Bose-Einstein condensation of photons with nonlocal nonlinearity in a dye-doped graded-index microcavity

We consider a microcavity made by a graded-index (GRIN) glass, doped by dye molecules, placed within two planar mirrors and study Bose-Einstein condensation (BEC) of photons. The presence of the mirrors leads to an effective photon mass, and the index grading provides an effective trapping frequency; the photon gas becomes formally equivalent to a two dimensional Bose gas trapped in an isotropic harmonic potential. The inclusion of nonlinear effects provides an effective interaction between photons. We discuss, in particular, thermal lensing effects and nonlocal nonlinearity, and quantitatively compare our results with the reported experimental data.Comment: 13 pages, 6 figure

Unifying Class-Based Representation Formalisms

The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues underlying such representation formalisms and single out both their common characteristics and their distinguishing features. Such investigation leads us to propose a unifying framework in which we are able to capture the fundamental aspects of several representation languages used in different contexts. The proposed formalism is expressed in the style of description logics, which have been introduced in knowledge representation as a means to provide a semantically well-founded basis for the structural aspects of knowledge representation systems. The description logic considered in this paper is a subset of first order logic with nice computational characteristics. It is quite expressive and features a novel combination of constructs that has not been studied before. The distinguishing constructs are number restrictions, which generalize existence and functional dependencies, inverse roles, which allow one to refer to the inverse of a relationship, and possibly cyclic assertions, which are necessary for capturing real world domains. We are able to show that it is precisely such combination of constructs that makes our logic powerful enough to model the essential set of features for defining class structures that are common to frame systems, object-oriented database languages, and semantic data models. As a consequence of the established correspondences, several significant extensions of each of the above formalisms become available. The high expressiveness of the logic we propose and the need for capturing the reasoning in different contexts forces us to distinguish between unrestricted and finite model reasoning. A notable feature of our proposal is that reasoning in both cases is decidable. We argue that, by virtue of the high expressive power and of the associated reasoning capabilities on both unrestricted and finite models, our logic provides a common core for class-based representation formalisms

Verification of Generalized Inconsistency-Aware Knowledge and Action Bases (Extended Version)

Knowledge and Action Bases (KABs) have been put forward as a semantically rich representation of a domain, using a DL KB to account for its static aspects, and actions to evolve its extensional part over time, possibly introducing new objects. Recently, KABs have been extended to manage inconsistency, with ad-hoc verification techniques geared towards specific semantics. This work provides a twofold contribution along this line of research. On the one hand, we enrich KABs with a high-level, compact action language inspired by Golog, obtaining so called Golog-KABs (GKABs). On the other hand, we introduce a parametric execution semantics for GKABs, so as to elegantly accomodate a plethora of inconsistency-aware semantics based on the notion of repair. We then provide several reductions for the verification of sophisticated first-order temporal properties over inconsistency-aware GKABs, and show that it can be addressed using known techniques, developed for standard KABs

From superconducting fluctuations to the bosonic limit in the response functions above the critical temperature

We investigate the density, current, and spin response functions above the critical temperature for a system of three-dimensional fermions interacting via an attractive short-range potential. In the strong-coupling (bosonic) limit of this interaction, we identify the dominant diagrammatic contributions for a ``dilute'' system of composite bosons which form as bound-fermion pairs, and compare them with the usual (Aslamazov-Larkin, Maki-Thompson, and density-of-states) terms occurring in the theory of superconducting fluctuations above the critical temperature for a clean system in the weak-coupling limit. We show that, at the zeroth order in the diluteness parameter for the composite bosons, the Aslamazov-Larkin term still represents formally the dominant contribution to the density and current response functions, while the Maki-Thompson and density-of-states terms are strongly suppressed. Corrections to the Aslamazov-Larkin term are then considered at the next order in the diluteness parameter for the composite bosons. The spin response function is also examined, and it is found to be exponentially suppressed in the bosonic limit only when appropriate sets of diagrams are considered simultaneously.Comment: 10 pages, 6 figure

Updating DL-Lite ontologies through first-order queries

In this paper we study instance-level update in DL-LiteA, the description logic underlying the OWL 2 QL standard. In particular we focus on formula-based approaches to ABox insertion and deletion. We show that DL-LiteA, which is well-known for enjoying first-order rewritability of query answering, enjoys a first-order rewritability property also for updates. That is, every update can be reformulated into a set of insertion and deletion instructions computable through a nonrecursive datalog program. Such a program is readily translatable into a first-order query over the ABox considered as a database, and hence into SQL. By exploiting this result, we implement an update component for DLLiteA-based systems and perform some experiments showing that the approach works in practice.Peer ReviewedPostprint (author's final draft

Synthesizing and executing plans in Knowledge and Action Bases

We study plan synthesis for a variant of Knowledge and Action Bases (KABs). KABs have been recently introduced as a rich, dynamic framework where states are full-fledged description logic (DL) knowledge bases (KBs) whose extensional part is manipulated by actions that can introduce new objects from an infinite domain. We show that, in general, plan existence over KABs is undecidable even under severe restrictions. We then focus on the class of state-bounded KABs, for which plan existence is decidable, and we provide sound and complete plan synthesis algorithms, through a novel combination of techniques based on standard planning, DL query answering, and finite-state abstractions. All results hold for any DL with decidable query answering. We finally show that for lightweight DLs, plan synthesis can be compiled into standard ADL planning. © 2016, CEUR-WS. All rights reserved