Occupation Probabilities Of States Research Articles

Theoretical neutralization rates for Rydberg states in ion-metal-surface scattering

The neutralization of highly charged ions in ion-metal-surface scattering via resonant transfer of conduction band electrons into Rydberg states is studied theoretically within the adiabatic approximation. Transition rates and the associated occupation probabilities of ionic hole states are calculated by applying a novel method for evaluating one-electron Coulomb matrix elements in closed form for arbitrary ion-surface distance, ionic quantum numbers, and momentum of the conduction band electrons. In the classically allowed region, oscillatory behavior of the transition rates as a function of ion-surface distance is revealed. The dependence of transition rates and occupation probabilities on the ionic angular momentum quantum numbers l and m is examined. A comparison is made with previous results obtained in the limit of very large ion-surface distance.

Dynamic Linear Models with Switching

Abstract The problem of modeling change in a vector time series is studied using a dynamic linear model with measurement matrices that switch according to a time-varying independent random process. We derive filtered estimators for the usual state vectors and also for the state occupancy probabilities of the underlying nonstationary measurement process. A maximum likelihood estimation procedure is given that uses a pseudo-expectation-maximization algorithm in the initial stages and nonlinear optimization. We relate the models to those considered previously in the literature and give an application involving the tracking of multiple targets.

Simulated Annealing Type Markov Chains and Their Order Balance Equations

Generalized simulated-annealing type Markov chains where the transition probabilities are proportional to powers of a vanishing small parameter are considered. An “order of recurrence,” which quantifies the asymptotic behavior of the state occupation probability, is associated with each state. These orders of recurrence satisfy a fundamental balance equation across every edge-cut in the graph of the Markov chain. Moreover, the Markov chain converges in a Cesaro-sense to the set of states having the largest recurrence orders. These results Convert the analytic problem of determining the asymptotic properties of the time-inhomogeneous stochastic process into a purely algebraic problem of solving the balance equations to determine the recurrence orders.Graph theoretic algorithms are provided to determine the solutions of the balance equations. By applying these results to the problem of optimization by simulated annealing, it is shown that the sum of the recurrence order and the cost is a constant for all st...

Time-dependent optical transitions in vibronic systems.

We show that the resonant interaction between a field mode and a pair of vibronic levels is influenced by dynamical coupling to nonresonant states. The dependence of the occupation probability of vibronic states on dipole coupling, displacement, and resonance condition is discussed.

Analysis of the Multi-Channel Epileptiform EEG Using the Markov Chains Formalism

A multi-level scheme of syntactic reduction of the epileptiform EEG data is briefly discussed and the possibilities it opens up in describing the dynamic behaviour of a multi-channel system are indicated. A new algorithm for the inference of a Markov network from finite sets of sample symbol strings is introduced. Formulae for the time-dependent state occupation probabilities, as well as joint probability functions for pairs of channels, are given. An exemplary case of analysis in these terms, taken from an investigation of anticonvulsant drug effects on EEG seizure patterns, is presented.

A microscopic theory of one-body dissipation

Zwanzig's projection operator method is applied to the equation of motion for the single-particle reduced density matrix of a many-fermion system. An approximate equation obeyed by the projected part is derived for the case the collision integral is treated in the Born Collision Approximation. The form of Balian and Vénéroni's equation is shown to be a Markovian limit of the resulting equation, if the Born collision term is neglected. Specializing the projection operator to give the diagonal elements of the single-particle density matrix in appropriately chosen fixed bases we obtain genealized “Master Equations” which are then compared to the equation of motion for the occupation probabilities of the natural single-particle states of the system. From the analysis we conclude that, microscopically, the so-called one-body dissipation mechanism introduced by Blocki et al. ( Ann. Phys. (N.Y.) 113 (1978), 330) is a mean-field effect which appears whenever a contracted single-particle description of a many-particle system is employed.

Occupation Probabilities of Shell-Model Orbits in the Lead Region

The occupation probabilities of shell-model orbits in the lead region are estimated by the addition of random-phase-approximation corrections to nuclear-matter results. The occupation probabilities of single-particle states in shells just below and above the Fermi energy are found to be \ensuremath{\sim} 0.7 and 0.1, respectively. It is shown that these estimates explain the quenching of the single-particle contribution observed in many elastic and inelastic electron-scattering experiments.

