Dissipative Dynamics with Trapping in Dimers

The trapping of excitations in systems coupled to an environment allows to study the quantum to classical crossover by different means. We show how to combine the phenomenological description by a non-hermitian Liouville-von Neumann Equation (LvNE) approach with the numerically exact path integral Monte-Carlo (PIMC) method, and exemplify our results for a system of two coupled two-level systems. By varying the strength of the coupling to the environment we are able to estimate the parameter range in which the LvNE approach yields satisfactory results. Moreover, by matching the PIMC results with the LvNE calculations we have a powerful tool to extrapolate the numerically exact PIMC method to long times.Comment: 5 pages, 2 figure

Quasifree Eta Photoproduction from Nuclei

Quasifree $\eta$ photoproduction from nuclei is studied in the Distorted Wave Impulse Approximation (DWIA). The elementary eta production operator contains Born terms, vector meson and nucleon resonance contributions and provides an excellent description of the recent low energy Mainz measurements on the nucleon. The resonance sector includes the $S_{11}(1535)$, $P_{11}(1440)$ and $D_{13}(1520)$ states whose couplings are fixed by independent electromagnetic and hadronic data. Different models for the $\eta N$ t-matrix are used to construct a simple $\eta A$ optical potential based on a $t \rho$-approximation. We find that the exclusive $A(\gamma,\eta N)B$ process can be used to study medium modifications of the $N^*$ resonances, particularly if the photon asymmetry can be measured. The inclusive $A(\gamma, \eta)X$ reaction is compared to new data obtained on $^{12}C$, $^{40}Ca$, and is found to provide a clear distinction between different models for the $\eta N$ t-matrix.Comment: 30 pages in RevTeX including 14 embedded PS figures; Replaced with revised version. Added more discussion about the imaginary part of the eta optical potentia

Exit problems for reflected Markov-modulated Brownian motion

Let (?, ?) denote a Markov-modulated Brownian motion (MMBM) and denote its supremum process by S. For some a > 0, let ? (a) denote the time when the reflected process ? := S -- ? first surpasses the level a. Furthermore, let ?_(a) denote the last time before ? (a) when ? attains its current supremum. In this paper we shall derive the joint distribution of S?(a), ?_(a), and ?(a), where the latter two will be given in terms of their Laplace transforms. We also provide some remarks on scale matrices for MMBMs with strictly positive variation parameters. This extends recent results for spectrally negative Lévy processes to MMBMs. Due to well-known fluid embedding and state-dependent killing techniques, the analysis applies to Markov additive processes with phase-type jumps as well. The result is of interest to applications such as the dividend problem in insurance mathematics and the buffer overflow problem in queueing theory. Examples will be given for the former

On the MAP/G/1 queue with Lebesgue-dominated service time distribution and LCFS preemptive repeat service discipline

The present paper contains an analysis of the MAP/G/1 queue with last come first served (LCFS) preemptive repeat service discipline and Lebesgue-dominated service time distribution. The transient distribution is given in terms of a recursive formula. The stationary distribution as well as the stability condition are obtained by means of Markov renewal theory via a QBD representation of the embedded Markov chain at departures and arrivals

Transient and stationary distributions for the GI/G/k queue with Lebesgue-dominated inter-arrival time distribution

In this paper, the multi-server queue with general service time distribution and Lebesgue-dominated iid inter-arival times is analyzed. This is done by introducing auxiliary variables for the remaining service times and then examining the embedded Markov chain at arrival instants. The concept of piecewise-deterministic Markov processes is applied to model the inter-arrival behaviour. It turns out that the transition probability kernel of the embedded Markov chain at arrival instants has the form of a lower Hessenberg matrix and hence admits an operator-geometric stationary distribution. Thus it is shown that matrix-analytical methods can be extended to provide a modeling tool even for the general multi-server queue

Continuity of the M/G/c queue

Consider an M/G/c queue with homogeneous servers and service time distribution F. It is shown that an approximation of the service time distribution F by stochastically smaller distributions, say F-n, leads to an approximation of the stationary distribution pi of the original M/G/c queue by the stationary distributions pi(n) of the M/G/c queues with service time distributions F-n. Here all approximations are in weak convergence. The argument is based on a representation of M/G/c queues in terms of piecewise deterministic Markov processes as well as some coupling methods

On Markov-additive jump processes

In 1995, Pacheco and Prabhu introduced the class of so-called Markov-additive processes of arrivals in order to provide a general class of arrival processes for queueing theory. In this paper, the above class is generalized considerably, including time-inhomogeneous arrival rates, general phase spaces and the arrival space being a general vector space (instead of the finite-dimensional Euclidean space). Furthermore, the class of Markov-additive jump processes introduced in the present paper is embedded into the existing theory of jump processes. The best known special case is the class of BMAP arrival processes