Higher Order Statistsics of Stokes Parameters in a Random Birefringent Medium

We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of the rotation group. We show how this model allows a detailed description of the propagation, giving analytical expressions for the probability densities of the Mueller matrix and the Stokes vector throughout the propagation. It also allows an exact description of the evolution of averaged quantities, such as the degree of polarization. We will also discuss how this model allows a generalization of the concepts of reduced Stokes parameters and degree of polarization to higher order statistics. We give some notes on how it can be extended to more general random media

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

Quantum mechanical reactive scattering for three-dimensional atom plus diatom systems. II. Accurate cross sections for H+H_2

Accurate three‐dimensional reactive and nonreactive quantum mechanical cross sections for the H+H_2 exchange reaction on the Porter–Karplus potential energy surface are presented. Tests of convergence in the calculations indicate an accuracy of better than 5% for most of the results in the energy range considered (0.3 to 0.7 eV total energy). The reactive differential cross sections are exclusively backward peaked, with peak widths increasing monotonically from about 32° at 0.4 eV to 51° at 0.7 eV. Nonreactive inelastic differential cross sections show backwards to sidewards peaking, while elastic ones are strongly forward peaked with a nearly monotonic decrease with increasing scattering angle. Some oscillations due to interferences between the direct and exchange amplitudes are obtained in the para‐to‐para and ortho‐to‐ortho antisymmetrized cross sections above the effective threshold for reaction. Nonreactive collisions do not show a tendency to satisfy a "j_z‐conserving" selection rule. The reactive cross sections show significant rotational angular momentum polarization with the m_j=m′_j=0 transition dominating for low reagent rotational quantum number j. In constrast, the degeneracy averaged rotational distributions can be fitted to statistical temperaturelike expressions to a high degree of accuracy. The integral cross sections have an effective threshold total energy of about 0.55 eV, and differences between this quantity and the corresponding 1D and 2D results can largely be interpreted as resulting from bending motions in the transition state. In comparing these results with those of previous approximate dynamical calculations, we find best overall agreement between our reactive integral and differential cross sections and the quasiclassical ones of Karplus, Porter, and Sharma [J. Chem. Phys. 43, 3259 (1965)], at energies above the quasiclassical effective thresholds. This results in the near equality of the quantum and quasiclassical thermal rate constants at 600 K. At lower temperatures, however, the effects of tunneling become very important with the quantum rate constant achieving a value larger than the quasiclassical one by a factor of 3.2 at 300 K and 18 at 200 K

Quantum dynamics in strong fluctuating fields

A large number of multifaceted quantum transport processes in molecular systems and physical nanosystems can be treated in terms of quantum relaxation processes which couple to one or several fluctuating environments. A thermal equilibrium environment can conveniently be modelled by a thermal bath of harmonic oscillators. An archetype situation provides a two-state dissipative quantum dynamics, commonly known under the label of a spin-boson dynamics. An interesting and nontrivial physical situation emerges, however, when the quantum dynamics evolves far away from thermal equilibrium. This occurs, for example, when a charge transferring medium possesses nonequilibrium degrees of freedom, or when a strong time-dependent control field is applied externally. Accordingly, certain parameters of underlying quantum subsystem acquire stochastic character. Herein, we review the general theoretical framework which is based on the method of projector operators, yielding the quantum master equations for systems that are exposed to strong external fields. This allows one to investigate on a common basis the influence of nonequilibrium fluctuations and periodic electrical fields on quantum transport processes. Most importantly, such strong fluctuating fields induce a whole variety of nonlinear and nonequilibrium phenomena. A characteristic feature of such dynamics is the absence of thermal (quantum) detailed balance.Comment: review article, Advances in Physics (2005), in pres