High Frequency Dynamics and Third Cumulant of Quantum Noise

The existence of the third cumulant $S_{3}$ of voltage fluctuations has demonstrated the non-Gaussian aspect of shot noise in electronic transport. Until now, measurements have been performed at low frequency, \textit{i.e.} in the classical regime $\hbar \omega < eV, k_BT$ where voltage fluctuations arise from charge transfer process. We report here the first measurement of $S_3$ at high frequency, in the quantum regime $\hbar \omega > eV, k_BT$. In this regime, experiment cannot be seen as a charge counting statistics problem anymore. It raises central questions of the statistics of quantum noise: 1) the electromagnetic environment of the sample has been proven to strongly influence the measurement, through the possible modulation of the noise of the sample. What happens to this mechanism in the quantum regime? 2) For $\hbar \omega > eV$, the noise is due to zero point fluctuations and keeps its equilibrium value: $S_2= G \hbar \omega$ with $G$ the conductance of the sample. Therefore, $S_2$ is independent of the bias voltage and no photon is emitted by the conductor. Is it possible, as suggested by some theories, that $S_3 \neq 0$ in this regime? With regard to these questions, we give theoretical and experimental answers to the environmental effects showing that they involve dynamics of the quantum noise. Using these results, we investigate the question of the third cumulant of quantum noise in the a tunnel junction

Effect of Inhomogeneity in Translocation of Polymers through Nanopores

The motion of polymers with inhomogeneous structure through nanopores is discussed theoretically. Specifically, we consider the translocation dynamics of polymers consisting of double-stranded and single-stranded blocks. Since only the single-stranded chain can go through the nanopore the double-stranded segment has to unzip before the translocation. Utilizing a simple analytical model, translocation times are calculated explicitly for different polymer orientations, i.e., when the single-stranded block enters the pore first and when the double-stranded segment is a leading one. The dependence of the translocation dynamics on external fields, energy of interaction in the double-stranded segment, size of the polymer and the fraction of double-stranded monomers is analyzed. It is found that the order of entrance into the pore has a significant effect on the translocation dynamics. The theoretical results are discussed using free-energy landscape arguments.Comment: 12 pages, 5 figures, submitted to 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

Markov Chain Modeling of Polymer Translocation Through Pores

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities which satisfy a specific balance constraint provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are taken into account and that (ii) the dynamical scaling exponents have a slow approach to their predicted asymptotic values as the polymer's length increases. We also address, along with strong support from additional numerical simulations, a critical discussion which points in a clear way the viability of the Markov chain approach put forward in this work.Comment: 17 pages, 5 figure

Fractional generalization of Fick's law: a microscopic approach

In the study of transport in inhomogeneous systems it is common to construct transport equations invoking the inhomogeneous Fick law. The validity of this approach requires that at least two ingredients be present in the system. First, finite characteristic length and time scales associated to the dominant transport process must exist. Secondly, the transport mechanism must satisfy a microscopic symmetry: global reversibility. Global reversibility is often satisfied in nature. However, many complex systems exhibit a lack of finite characteristic scales. In this Letter we show how to construct a generalization of the inhomogeneous Fick law that does not require the existence of characteristic scales while still satisfying global reversibility.Comment: 4 pages. Published versio

Fluctuation spectrum of quasispherical membranes with force-dipole activity

The fluctuation spectrum of a quasi-spherical vesicle with active membrane proteins is calculated. The activity of the proteins is modeled as the proteins pushing on their surroundings giving rise to non-local force distributions. Both the contributions from the thermal fluctuations of the active protein densities and the temporal noise in the individual active force distributions of the proteins are taken into account. The noise in the individual force distributions is found to become significant at short wavelengths.Comment: 9 pages, 2 figures, minor changes and addition

Coarse-Grained Modeling of Genetic Circuits as a Function of the Inherent Time Scales

From a coarse-grained perspective the motif of a self-activating species, activating a second species which acts as its own repressor, is widely found in biological systems, in particular in genetic systems with inherent oscillatory behavior. Here we consider a specific realization of this motif as a genetic circuit, in which genes are described as directly producing proteins, leaving out the intermediate step of mRNA production. We focus on the effect that inherent time scales on the underlying fine-grained scale can have on the bifurcation patterns on a coarser scale in time. Time scales are set by the binding and unbinding rates of the transcription factors to the promoter regions of the genes. Depending on the ratio of these rates to the decay times of the proteins, the appropriate averaging procedure for obtaining a coarse-grained description changes and leads to sets of deterministic equations, which differ in their bifurcation structure. In particular the desired intermediate range of regular limit cycles fades away when the binding rates of genes are of the same order or less than the decay time of at least one of the proteins. Our analysis illustrates that the common topology of the widely found motif alone does not necessarily imply universal features in the dynamics.Comment: 29 pages, 16 figure

The Omega Dependence of the Evolution of xi(r)

The evolution of the two-point correlation function, xi(r,z), and the pairwise velocity dispersion, sigma(r,z), for both the matter and halo population, in three different cosmological models: (Omega_M,Omega_Lambda)=(1,0), (0.2,0) and (0.2,0.8) are described. If the evolution of xi is parameterized by xi(r,z)=(1+z)^{-(3+eps)}xi(r,0), where xi(r,0)=(r/r_0)^{-gamma}, then eps(mass) ranges from 1.04 +/- 0.09 for (1,0) to 0.18 +/- 0.12 for (0.2,0), as measured by the evolution of at 1 Mpc (from z ~ 5 to the present epoch). For halos, eps depends on their mean overdensity. Halos with a mean overdensity of about 2000 were used to compute the halo two-point correlation function tested with two different group finding algorithms: the friends of friends and the spherical overdensity algorithm. It is certainly believed that the rate of growth of this xihh will give a good estimate of the evolution of the galaxy two-point correlation function, at least from z ~ 1 to the present epoch. The values we get for eps(halos) range from 1.54 for (1,0) to -0.36 for (0.2,0), as measured by the evolution of xi(halos) from z ~ 1.0 to the present epoch. These values could be used to constrain the cosmological scenario. The evolution of the pairwise velocity dispersion for the mass and halo distribution is measured and compared with the evolution predicted by the Cosmic Virial Theorem (CVT). According to the CVT, sigma(r,z)^2 ~ G Q rho(z) r^2 xi(r,z) or sigma proportional to (1+z)^{-eps/2}. The values of eps measured from our simulated velocities differ from those given by the evolution of xi and the CVT, keeping gamma and Q constant: eps(CVT) = 1.78 +/- 0.13 for (1,0) or 1.40 +/- 0.28 for (0.2,0).Comment: Accepted for publication in the ApJ. Also available at http://manaslu.astro.utoronto.ca/~carlberg/cnoc/xiev/xi_evo.ps.g

Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation

The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a Gamma distribution or rational function approximation to its Laplace transform

Casimir effect with rough metallic mirrors

We calculate the second order roughness correction to the Casimir energy for two parallel metallic mirrors. Our results may also be applied to the plane-sphere geometry used in most experiments. The metallic mirrors are described by the plasma model, with arbitrary values for the plasma wavelength, the mirror separation and the roughness correlation length, with the roughness amplitude remaining the smallest length scale for perturbation theory to hold. From the analysis of the intracavity field fluctuations, we obtain the Casimir energy correction in terms of generalized reflection operators, which account for diffraction and polarization coupling in the scattering by the rough surfaces. We present simple analytical expressions for several limiting cases, as well as numerical results that allow for a reliable calculation of the roughness correction in real experiments. The correction is larger than the result of the Proximity Force Approximation, which is obtained from our theory as a limiting case (very smooth surfaces).Comment: 16 page