1,449 research outputs found
Effective Free Energy for Individual Dynamics
Physics and economics are two disciplines that share the common challenge of
linking microscopic and macroscopic behaviors. However, while physics is based
on collective dynamics, economics is based on individual choices. This
conceptual difference is one of the main obstacles one has to overcome in order
to characterize analytically economic models. In this paper, we build both on
statistical mechanics and the game theory notion of Potential Function to
introduce a rigorous generalization of the physicist's free energy, which
includes individual dynamics. Our approach paves the way to analytical
treatments of a wide range of socio-economic models and might bring new
insights into them. As first examples, we derive solutions for a congestion
model and a residential segregation model.Comment: 8 pages, 2 figures, presented at the ECCS'10 conferenc
Coherent state triplets and their inner products
It is shown that if H is a Hilbert space for a representation of a group G,
then there are triplets of spaces F_H, H, F^H, in which F^H is a space of
coherent state or vector coherent state wave functions and F_H is its dual
relative to a conveniently defined measure. It is shown also that there is a
sequence of maps F_H -> H -> F^H which facilitates the construction of the
corresponding inner products. After completion if necessary, the F_H, H, and
F^H, become isomorphic Hilbert spaces. It is shown that the inner product for H
is often easier to evaluate in F_H than F^H. Thus, we obtain integral
expressions for the inner products of coherent state and vector coherent state
representations. These expressions are equivalent to the algebraic expressions
of K-matrix theory, but they are frequently more efficient to apply. The
construction is illustrated by many examples.Comment: 33 pages, RevTex (Latex2.09) This paper is withdrawn because it
contained errors that are being correcte
Irreducible decomposition for tensor prodect representations of Jordanian quantum algebras
Tensor products of irreducible representations of the Jordanian quantum
algebras U_h(sl(2)) and U_h(su(1,1)) are considered. For both the highest
weight finite dimensional representations of U_h(sl(2)) and lowest weight
infinite dimensional ones of U_h(su(1,1)), it is shown that tensor product
representations are reducible and that the decomposition rules to irreducible
representations are exactly the same as those of corresponding Lie algebras.Comment: LaTeX, 14pages, no figur
Nonlinear collective nuclear motion
For each real number a Lie algebra of nonlinear vector fields on
three dimensional Euclidean space is reported. Although each algebra is
mathematically isomorphic to , only the vector
fields correspond to the usual generators of the general linear group. The
vector fields integrate to a nonstandard action of the general
linear group; the case integrates to a local Lie semigroup. For
each , a family of surfaces is identified that is invariant with
respect to the group or semigroup action. For positive the surfaces
describe fissioning nuclei with a neck, while negative surfaces
correspond to exotic bubble nuclei. Collective models for neck and bubble
nuclei are given by irreducible unitary representations of a fifteen
dimensional semidirect sum spectrum generating algebra spanned by its
nonlinear subalgebra plus an abelian nonlinear inertia tensor
subalgebra.Comment: 13 pages plus two figures(available by fax from authors by request
The Dirac Oscillator. A relativistic version of the Jaynes--Cummings model
The dynamics of wave packets in a relativistic Dirac oscillator is compared
to that of the Jaynes-Cummings model. The strong spin-orbit coupling of the
Dirac oscillator produces the entanglement of the spin with the orbital motion
similar to what is observed in the model of quantum optics. The collapses and
revivals of the spin which result extend to a relativistic theory our previous
findings on nonrelativistic oscillator where they were known under the name of
`spin-orbit pendulum'. There are important relativistic effects (lack of
periodicity, zitterbewegung, negative energy states). Many of them disappear
after a Foldy-Wouthuysen transformation.Comment: LaTeX2e, uses IOP style files (included), 14 pages, 9 separate
postscript figure
Computing a maximum clique in geometric superclasses of disk graphs
In the 90's Clark, Colbourn and Johnson wrote a seminal paper where they
proved that maximum clique can be solved in polynomial time in unit disk
graphs. Since then, the complexity of maximum clique in intersection graphs of
d-dimensional (unit) balls has been investigated. For ball graphs, the problem
is NP-hard, as shown by Bonamy et al. (FOCS '18). They also gave an efficient
polynomial time approximation scheme (EPTAS) for disk graphs. However, the
complexity of maximum clique in this setting remains unknown. In this paper, we
show the existence of a polynomial time algorithm for a geometric superclass of
unit disk graphs. Moreover, we give partial results toward obtaining an EPTAS
for intersection graphs of convex pseudo-disks
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