623 research outputs found
On Coherent States and q-Deformed Algebras
We review some aspects of the relation between ordinary coherent states and
q-deformed generalized coherent states with some of the simplest cases of
quantum Lie algebras. In particular, new properties of (q-)coherent states are
utilized to provide a path integral formalism allowing to study a modified form
of q-classical mechanics, to probe some geometrical consequences of the
q-deformation and finally to construct Bargmann complex analytic realizations
for some quantum algebras.Comment: Presented at the 'International Symposium on Coherent States' June
1993, USA 14 pages, plain LATEX, FTUV/93-37, IFIC/93-2
Brownian motion on a smash line
Brownian motion on a smash line algebra (a smash or braided version of the
algebra resulting by tensoring the real line and the generalized paragrassmann
line algebras), is constructed by means of its Hopf algebraic structure.
Further, statistical moments, non stationary generalizations and its diffusion
limit are also studied. The ensuing diffusion equation posseses triangular
matrix realizations.Comment: Latex, 6 pages no figures. Submitted to Journal of Nonlinear
Mathematical Physics. Special Issue of Proccedings of NEEDS'9
Quantum Optical Random Walk: Quantization Rules and Quantum Simulation of Asymptotics
Rules for quantizing the walker+coin parts of a classical random walk are
provided by treating them as interacting quantum systems. A quantum optical
random walk (QORW), is introduced by means of a new rule that treats quantum or
classical noise affecting the coin's state, as sources of quantization. The
long term asymptotic statistics of QORW walker's position that shows enhanced
diffusion rates as compared to classical case, is exactly solved. A quantum
optical cavity implementation of the walk provides the framework for quantum
simulation of its asymptotic statistics. The simulation utilizes interacting
two-level atoms and/or laser randomly pulsating fields with fluctuating
parameters.Comment: 18 pages, 3 figure
q-Symmetries in DNLS-AL chains and exact solutions of quantum dimers
Dynamical symmetries of Hamiltonians quantized models of discrete non-linear
Schroedinger chain (DNLS) and of Ablowitz-Ladik chain (AL) are studied. It is
shown that for -sites the dynamical algebra of DNLS Hamilton operator is
given by the algebra, while the respective symmetry for the AL case is
the quantum algebra su_q(n). The q-deformation of the dynamical symmetry in the
AL model is due to the non-canonical oscillator-like structure of the raising
and lowering operators at each site.
Invariants of motions are found in terms of Casimir central elements of su(n)
and su_q(n) algebra generators, for the DNLS and QAL cases respectively.
Utilizing the representation theory of the symmetry algebras we specialize to
the quantum dimer case and formulate the eigenvalue problem of each dimer
as a non-linear (q)-spin model. Analytic investigations of the ensuing
three-term non-linear recurrence relations are carried out and the respective
orthonormal and complete eigenvector bases are determined.
The quantum manifestation of the classical self-trapping in the QDNLS-dimer
and its absence in the QAL-dimer, is analysed by studying the asymptotic
attraction and repulsion respectively, of the energy levels versus the strength
of non-linearity. Our treatment predicts for the QDNLS-dimer, a
phase-transition like behaviour in the rate of change of the logarithm of
eigenenergy differences, for values of the non-linearity parameter near the
classical bifurcation point.Comment: Latex, 19pp, 4 figures. Submitted for publicatio
Dynamics of organizational culture: Individual beliefs vs. social conformity
The complex nature of organizational culture challenges our ability to infers
its underlying dynamics from observational studies. Recent computational
studies have adopted a distinct different view, where plausible mechanisms are
proposed to describe a wide range of social phenomena, including the onset and
evolution of organizational culture. In this spirit, this work introduces an
empirically-grounded, agent-based model which relaxes a set of assumptions that
describes past work - (a) omittance of an individual's strive for achieving
cognitive coherence, (b) limited integration of important contextual factors -
by utilizing networks of beliefs and incorporating social rank into the
dynamics. As a result, we illustrate that: (i) an organization may appear to be
increasingly coherent in terms of organizational culture, yet be composed of
individuals with reduced levels of coherence, (ii) the components of social
conformity - peer-pressure and social rank - are influential at different
aggregation levels.Comment: 20 pages, 8 figure
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