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 $x$ as $x$ and $|x|^{\alpha}$. 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 $4\pi$ 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 $\xi\sim\ell^{1.25}$ between the characteristic size $\xi$, in which the cluster undergoes a morphological transition, and the persistence length $\ell$, 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