463 research outputs found
Geometric models of (d+1)-dimensional relativistic rotating oscillators
Geometric models of quantum relativistic rotating oscillators in arbitrary
dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It
is shown that these models are analytically solvable, deriving the formulas of
the energy levels and corresponding normalized energy eigenfunctions. An
important property is that all these models have the same nonrelativistic
limit, namely the usual harmonic oscillator.Comment: 7 pages, Late
The CONEstrip algorithm
Uncertainty models such as sets of desirable gambles and (conditional) lower previsions can be represented as convex cones. Checking the consistency of and drawing inferences from such models requires solving feasibility and optimization problems. We consider finitely generated such models. For closed cones, we can use linear programming; for conditional lower prevision-based cones, there is an efficient algorithm using an iteration of linear programs. We present an efficient algorithm for general cones that also uses an iteration of linear programs
On the Relationship between Convex Bodies Related to Correlation Experiments with Dichotomic Observables
In this paper we explore further the connections between convex bodies
related to quantum correlation experiments with dichotomic variables and
related bodies studied in combinatorial optimization, especially cut polyhedra.
Such a relationship was established in Avis, Imai, Ito and Sasaki (2005 J.
Phys. A: Math. Gen. 38 10971-87) with respect to Bell inequalities. We show
that several well known bodies related to cut polyhedra are equivalent to
bodies such as those defined by Tsirelson (1993 Hadronic J. S. 8 329-45) to
represent hidden deterministic behaviors, quantum behaviors, and no-signalling
behaviors. Among other things, our results allow a unique representation of
these bodies, give a necessary condition for vertices of the no-signalling
polytope, and give a method for bounding the quantum violation of Bell
inequalities by means of a body that contains the set of quantum behaviors.
Optimization over this latter body may be performed efficiently by semidefinite
programming. In the second part of the paper we apply these results to the
study of classical correlation functions. We provide a complete list of tight
inequalities for the two party case with (m,n) dichotomic observables when
m=4,n=4 and when min{m,n}<=3, and give a new general family of correlation
inequalities.Comment: 17 pages, 2 figure
Looking for symmetric Bell inequalities
Finding all Bell inequalities for a given number of parties, measurement
settings, and measurement outcomes is in general a computationally hard task.
We show that all Bell inequalities which are symmetric under the exchange of
parties can be found by examining a symmetrized polytope which is simpler than
the full Bell polytope. As an illustration of our method, we generate 238885
new Bell inequalities and 1085 new Svetlichny inequalities. We find, in
particular, facet inequalities for Bell experiments involving two parties and
two measurement settings that are not of the
Collins-Gisin-Linden-Massar-Popescu type.Comment: Joined the associated website as an ancillary file, 17 pages, 1
figure, 1 tabl
Guarding curvilinear art galleries with edge or mobile guards via 2-dominance of triangulation graphs
AbstractIn this paper we consider the problem of monitoring an art gallery modeled as a polygon, the edges of which are arcs of curves, with edge or mobile guards. Our focus is on piecewise-convex polygons, i.e., polygons that are locally convex, except possibly at the vertices, and their edges are convex arcs.We transform the problem of monitoring a piecewise-convex polygon to the problem of 2-dominating a properly defined triangulation graph with edges or diagonals, where 2-dominance requires that every triangle in the triangulation graph has at least two of its vertices in its 2-dominating set. We show that: (1) ân+13â diagonal guards are always sufficient and sometimes necessary, and (2) â2n+15â edge guards are always sufficient and sometimes necessary, in order to 2-dominate a triangulation graph. Furthermore, we show how to compute: (1) a diagonal 2-dominating set of size ân+13â in linear time and space, (2) an edge 2-dominating set of size â2n+15â in O(n2) time and O(n) space, and (3) an edge 2-dominating set of size â3n7â in O(n) time and space.Based on the above-mentioned results, we prove that, for piecewise-convex polygons, we can compute: (1) a mobile guard set of size ân+13â in O(nlogn) time, (2) an edge guard set of size â2n+15â in O(n2) time, and (3) an edge guard set of size â3n7â in O(nlogn) time. All space requirements are linear. Finally, we show that ân3â mobile or ân3â edge guards are sometimes necessary.When restricting our attention to monotone piecewise-convex polygons, the bounds mentioned above drop: ân+14â edge or mobile guards are always sufficient and sometimes necessary; such an edge or mobile guard set, of size at most ân+14â, can be computed in O(n) time and space
Entropy of scalar fields in 3+1 dimensional constant curvature black hole background
We consider the thermodynamics of minimally coupled massive scalar field in
3+1 dimensional constant curvature black hole background. The brick wall model
of 't Hooft is used. When Scharzschild like coordinates are used it is found
that apart from the usual radial brick wall cut-off parammeter an angular
cut-off parameter is required to regularize the solution. Free energy of the
scalar field is obtained through counting of states using the WKB
approximation. It is found that the free energy and the entropy are
logarithmically divergent in both the cut-off parameters.Comment: 9 pages, LaTe
Pruning Algorithms for Pretropisms of Newton Polytopes
Pretropisms are candidates for the leading exponents of Puiseux series that
represent solutions of polynomial systems. To find pretropisms, we propose an
exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton
polytopes. We prefer exact arithmetic not only because of the exact input and
the degrees of the output, but because of the often unpredictable growth of the
coordinates in the face normals, even for polytopes in generic position. We
provide experimental results with our preliminary implementation in Sage that
compare favorably with the pruning method that relies only on cone
intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning,
accepted for presentation at Computer Algebra in Scientific Computing, CASC
201
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