Stability, complex modes and non-separability in rotating quadratic potentials
arXiv:1112.1311 · doi:10.1103/PhysRevA.79.062103
Abstract
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 as well discussed.
7 pages, 2 figures
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Cited by in corpus (7)
- Dynamics of entanglement between two harmonic modes in stable and unstable regimes
- Entanglement of two harmonic modes coupled by angular momentum
- Spectrum and normal modes of non-hermitian quadratic boson operators
- Nonlinear dynamics of a semiquantum Hamiltonian in the vicinity of quantum unstable regimes
- Nonlinear effects on the dynamics of quantum harmonic modes coupled through angular momentum
- Algebraic analysis of non-Hermitian quadratic Hamiltonians
- Conserved operators and exact conditions for pair condensation