Non Markovian Quantum Repeated Interactions and Measurements

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.Comment: 22 page

A Measurement of Photon Production in Electron Avalanches in CF4

This paper presents a measurement of the ratio of photon to electron production and the scintillation spectrum in a popular gas for time pro jection chambers, carbon tetrafluoride (CF4), over the range of 200 to 800 nm; the ratio is measured to be 0.34+/-0.04. This result is of particular importance for a new generation of dark matter time projection chambers with directional sensitivity which use CF4 as a fill gas.Comment: 19 pages, including appendix. 8 figure

New Douglas-Rachford algorithmic structures and their convergence analyses

In this paper we study new algorithmic structures with Douglas- Rachford (DR) operators to solve convex feasibility problems. We propose to embed the basic two-set-DR algorithmic operator into the String-Averaging Projections (SAP) and into the Block-Iterative Pro- jection (BIP) algorithmic structures, thereby creating new DR algo- rithmic schemes that include the recently proposed cyclic Douglas- Rachford algorithm and the averaged DR algorithm as special cases. We further propose and investigate a new multiple-set-DR algorithmic operator. Convergence of all these algorithmic schemes is studied by using properties of strongly quasi-nonexpansive operators and firmly nonexpansive operators.Comment: SIAM Journal on Optimization, accepted for publicatio

A new method of projection-based inference in GMM with weakly identified nuisance parameters

Projection-based methods of inference on subsets of parameters are useful for obtaining tests that do not over-reject the true parameter values. However, they are also often criticized for being conservative. We show that the usual method of pro jection can be modifed to obtain tests that are as powerful as the conventional tests for subsets of parameters. Like the usual projection-based methods, one can always put an upper bound to the rate at which the new method over-rejects the true value of the parameters of interest. The new method is described in the context of GMM with possibly weakly identifed parameters.

Some Cautionary Remarks on Abelian Projection and Abelian Dominance

Some critical remarks are presented, concerning the abelian projection theory of quark confinement.Comment: Talk presented at LATTICE96(topology) plenary session, uses psfig and espcrc2 package

Non-Markovian quantum dynamics: Correlated projection superoperators and Hilbert space averaging

The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We introduce a class of projection superoperators which project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the non-perturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations which is determined by a suitable Hilbert space average. The general approach is illustrated by means of the model of a spin which interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schroedinger equation of the model reveal the power and efficiency of the method.Comment: 14 pages, 5 figure

The use of discrete orthogonal projections in boundary element methods

In recent papers by Sloan and Wendland Grigorie and Sloan and Grigorie Sloan and Brandts a formalismwas developed that serves many important and interesting applications in boundary element methods the commutator property for splines Based on superapproximation results this property is for example a tool of central importance in stability and convergence proofs for qualocation methods for boundary integral equations with variable coecients Another application is the transfer of superconvergence properties from constantcoecient boundary integral equations to the variable coecient case The heart of the theory is formed by the concept discrete orthogonal pro jection that arises when the Lorthogonal inner product is discretized by possibly nonstandard quadrature rules In this paper we present an overview of the theory of discrete orthogonal projections and a new set of numerical experiments that conrm the theory The main conclusion is that the presence of variable coecients of a certain smoothness does not inuence superconvergence in a negative way and that henceforth the use of superconvergencebased a posteriori error estimators in this particular case is theoretically justie