Effective convergence of the 2PI-1/N expansion for nonequilibrium quantum fields

The 1/N expansion of the two-particle irreducible effective action offers a powerful approach to study quantum field dynamics far from equilibrium. We investigate the effective convergence of the 1/N expansion in the O(N) model by comparing results obtained numerically in 1+1 dimensions at leading, next-to-leading and next-to-next-to-leading order in 1/N as well as in the weak coupling limit. A comparison in classical statistical field theory, where exact numerical results are available, is made as well. We focus on early-time dynamics and quasi-particle properties far from equilibrium and observe rapid effective convergence already for moderate values of 1/N or the coupling.Comment: 4 pages, 4 eps figure

Nonequilibrium dynamics in the O(N) model to next-to-next-to-leading order in the 1/N expansion

Nonequilibrium dynamics in quantum field theory has been studied extensively using truncations of the 2PI effective action. Both 1/N and loop expansions beyond leading order show remarkable improvement when compared to mean-field approximations. However, in truncations used so far, only the leading-order parts of the self energy responsible for memory loss, damping and equilibration are included, which makes it difficult to discuss convergence systematically. For that reason we derive the real and causal evolution equations for an O(N) model to next-to-next-to-leading order in the 2PI-1/N expansion. Due to the appearance of internal vertices the resulting equations appear intractable for a full-fledged 3+1 dimensional field theory. Instead, we solve the closely related three-loop approximation in the auxiliary-field formalism numerically in 0+1 dimensions (quantum mechanics) and compare to previous approximations and the exact numerical solution of the Schroedinger equation.Comment: 29 pages, minor changes, references added; to appear in PR

A Complete and Recursive Feature Theory

Various feature descriptions are being employed in logic programming languages and constrained-based grammar formalisms. The common notational primitive of these descriptions are functional attributes called features. The descriptions considered in this paper are the possibly quantified first-order formulae obtained from a signature of binary and unary predicates called features and sorts, respectively. We establish a first-order theory FT by means of three axiom schemes, show its completeness, and construct three elementarily equivalent models. One of the models consists of so-called feature graphs, a data structure common in computational linguistics. The other two models consist of so-called feature trees, a record-like data structure generalizing the trees corresponding to first-order terms. Our completeness proof exhibits a terminating simplification system deciding validity and satisfiability of possibly quantified feature descriptions.Comment: Short version appeared in the 1992 Annual Meeting of the Association for Computational Linguistic

Urban landscape survey in Italy and the Mediterranean

Field survey has been making a major contribution to our understanding of the rural landscapes of the Mediterranean for nearly forty years. During that time the techniques used to map ancient settlement patterns have grown in sophistication from being a process of simply identifying sites in the landscape, to one which provided nuanced understandings of their layouts, chronologies and contexts. This has led to a revolution in how archaeologists approach urban sites, with survey techniques being used increasingly often to generate a plan of a town site prior to excavation as a way of ensuring that the excavation can be used to address site-specific questions in a way that had not been possible before. Most recently, research has begun to reveal the advantages of integrating a range of different non-destructive techniques on urban sites. In combination with exciting new computer-based means of data visualization, all of this work means that it is now possible to virtually reconstruct a buried town within a relatively short space of time, as opposed to the old and destructive excavation-centered approach that could take generations. Unsurprisingly these advances are starting to make a very important understanding to urbanism in general and the Roman Empire in particular. Urban Landscape Survey in Italy and the Mediterranean builds upon all these new developments and is one of the first publications to focus exclusively upon the contribution of survey techniques to our understanding of ancient towns. It addresses methodology led enquiry into the nature of urban settlements primarily in Italy, but also in Greece, Turkey, Croatia, Portugal and Spain. The twenty-two papers from leading specialists in the field focus on two underlying themes. The first deals with the characterization of urban sites and draws upon a wide range of case studies. These range from key protohistoric centres in central and south Italy, to towns that epitomise the contradictions of cultural change under Rome, such as Paestum, Aquinum and Sagalassos, to Roman centres such as Teano, Suasa and Ammaia. The second theme is inter-urban relationships, looking in particular at wider urbanized landscapes in Italy. The fascinating selection of recent and on-going projects presented here significantly moves the limits of our current knowledge about ancient towns