Comments on "M/M/1 Transient State Occupancy Probabilities Via the Discrete Fourier Transform"

Comments on "M/M/1 Transient State Occupancy Probabilities Via the Discrete Fourier Transform"

Time-dependent shell-model theory of dissipative heavy-ion collisions

A transport theory is formulated within a time-dependent shell-model approach. Time averaging of the equations for macroscopic quantities lead to irreversibility and justifies weak-coupling limit and Markov approximation for the (energy-conserving) one- and two-body collision terms. Two coupled equations for the occupation probabilities of dynamical single-particle states and for the collective variable are derived and explicit formulas for transition rates, dynamical forces, mass parameters and friction coefficients are given. The applicability of the formulation in terms of characteristic quantities of nuclear systems is considered in detail and some peculiarities due to memory effects in the initial equilibration process of heavy-ion collisions are discussed.

M/M/1 Transient State Occupancy Probabilities Via the Discrete Fourier Transform

A procedure is given for the computation of the transient state occupancy probabilities of the M/M/1 queue. The method makes use of the inverse discrete Fourier transform, computed by means of the fast Fourier transform. It avoids the direct evaluation of modified Bessel functions and sidesteps difficulties due to the computation of very large and very small intermediate quantities.

Influence of point defect trapping on sink strengths

Under constant irradiation, immobile point defect trapping sites acquire a steady state occupation probability. The value of this probability depends upon the proximity of other sinks or sources. This in turn modifies the steady state point defect flux to (from) the sink (source) in question, thereby influencing its strength. An approximate theory of this effect is developed for a void embedded in a sea of point-impurity-associated trapping sites and of dislocations distributed at random. The sink strength of a set of such voids is determined. The theory is compared at length with the results of an earlier analysis in which the boundary layer phenomenon was not included.

Availability of a 2-Component Dependent System

This paper investigates the effect of s-dependence among components on the availability of a 2-component repairable system with bivariate exponential failure time and repair time. Expressions are derived for state occupancy probabilities as well as system availability.

Equations-of-motion method and pairing correlations in odd-Anuclei

An equations-of-motion method is presented for treating pairing correlations in odd-$A$ nuclei. This method is the natural extension of a previous study of the pairing problem in doubly even nuclei, which provides the input data for the present work. It is shown that the spurious states arising from the use of an overcomplete set of basis vectors can be removed through a procedure analogous to that developed for the doubly even case. The energies, spectroscopic factors, and occupation probabilities of seniority-one states in the Ni isotopes are calculated in the first-order theory. By comparison with exact results, the accuracy of the method is seen to be very good.NUCLEAR STRUCTURE Equations-of-motion method in pairing-force theory.

An Efficient Computational Procedure for the Evaluation of the M/M/I Transient State Occupancy Probabilities

In this note a procedure is given for the numerical evaluation of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M/M/1</tex> queue transient state occupancy probabilities which arise in the analysis of dynamic buffer behavior in store and forward networks. The procedure uses the circular coverage function of radar and communication theory to eliminate an infinite series of modified Bessel functions. Computational savings are illustrated by several numerical examples.

Stochastic theory of multistate diffusion in perfect and defective systems. I. Mathematical formalism

A stochastic theory of multistate transport on ideal and defective lattices is presented. A continuous-time random-walk formalism with the inclusion of internal states is used in the derivation of a matrix (whose dimensions are the number of internal states) probability propagator. The propagator describing motion on an ideal lattice is modified owing to the presence of a periodic arrangement of defects. The expression for the modified probability propagator greatly simplifies in the long-time (diffusion) limit. In this limit the presence of defects renormalizes the ideal-lattice propagator through the inclusion of a self-energy-type term which depends upon the concentration of defect sites and the differences in transition rates of the propagating species associated with these sites and ideal ones. The formalism enables the study of complex diffusion mechanisms, as illustrated in the following paper, and allows the calculation of observables such as positional moments, diffusion coefficients, and occupation probability of states.

