Observation of Metastable and Stable Energy Levels of EL2 in Semi-insulating GaAs

By using combination of detailed experimental studies, we identify the metastable and stable energy levels of EL2 in semi-insulating GaAs. These results are discussed in the light of the recently proposed models for stable and metastable configurations of EL2 in GaAs

Static potential in scalar QED3_3 with non-minimal coupling

Here we compute the static potential in scalar $QED_3$ at leading order in $1/N_f$. We show that the addition of a non-minimal coupling of Pauli-type (\eps j^{\mu}\partial^{\nu}A^{\alpha}), although it breaks parity, it does not change the analytic structure of the photon propagator and consequently the static potential remains logarithmic (confining) at large distances. The non-minimal coupling modifies the potential, however, at small charge separations giving rise to a repulsive force of short range between opposite sign charges, which is relevant for the existence of bound states. This effect is in agreement with a previous calculation based on M$\ddot{o}$ller scattering, but differently from such calculation we show here that the repulsion appears independently of the presence of a tree level Chern-Simons term which rather affects the large distance behavior of the potential turning it into constant.Comment: 13 pages, 3 figure

On solving discrete optimization problems with one random element under general regret functions

In this paper we consider the class of stochastic discrete optimization problems in which the feasibility of a solution does not depend on the particular values the random elements in the problem take. Given a regret function, we introduce the concept of the risk associated with a solution, and define an optimal solution as one having the least possible risk. We show that for discrete optimization problems with one random element and with min-sum objective functions a least risk solution for the stochastic problem can be obtained by solving a non-stochastic counterpart where the latter is constructed by replacing the random element of the former with a suitable parameter. We show that the above surrogate is the mean if the stochastic problem has only one symmetrically distributed random element. We obtain bounds for this parameter for certain classes of asymmetric distributions and study the limiting behavior of this parameter in details under two asymptotic frameworks. \u

Discrete optimization problems with random cost elements

In a general class of discrete optimization problems, some of the elements mayhave random costs associated with them. In such a situation, the notion of optimalityneeds to be suitably modified. In this work we define an optimal solutionto be a feasible solution with the minimum risk. We focus on the minsumobjective function, for which we prove that knowledge of the mean values ofthese random costs is enough to reduce the problem into one with fixed costs.We discuss the implications of using sample means when the true means ofthe costs of the random elements are not known, and explore the relation betweenour results and those from post-optimality analysis. We also show thatdiscrete optimization problems with min-max objective functions depend moreintricately on the distributions of the random costs.

Complete local search with memory

Neighborhood search heuristics like local search and its variants are some of the most popular approaches to solve discrete optimization problems of moderate to large size. Apart from tabu search, most of these heuristics are memoryless. In this paper we introduce a new neighborhood search heuristic that makes effctive use of memory structures in a way that is different from tabu search. We report computational experiments with this heuristic on the traveling salesperson problem and the subset sum problem.

On solving discrete optimization problems with multiple random elements under general regret functions

In this paper we attempt to find least risk solutions for stochastic discrete optimization problems (SDOP) with multiple random elements, where the feasibility of a solution does not depend on the particular values the random elements in the problem take. While the optimal solution, for a linear regret function, can be obtained by solving an auxiliary (non-stochastic) discrete optimization problem (DOP), the situation is complex under general regret. We characterize a finite number of solutions which will include the optimal solution. We establish through various examples that the results from Ghosh, Mandal and Das (2005) can be extended only partially for SDOPs with additional characteristics. We present a result where in selected cases, a complex SDOP may be decomposed into simpler ones facilitating the job of finding an optimal solution to the complex problem. We also propose numerical local search algorithms for obtaining an optimal solution. \u