Coulomb pair density matrix I

The Coulomb pair density matrixG (r, r) for attractive and repulsive potentials is not only interesting for determining the two-particle effective potentials, but it is also essential in numerical studies of quantum systems. A high-temperature approximation is obtained for logG (r, r), in the form of simple integrals or series expansions; large-distance expansions are also given.     

Coupling of the GB set property for ergodic averages

Let (Y,,,T) be an ergodic dynamical system. LetA be an nonempty subset ofL ²() such that , whereA=sup{||sȒt||₂ ,s, tA} andN(A, u) is the smallest number ofL ²()-open balls of radiusu, centered inA, enough to coverA. Let . We prove as a consequence of a more general result, thatC(A) is aGB subset ofL ²().     

Optimality of a Threshold Policy in theM/M/ queue with repeated vacations

Consider anM/M/1 queueing system with server vacations where the server is turned off as soon as the queue gets empty. We assume that the vacation durations form a sequence of i.i.d. random variables with exponential distribution. At the end of a vacation period, the server may either be turned on if the queue is non empty or take another vacation. The following costs are incurred: a holding cost ofh per unit of time and per customer in the system and a fixed cost of each time the server is turned on. We show that there exists a threshold policy that minimizes the long-run average cost criterion. The approach we use was first proposed in Blanc et al. (1990) and enables us to determine explicitly the optimal threshold and the optimal long-run average cost in terms of the model parameters.     

On two--block--factor sequences and one--dependence

The distributions of two--block--factors arising from i.i.d. sequences are observed to coincide with the distributions of the superdiagonals of jointly exchangeable and dissociated arrays . An inequality for superdiagonal probabilities of the arrays is presented. It provides, together with the observation, a simple proof of the fact that a special one--dependent Markov sequence of Aaronson, Gilat and Keane (1992) is not a two--block factor.

     

The matched queueing network PH/M/c→oPH/PH/1

We consider a matched queueing network PH/M/coPH/PH/1, where the output of the first subsystem PH/M/c is regarded as one of the inputs of the second subsystem and matched with another input of PH-renewal process, and they are served by a single server with PH-service-distribution. The stationary state probabilities, the distribution of the virtual waiting times in the two subsystems, and the distribution of the total virtual waiting time are derived.The work was supported by the Max-Planck-Gesellschaft, Germany, and the Chinese Academy ofSciences.     

Random walk on distant mesh points Monte Carlo methods

A new technique for obtaining Monte Carlo algorithms based on the Markov chains with a finite number of states is suggested. Instead of the classical random walk on neighboring mesh points, a general way of constructing Monte Carlo algorithms that could be called random walk on distant mesh points is considered. It is applied to solve boundary value problems. The numerical examples indicate that the new methods are less laborious and therefore more efficient.In conclusion, we mention that all Monte Carlo algorithms are parallel and could be easily realized on parallel computers.     

Renormalization group for Markov chains and application to metastability

In this paper we introduce a new renormalization group method for the study of the long-time behavior of Markov chains with finite state space and with transition probabilities exponentially small in an external parameter. A general approach of metastability problems emerges from this analysis and is discussed in detail in the case of a two-dimensional Ising system at low temperature,     

Chemical diffusion of oxygen in tin dioxide: Effects of dopants and oxygen partial pressure

Tin dioxide SnO_2−δ is a pronounced n-type electron conductor due to its oxygen deficiency. This study investigates the rate of chemical diffusion of oxygen in SnO_2−δ single crystals, which is a crucial step in the overall stoichiometry change of the material. The chemical diffusion coefficient D^δ was determined from conductivity- and EPR-relaxation methods. The temperature dependence was found to be . The dependence on crystal orientation, dopant content and oxygen partial pressure was below experimental error. The latter observation leads to the conclusion that the chemical diffusion coefficient is close to the diffusion coefficient of oxygen vacancies. Along with the relaxation process resulting from the chemical diffusion of oxygen, additional processes were observed. One of these was attributed to complications in the defect chemistry of the material. The relevance of the results for the kinetics of drift processes of Taguchi sensors is discussed.     

Nonstationary Markov chains and convergence of the annealing algorithm

We study the asymptotic behavior as timet + of certain nonstationary Markov chains, and prove the convergence of the annealing algorithm in Monte Carlo simulations. We find that in the limitt + , a nonstationary Markov chain may exhibit phase transitions. Nonstationary Markov chains in general, and the annealing algorithm in particular, lead to biased estimators for the expectation values of the process. We compute the leading terms in the bias and the variance of the sample-means estimator. We find that the annealing algorithm converges if the temperatureT(t) goes to zero no faster thanC/log(t/t ₀) ast+, with a computable constantC andt ₀ the initial time. The bias and the variance of the sample-means estimator in the annealing algorithm go to zero likeO(t^–1+) for some 0<1, with =0 only in very special circumstances. Our results concerning the convergence of the annealing algorithm, and the rate of convergence to zero of the bias and the variance of the sample-means estimator, provide a rigorous procedure for choosing the optimal annealing schedule. This optimal choice reflects the competition between two physical effects: (a) The adiabatic effect, whereby if the temperature is loweredtoo abruptly the system may end up not in a ground state but in a nearby metastable state, and (b) the super-cooling effect, whereby if the temperature is loweredtoo slowly the system will indeed approach the ground state(s) but may do so extremely slowly.     

Stationary queues with one autonomous server

Given a stationary stochastic continuous demand of service σ(θ_tω) dt with ∫ σ(ω)P(dω) < 1, we construct real stationary point processes $\text{(T}{}_{\mathrm{n}}\text{, n ∈}\text{Z}\text{)[T}{}_{\mathrm{n}}\text{< T}{}_{\mathrm{n}}\text{+1, lim}{}_{\mathrm{\pm \infty }}\text{T}{}_{\mathrm{n}}\text{= ±∞]}$ such that

for a given constant D \2>0. These point processes correspond to a service discipline for which a single server services during the time intervals [T_n, T_n+1[ the demand of service accumulated during the proceding intervals [T_n?1, T_n[ and take a rest of fixed duration D.