11,197 research outputs found
Algebraic Nijenhuis operators and Kronecker Poisson pencils
We give a criterion of (micro-)kroneckerity of the linear Poisson pencil on
related to an algebraic Nijenhuis operator on a finite-dimensional Lie algebra . As an application we
get a series of examples of completely integrable systems on semisimple Lie
algebras related to Borel subalgebras and a new proof of the complete
integrability of the free rigid body system on .Comment: 10 pages, references adde
Pricing options in illiquid markets: optimal systems, symmetry reductions and exact solutions
We study a class of nonlinear pricing models which involves the feedback
effect from the dynamic hedging strategies on the price of asset introduced by
Sircar and Papanicolaou. We are first to study the case of a nonlinear demand
function involved in the model. Using a Lie group analysis we investigate the
symmetry properties of these nonlinear diffusion equations. We provide the
optimal systems of subalgebras and the complete set of non-equivalent
reductions of studied PDEs to ODEs. In most cases we obtain families of exact
solutions or derive particular solutions to the equations.Comment: 14 page
Observables and Entanglement in the Two-Body System
Using the quantum two-body system as a familiar model, this talk will
describe how entanglement can be used to select preferred observables for
interrogating a physical system. The symmetries and dynamics of the quantum
two-body system provide a backdrop for testing the relativity of entanglement
with respect to observable-induced tensor product structures. We believe this
exploration leads us to a general statement: the physically-meaningful
observable subalgebras are the ones that minimize entanglement in typical
states.Comment: 5 pages, no figs. Contributed to conference proceedings for Quantum
Theory: Reconsideration of Foundations 6 at Linnaeus University, June 11-14,
201
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