Dependence Of Transition Probability Research Articles

Generalized kinetic theory of sticking and desorption

We describe the kinetic processes of gas particles interacting with a solid surface in terms of Green functions. A ladder approximation to the Bethe-Salpeter equation of a corresponding non-equilibrium diagrammatic representation is applied to calculate a time dependent transition probability. Restricting the formalism to diagonal elements of the particle Green functions the theory turns out to be equivalent to a treatment using a Master equation for occupation numbers of energy levels. Cutting the iteration after a finite number of steps leads to useful approximations for the sticking coefficient. As the main result we include off-diagonal elements to obtain a generalized kinetic description. Such a theory has to be applied in the case of overlapping energy levels. Dyson's equation is diagonalized including off-diagonal elements of the self-energies. A corresponding transformation of the Bethe-Salpeter equation allows for the calculation of a generalized time dependent transition probability which can be used to extract the complete kinetic time evolution. Within a simple model we calculate sticking coefficients and desorption rates.

Scaling behaviour in extended coalescing random walker model

A simple aggregation model on one-dimensional lattice is presented to study the scaling behaviour. The model is an extended version of the coalescing random walker model to take into account the dependence of transition probability upon mass s of particle. A particle moves ahead one step with transition probability T and is stopped with probability 1- T where T=a+bs- alpha ( alpha >0, a,b>or=0 and a+b 0, the scaling relation beta =max(0.5,1/(1+ alpha )) is satisfied. We discuss the relation between our model and the extended KPZ equation.

Thermally activated configurational tunneling at trapping and recombination in glassy semiconductors

A semiclassical approach is applied to investigate electron trapping and recombination at gap states in glassy semiconductors. Dependence of transition probability on bare and self-trapping energy is obtained and compared with some earlier discussed dependences.

QUANTUM CALCULATIONS OF HARMONIC-VIBRATIONAL TRANSITION PROBABILITIES IN COLLINEAR X2Y2 + X2Z2COLLISIONS

Quantum-mechanical calculations of harmonic-vibrational transition probabilities were reported for nonreactive collinear X2Y2 + X2Z2 collisions. Calculations are carried out for C2H2 + C2H2, C2H2 + C2D2 and C2D2 + C2D2 systems. The dependence of transition probabilities on doubly and triply degenerate states was investigated.

Resonant two photon dissociation dynamics of HD+ in intense infrared laser field

The intensity dependent line shapes of resonant two photon dissociation process in HD+ from the 1sσg (v=6, J=0) are obtained at three different intensities (1.53×1010, 1.53×1012, and 6.12×1012 W/cm2 ) in the wavelength range 16 000–17 200 Å using the resolvent operator formalism. The discrete state v=11, J=1 (1sσg) is the intermediate resonant state. The position of the resonance on the wavelength scale depends strongly on intensity. It is shown that for sufficiently strong fields the earlier semiperturbative theory formulated in analogy with Fano’s theory of atomic autoionization breaks down near resonance due to saturation of the strongly coupled resonant transition. Also, when the dissociative transitions to both the electronic states 1sσg and 2pσu are considered simultaneously, the line shape is altered from that obtained by the superposition of the line shapes of these two transitions separately. The conditions under which a unique time independent transition rate is ill defined are discussed. For such situations the time dependent transition probabilities can be obtained from the effective Fano asymmetry parameters, and line shifts and widths of the ground and resonant states. The limiting transition rates for such cases for short and long pulse times are also shown.

Communication Equilibria in Repeated Games with Incomplete Information

Correlated equilibria (in the sense of Aumann, i.e., normal form correlated equilibria) are studied in two-person infinitely repeated games with lack of information on one side. Extensions of the solution concept are introduced, several of which are shown to be payoff equivalent in the model under consideration. A normal form correlated equilibrium is a Nash equilibrium of the game where each player gets a private output from a correlation device before the beginning of the original game. An r-device (r = 0, 1, …, ∞) is a communication device, receiving an input from each player before every stage t = 1, …, r and selecting a pair of outputs, one for each player, at every stage t = 1, 2, …, according to a memory dependent transition probability. An r-communication equilibrium is a Nash equilibrium of the game extended by means of an r-device. Let C (resp. Dr, r = 0, 1, …, ∞) be the set of normal form correlated (resp. r-communication) equilibrium payoffs. D0 is the set of “extensive form correlated equilibrium payoffs,” achieved by means of an “autonomous device,” acting only by sending a stream of outputs to each player. And D∞ is the set of all communication equilibrium payoffs, corresponding to communication devices which can receive inputs at every stage (even arbitrarily large). The paper characterizes the different sets and investigate whether they coincide.

