6,879 research outputs found
Tensor Representation of Spin States
We propose a generalization of the Bloch sphere representation for arbitrary
spin states. It provides a compact and elegant representation of spin density
matrices in terms of tensors that share the most important properties of Bloch
vectors. Our representation, based on covariant matrices introduced by Weinberg
in the context of quantum field theory, allows for a simple parametrization of
coherent spin states, and a straightforward transformation of density matrices
under local unitary and partial tracing operations. It enables us to provide a
criterion for anticoherence, relevant in a broader context such as quantum
polarization of light.Comment: 5 pages + 7 pages of supplementary informatio
Antisymmetrization of a Mean Field Calculation of the T-Matrix
The usual definition of the prior(post) interaction between
projectile and target (resp. ejectile and residual target) being contradictory
with full antisymmetrization between nucleons, an explicit antisymmetrization
projector must be included in the definition of the transition
operator, We derive the
suitably antisymmetrized mean field equations leading to a non perturbative
estimate of . The theory is illustrated by a calculation of forward
- scattering, making use of self consistent symmetries.Comment: 30 pages, no figures, plain TeX, SPHT/93/14
Multifractal wave functions of simple quantum maps
We study numerically multifractal properties of two models of one-dimensional
quantum maps, a map with pseudointegrable dynamics and intermediate spectral
statistics, and a map with an Anderson-like transition recently implemented
with cold atoms. Using extensive numerical simulations, we compute the
multifractal exponents of quantum wave functions and study their properties,
with the help of two different numerical methods used for classical
multifractal systems (box-counting method and wavelet method). We compare the
results of the two methods over a wide range of values. We show that the wave
functions of the Anderson map display a multifractal behavior similar to
eigenfunctions of the three-dimensional Anderson transition but of a weaker
type. Wave functions of the intermediate map share some common properties with
eigenfunctions at the Anderson transition (two sets of multifractal exponents,
with similar asymptotic behavior), but other properties are markedly different
(large linear regime for multifractal exponents even for strong
multifractality, different distributions of moments of wave functions, absence
of symmetry of the exponents). Our results thus indicate that the intermediate
map presents original properties, different from certain characteristics of the
Anderson transition derived from the nonlinear sigma model. We also discuss the
importance of finite-size effects.Comment: 15 pages, 21 figure
Coalition Stability with Heterogeneous Agents
We analyze coalition formation with heterogeneous agents based on an individual stability concept. Defining exchanging and refractory agents, we give existence and enlargement conditions for coalitions with heterogeneous agents. Using the concept of exchanging agents we give necessary conditions for internal stability and show that refraction is a sufficient condition for the failure of an enlargement of the coalition.Heterogeneity, Coalition, Exchanging, Refraction.
L'expansion coloniale de la fourmi d'Argentine
La fourmi Linepithema humile fait preuve d'une exceptionnelle aptitude à coloniser de trÚs larges territoires. Cette expansion est favorisée par une organisation sociale bien différente de celle qu'elle adopte dans son pays d'origine. Quelle est la clé de ce changement
Parallel scalability study of three dimensional additive Schwarz preconditioners in non-overlapping domain decomposition
In this paper we study the parallel scalability of variants of additive Schwarz preconditioners for three dimensional non-overlapping domain decomposition methods. To alleviate the
computational cost, both in terms of memory and floating-point complexity, we investigate
variants based on a sparse approximation or on mixed 32- and 64-bit calculation. The robustness of the preconditioners is illustrated on a set of linear systems arising from the finite
element discretization of elliptic PDEs through extensive parallel experiments on up to 1000
processors. Their efficiency from a numerical and parallel performance view point are studied
Finite geometries and diffractive orbits in isospectral billiards
Several examples of pairs of isospectral planar domains have been produced in
the two-dimensional Euclidean space by various methods. We show that all these
examples rely on the symmetry between points and blocks in finite projective
spaces; from the properties of these spaces, one can derive a relation between
Green functions as well as a relation between diffractive orbits in isospectral
billiards.Comment: 10 page
Complex Scaled Spectrum Completeness for Coupled Channels
The Complex Scaling Method (CSM) provides scattering wave functions which
regularize resonances and suggest a resolution of the identity in terms of such
resonances, completed by the bound states and a smoothed continuum. But, in the
case of inelastic scattering with many channels, the existence of such a
resolution under complex scaling is still debated. Taking advantage of results
obtained earlier for the two channel case, this paper proposes a representation
in which the convergence of a resolution of the identity can be more easily
tested. The representation is valid for any finite number of coupled channels
for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure
Intermediate statistics in quantum maps
We present a one-parameter family of quantum maps whose spectral statistics
are of the same intermediate type as observed in polygonal quantum billiards.
Our central result is the evaluation of the spectral two-point correlation form
factor at small argument, which in turn yields the asymptotic level
compressibility for macroscopic correlation lengths
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