Quantum stochastici ty (the nature of wave functions and eigenvalues when the short-wave-limit Hamiltonian has stochastic trajectories) is studied for the two-dimensional Helmholtz equation with "stadium" boundary.The eigenvalue separations have a Wigner distribution (characteristic ot' a random Hamiltonian), in contrast to the clustering found for a separable equation. The eigenfunctions exhibit a random pattern for the nodal curves, with isotropic distribution of local wave-vectors.
In a toroidal plasma with axial symmetry, the three adiabatically invariant actions of a particle are the magnetic mcment, the c'anonical angular momentum, and Both the diffUsion tensor and the growth rate depend upon a coupling coefficient which represents the work done by a normal-mode field eigenftinctionon the current density of an unperturbed particle orbit. The diffUsion of the plasma causes adiabatic changes in the electric and magnetic self-consistent fields. Accordingly, energy is not conserved, but is exchanged with external currents.-2-
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