Estimates of Molecular Effects on the Neutrino Mass Determination by Triton β Decay

Molecular effects on the β-ray spectra of triton decay are carefully estimated for two alkane molecules, CH 3 T and CH 3 –CHT–CH 3 in the sudden approximation by ab initio SCF–MO methods. (1) The basis set dependence of transition probabilities is examined for CH 3 T using four types of basis sets of the double zeta quality with and without diffuse and polarization functions. (2) The excitation energy spectrum for the transition of CH 3 –CHT–CH 3 is shown to have two broad peaks at ∼20 eV and 35 eV corresponding to the molecular excitations, which is rather similar to the distribution for valine II obtained by Kaplan et al. (3) The validity of the adopted basis set is also checked for the case of propane by examining the saturation of the unitarity and of the sum rules for the excitation energy. The rate of the two-particle excitation turns out to be 4.8%, the inclusion of which improves the saturation of the unitarity to 98.6%.

Probability oscillations in single pass curve crossings: Semiclassical predictions of nonmonotonic dependence on crossing velocity

We consider dynamical curve crossing behavior for one dimensional intermolecular potentials of arbitrary curvature. Our focus is threefold. (1) A semiclassical WKB formalism yields simple analytic expressions for time dependent transition probabilities throughout the crossing region. For low velocities v, our results reduce to the required quasistatic unitary transformation between diabatic and adiabatic representations. At higher v, the WKB solutions exhibit time dependent oscillations (‘‘beating’’ between the stationary adiabatic states) in excellent quantitative agreement with exact numerical solutions. (2) The WKB analysis indicates that an oscillatory dependence of curve crossing probability Pcr on v occurs for potential crossings of sufficient curvature, in qualitative disagreement with the extensively used Landau–Zener expression. These probability oscillations can be understood and predicted from simple considerations of potential curvature and coupling strengths. (3) We explore this oscillatory behavior for realistic curve crossing geometries. The results indicate that a nonmonotonic dependence of Pcr on velocity may occur in real molecular systems and could be experimentally observed in favorable albeit special circumstances. Even in the absence of oscillations, however, pronounced departure from Landau–Zener predictions can be anticipated.

M-preserving propensities for rotationally inelastic NH3-He collisions. In the kinematic apse frame

Abstract Semiclassical calculations are used to obtain integral cross sections in both the initial velocity, or collision-fixed, frame and the kinematic apse frame (defined by Khare et al.) for rotational excitation in the NH 3 -He system at a collision energy of 100 cm − . A comparison with earlier close-coupling calculations in the initial velocity frame. using the same interaction potential, shows that the semiclassical method predicts relative M -dependence quite accurately. The kinematic apse cross sections, unlike those in the initial velocity frame, are highly diagonal in the quantum number M . An examination of the M -dependent transition probabilities as a function of impact parameter indicates that the propensity for conservation of M in the kinematic apse frame is due to the dominance of backward, or high-angle, scattering in the cross section. The propensity for conservation of M breaks down for large impact parameters where the interaction is attractive.

Short-Term Single-Station Forecasting of Precipitation

Forecast probabilities of rain were calculated up to 12 hours in advance using a Markov chain model applied to three-hourly observations from five major Australian cities. The four weather states chosen in this first study were three cloudiness states (0–2 oktas, 3–5 oktas and 6–8 oktas) and a rain state. Second-order Markov models with time-of-day dependent transition probabilities were fitted after appropriate statistical testing. Forecasts were made using transition probabilities for summer and winter seasons. The skill of the Markov chain forecast probabilities of rain was evaluated in terms of Brier scores using to years of independent data, and compared with forecasts based upon persistence and climatology. The skill of the Markov model forecasts appreciably exceeded that of persistence and climatology and a real time trial of the procedure is being planned.

Gamma-ray energy dependence of transition probabilities in the continuum

The multiplicities of unresolved ..gamma.. rays depopulating low spin states in /sup 148/Sm have been measured for excitation energies up to the neutron binding energy. The general increase in multiplicity with excitation energy is well accounted for by a Fermi gas model. The comparison with theory shows that the dipole transition probabilities are not influenced by the giant dipole resonance.

