150 research outputs found
Semigroups and abstract Gevrey spaces
AbstractConditions are found under which a closed linear operator A in a Banach space X generates a continuous semigroup in a linear topological space Y which is dense in X. The space Y is an abstract Gevrey space associated with the operator A. This is an abstract setting for some results for hyperbolic systems with data in spaces of Gevrey functions
Action-Angle variables for the Gel'fand-Dikii flows
Using the scattering transform for order linear scalar operators,
the Poisson bracket found by Gel'fand and Dikii, which generalizes the Gardner
Poisson bracket for the KdV hierarchy, is computed on the scattering side.
Action-angle variables are then constructed. Using this, complete integrability
is demonstrated in the strong sense. Real action-angle variables are
constructed in the self-adjoint case
A Dirac Sea and thermodynamic equilibrium for the quantized three-wave interaction
The classical version of the three wave interaction models the creation and
destruction of waves; the quantized version models the creation and destruction
of particles. The quantum three wave interaction is described and the Bethe
Ansatz for the eigenfunctions is given in closed form. The Bethe equations are
derived in a rigorous fashion and are shown to have a thermodynamic limit. The
Dirac sea of negative energy states is obtained as the infinite density limit.
Finite particle/hole excitations are determined and the asymptotic relation of
energy and momentum is obtained. The Yang-Yang functional for the relative free
energy of finite density excitations is constructed and is shown to be convex
and bounded below. The equations of thermal equilibrium are obtained
Metrics and geodesics induced by order relations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46255/1/209_2005_Article_BF01115107.pd
- …