4 research outputs found
Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms
We exhibit scarring for certain nonlinear ergodic toral automorphisms. There
are perturbed quantized hyperbolic toral automorphisms preserving certain
co-isotropic submanifolds. The classical dynamics is ergodic, hence in the
semiclassical limit almost all eigenstates converge to the volume measure of
the torus. Nevertheless, we show that for each of the invariant submanifolds,
there are also eigenstates which localize and converge to the volume measure of
the corresponding submanifold.Comment: 17 page
Wigner Functions on a Lattice
The Wigner functions on the one dimensional lattice are studied. Contrary to
the previous claim in literature, Wigner functions exist on the lattice with
any number of sites, whether it is even or odd. There are infinitely many
solutions satisfying the conditions which reasonable Wigner functions should
respect. After presenting a heuristic method to obtain Wigner functions, we
give the general form of the solutions. Quantum mechanical expectation values
in terms of Wigner functions are also discussed.Comment: 11 pages, no figures, REVTE