Time-of-flight measurements of the rotational excitation of para- and ortho-H2 by collisions with Li+ ions. I. Angular dependent transition probabilities for the j=0→2, 2→0, 2→4, and 1→3 transitions at Ec.m.=0.6 eV

Time-of-flight spectra for the scattering of Li+ ions from para-H2 in the j=0 and j=2 rotational states and from ortho-H2 in the j=1 state have been measured for center of mass scattering angles between 17° and 50° at a center of mass energy of 0.6 eV. In all the spectra two or more maxima were observed. For 100 °K para-H2 they could be attributed to the j=0→0 and j=0→2 transitions. For para-H2 at 300 °K additional maxima due to the j=2→0 and the j=2→4 transitions were observed. By using normal H2 and subtracting off the known contributions from para-H2 the transition probability for the j=1→3 transition was also obtained. The angular resolution was sufficient to resolve the ’’fast’’ undulations as well as the rainbow maximum for both the j=0→0 and j=0→2 transitions. The results are compared directly with differential cross sections calculated by Schaefer and Lester [J. Chem. Phys. 62, 1913 (1975)] using a close coupling procedure with the inclusion of a number of closed channels for the best ab initio CI-type potential hypersurface. The comparison reveals a noticeable discrepancy in the angular location of the rainbow. This difference suggests that the ab initio potential well is too shallow in the experimentally probed region by about 17% to 35%.

On the Electronic Structure of As2O3, Sb2O3, and As2S3

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Monte Carlo simulation of random walks with residence time dependent transition probability rates

An exact, computer-oriented, Monte Carlo procedure is derived for numerically simulating continuous-time/discrete-state random walks in which the transition probability per unit time from state S m to state S n may depend upon the residence time τ in the state S m . Conditions for applicational feasibility of the simulation procedure are briefly indicated, and explicit stepping algorithms for some simple τ-dependencies are obtained.

On the time-dependent reversible stochastic compartmental model—II. A class of n-compartment systems

This paper discusses the solution of a general n-compartment system with time dependent transition probabilities utilizing the technique described by Cardenas and Matis (1975) (hereafter abbreviated (CM)). In addition, the cumulant generating function is derived for a special class of reversible n-compartment systems where the time-dependent intensity coefficients corresponding to the migration and death rates are some multiple of each other. The immigration rates can be any integrable function of time. The moments are also obtained and the solution to the two-compartment system is presented explicitly. The solution is illustrated with a linear and a periodic function which forms have been widely reported in the literature.

Breakdown of local equilibrium in coupled relaxation processes: Translational nonequilibrium during vibrational relaxation

Coupled relaxation processes involving several variables are examined using the theory of Markov Processes. This leads naturally to a relaxation equation for one of the variables which has the form of a master equation, but involves time dependent transition probabilities. The equation agrees with usual theories based on local equilibrium and time independent transition probabilities when both the correlations between the variables and the distribution function of the suppressed variables reach their equilibrium form more rapidly than the variable of interest. In order to test the relevance of deviations from local equilibrium, a model which mimics many of the properties of the coupled relaxation of translation and vibration for V−T energy exchange in a thermal reservoir is proposed and solved. Using cross sections which are like those for energy transfer in diatomic molecules, it is shown that important nonequilibrium correlations persist on the transient time scale of the relaxation of the translational degrees of freedom. These correlations can be large when the preponderance of molecules are initially in the ground state and are the order of magnitude of the enhancement of vibrational relaxation times observed at low temperatures.

Unelastische Elektronenstreuung am 1,78 MeV- und 11,4 MeV-Niveau des Si28

TheE2 transition at 1.78 MeV and the strongM1 transition at (11.42±0.02) MeV (measured excitation energy) in Si28 have been studied by inelastic electron scattering at the Darmstadt linear accelerator. Primary energies between 30 and 56 MeV, and scattering angles from 104° to 165° were used. In Born approximation, the following radiation widths to the ground state have been deduced: (1.21±0.17) · 10−3eV (1.78 MeV,E2), and (32.4±4.5)eV (11.4 MeV,M1). Transition radii have been determined from the dependence of transition probability on momentum transfer.

A semi-markov model for clinical trials

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.

A semi-markov model for clinical trials

This paper applies the theory of semi-Markov processes to the construction of a stochastic model for interpreting data obtained from clinical trials. The model characterizes the patient as being in one of a finite number of states at any given time with an arbitrary probability distribution to describe the length of stay in a state. Transitions between states are assumed to be chosen according to a stationary finite Markov chain.Other attempts have been made to develop stochastic models of clinical trials. However, these have all been essentially Markovian with constant transition probabilities which implies that the distribution of time spent during a visit to a state is exponential (or geometric for discrete Markov chains). Markov models need also to assume that the transitions in the state of a patient depend only on absolute time whereas the semi-Markov model assumes that transitions depend on time relative to a patient. Thus the models are applicable to degenerative diseases (cancer, acute leukemia), while Markov models with time dependent transition probabilities are applicable to colds and epidemic diseases. In this paper the Laplace transforms are obtained for (i) probability of being in a state at timet, (ii) probability distribution to reach absorption state and (iii) the probability distribution of the first passage times to go from initial states to transient or absorbing states, transient to transient, and transient to absorbing. The model is applied to a clinical study of acute leukemia in which patients have been treated with methotrexate and 6-mercaptopurine. The agreement between the data and the model is very good.