Stability, complex modes and non-separability in rotating quadratic potentials

R. ROSSIGNOLI; A.M. KOWALSKI

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

American Physical Society

Lugar: NY; Año: 2009 vol. A 79 p. 621031 - 621037

1050-2947

We examine the dynamics of a particle in a general rotating quadratic potential, not necessarily stable or isotropic, using a general complex mode formalism. The problem is equivalent to that of a charged particle in a quadratic potential in the presence of a uniform magnetic field. It is shown that the unstable system exhibits a rich structure, with complex normal modes as well as non-standard modes of evolution characterized by equations of motion which cannot be decoupled (non-separable cases). It is also shown that in some unstable cases the dynamics can be stabilized by increasing the magnetic field or tuning the rotational frequency, giving rise to dynamical stability or instability windows. The evolution in general non-diagonalizable cases is aswell discussed.