2,145 research outputs found
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
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
Gap equation with pairing correlations beyond mean field and its equivalence to a Hugenholtz-Pines condition for fermion pairs
The equation for the gap parameter represents the main equation of the
pairing theory of superconductivity. Although it is formally defined through a
single-particle property, physically it reflects the pairing correlations
between opposite-spin fermions. Here, we exploit this physical connection and
cast the gap equation in an alternative form which explicitly highlights these
two-particle correlations, by showing that it is equivalent to a
Hugenholtz-Pines condition for fermion pairs. At a formal level, a direct
connection is established in this way between the treatment of the condensate
fraction in condensate systems of fermions and bosons. At a practical level,
the use of this alternative form of the gap equation is expected to make easier
the inclusion of pairing fluctuations beyond mean field. As a proof-of-concept
of the new method, we apply the modified form of the gap equation to the
long-pending problem about the inclusion of the Gorkov-Melik-Barkhudarov
correction across the whole BCS-BEC crossover, from the BCS limit of strongly
overlapping Cooper pairs to the BEC limit of dilute composite bosons, and for
all temperatures in the superfluid phase. Our numerical calculations yield
excellent agreement with the recently determined experimental values of the gap
parameter for an ultra-cold Fermi gas in the intermediate regime between BCS
and BEC, as well as with the available quantum Monte Carlo data in the same
regime.Comment: 24 pages, 13 figure
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
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