to Phys. Rev. Let
Robust control of decoherence in realistic one-qubit quantum gates
We present an open loop (bang-bang) scheme to control decoherence in a
generic one-qubit quantum gate and implement it in a realistic simulation. The
system is consistently described within the spin-boson model, with interactions
accounting for both adiabatic and thermal decoherence. The external control is
included from the beginning in the Hamiltonian as an independent interaction
term. After tracing out the environment modes, reduced equations are obtained
for the two-level system in which the effects of both decoherence and external
control appear explicitly. The controls are determined exactly from the
condition to eliminate decoherence, i.e. to restore unitarity. Numerical
simulations show excellent performance and robustness of the proposed control
scheme.Comment: 21 pages, 8 figures, VIth International Conference on Quantum
Communication, Measurement and Computing (Boston, 2002
Scaling laws in the diffusion limited aggregation of persistent random walkers
We investigate the diffusion limited aggregation of particles executing
persistent random walks. The scaling properties of both random walks and large
aggregates are presented. The aggregates exhibit a crossover between ballistic
and diffusion limited aggregation models. A non-trivial scaling relation
between the characteristic size , in which the
cluster undergoes a morphological transition, and the persistence length
, between ballistic and diffusive regimes of the random walk, is
observed.Comment: 13 pages, 7 figures; Physica A: Statistical Mechanics and its
Applications, In Press, Uncorrected Proof, Available online 8 July 2011, ISSN
0378-437
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