173 research outputs found
Generalized coherent states for SU(n) systems
Generalized coherent states are developed for SU(n) systems for arbitrary
. This is done by first iteratively determining explicit representations for
the SU(n) coherent states, and then determining parametric representations
useful for applications. For SU(n), the set of coherent states is isomorphic to
a coset space , and thus shows the geometrical structure of the
coset space. These results provide a convenient --dimensional space
for the description of arbitrary SU(n) systems. We further obtain the metric
and measure on the coset space, and show some properties of the SU(n) coherent
states.Comment: 11 page
Variational optimization of probability measure spaces resolves the chain store paradox
In game theory, players have continuous expected payoff functions and can use fixed point theorems to locate equilibria. This optimization method requires that players adopt a particular type of probability measure space. Here, we introduce alternate probability measure spaces altering the dimensionality, continuity, and differentiability properties of what are now the game's expected payoff functionals. Optimizing such functionals requires generalized variational and functional optimization methods to locate novel equilibria. These variational methods can reconcile game theoretic prediction and observed human behaviours, as we illustrate by resolving the chain store paradox. Our generalized optimization analysis has significant implications for economics, artificial intelligence, complex system theory, neurobiology, and biological evolution and development.optimization; probability measure space; noncooperative game; chain store paradox
Superpositions of SU(3) coherent states via a nonlinear evolution
We show that a nonlinear Hamiltonian evolution can transform an SU(3)
coherent state into a superposition of distinct SU(3) coherent states, with a
superposition of two SU(2) coherent states presented as a special case. A phase
space representation is depicted by projecting the multi-dimensional -symbol
for the state to a spherical subdomain of the coset space. We discuss
realizations of this nonlinear evolution in the contexts of nonlinear optics
and Bose--Einstein condensates
Variational optimization of probability measure spaces resolves the chain store paradox
In game theory, players have continuous expected payoff functions and can use
fixed point theorems to locate equilibria. This optimization method requires
that players adopt a particular type of probability measure space. Here, we
introduce alternate probability measure spaces altering the dimensionality,
continuity, and differentiability properties of what are now the game's
expected payoff functionals. Optimizing such functionals requires generalized
variational and functional optimization methods to locate novel equilibria.
These variational methods can reconcile game theoretic prediction and observed
human behaviours, as we illustrate by resolving the chain store paradox. Our
generalized optimization analysis has significant implications for economics,
artificial intelligence, complex system theory, neurobiology, and biological
evolution and development.Comment: 11 pages, 5 figures. Replaced for minor notational correctio
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