Stochastic theory of multistate diffusion in perfect and defective systems. II. Case studies

The time development of a number of physical systems can be described in terms of the temporal passage of the system through its allowable states. These states may correspond to spatial configurations, energy levels, competing transition mechanisms, or correlated processes. The evolution of certain of these systems can be analyzed by mapping onto a continuous-time random walk on a lattice whose unit cell may contain several internal states. In addition, we study the influence of periodically placed defects, which modify transition rates, on transport properties in several condensed-matter systems. A propagator formalism is reviewed where the matrix propagator (whose dimensions equal the number of internal states in a unit cell) is renormalized owing to the presence of defects. Knowledge of the propagator allows the evaluation of observable quantities such as positional moments, diffusion coefficients, occupation probabilities of states, and line shapes of scattering from diffusing particles. The formalism allows the study of diverse transport systems in a unified manner. We study the multistate diffusion of particles and clusters (specifically dimers) observed via field-ion microscopy on defective surfaces and derive expressions for observables pertinent to the analysis of these experiments. The lattice structure dependence of particle diffusion in systems containing defects which influence their neighbors is demonstrated. Next, the anomalous, non-Arrhenius behavior of the vacancy diffusion constant, observed via tracer-diffusion measurements, is described in terms of competing monovacancy mechanisms: nearest-neighbor and next-nearest-neighbor single jumps, and double jumps in which two atoms jump almost simultaneously, collinearly, as suggested by recent molecular-dynamics studies. We derive an analytic expression for the vacancy diffusion which provides a reinterpretation of fits to experimental data. As a further application of our method we investigate non-Markovian transport due to relaxation effects. Finally, we provide an analytic expression for the scattering law, $S(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$, of quasielastic neutron scattering and demonstrate the non-Lorentzian line shape of the scattered intensity for systems containing defects and for correlated motion.

The reactions 6, 7Li, 9Be, 10B(e, e′p) at 700 MeV and DWIA analysis

The proton spectral functions of 6Li, 7Li, 9Be and 10B obtained from the (e, e′p) reactions at 700 MeV are presented. The results were analyzed in the distorted-wave impulse approximation, using the shell-model single-particle wave functions consistent with the elastic electron scattering results. The observed Ip proton momentum distributions for the nuclei 6Li, 7Li and 9Be show significant disagreement with the shell-model momentum distributions. The occupation probabilities of the proton single-particle states are around 0.7, with a few exceptions.

Electronic behaviors of the gap states in amorphous semiconductors

An extension of the Adler-Yoffa's calculation on the localized gap states in amorphous semiconductors has been made with a more realistic model which takes into account an influence of the diffused gap states and impurity states. A considerable large difference in the electron occupation probability of the gap states with sign of the correlation energy U has been examined on the tetrahedrally bonded and chalcogenide glasses. Variations of the Fermi level as a function of doped impurity concentration and gap state density have been studied.

Theory of vibrational relaxation in isolated molecules

A quantum mechanical theory of intramolecular energy transfer is presented which treats the approach to statistical equilibrium of the vibrations in isolated molecules. The theory is appropriate for nonreactive molecules which have at least 6–9 atoms and which are so highly excited that the vibrational interaction couples together many degrees of freedom at a time and causes the simultaneous exchange of a large number of quanta. A generalized master equation of the Van Hove type and a weak-coupling master equation of the Pauli type are obtained for functions related to occupation probabilities of zero-order states. The asymptotic behavior of the coarse-grained occupation probabilities is examined and molecular ergodicity is proved. Convergent infinite expansions for the probabilities are also derived. These analytical expressions make it possible to study the intramolecular dynamics for all relevant times.

Electron-phonon interactions and the states of a crystal electron in an external electric field

The effect of the electron-phonon interactions on the states of a single tightly bound electron in a one-dimensional crystal in an external electric field F is discussed with the help of a master equation for the occupation probabilities of electron states. It is found that the occupation probabilities of the Stark ladder states usually do not provide a good description of the state of the system despite the fact that these were eigenstates in the absence of the interactions. A good description is possible in terms of the occupation probabilities of time-dependent band states with k(t) = k o + eFt/ h ̵ since these probabilities satisfy a markoffian master equation.