Structure, Time Propagation and Dissipative Terms for Resonances

Abstract

For odd anharmonic oscillators, it is well known that complex scaling can be used to determine resonance energy eigenvalues and the corresponding eigenvectors in complex rotated space. We briefly review and discuss various methods for the numerical determination of such eigenvalues, and also discuss the connection to the case of purely imaginary coupling, which is PT-symmetric. Moreover, we show that a suitable generalization of the complex scaling method leads to an algorithm for the time propagation of wave packets in potentials which give rise to unstable resonances. This leads to a certain unification of the structure and the dynamics. Our time propagation results agree with known quantum dynamics solvers and allow for a natural incorporation of structural perturbations (e.g., due to dissipative processes) into the quantum dynamics.

14 pages; LaTeX; minor changes

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Cited by in corpus (9)

• Multi-Instantons and Exact Results III: Unified Description of the Resonances of Even and Odd Anharmonic Oscillators
• Imaginary Cubic Perturbation: Numerical and Analytic Study
• Localizability of Tachyonic Particles and Neutrinoless Double Beta Decay
• Remark on the Dunne-Unsal relation in exact semi-classics
• Generalized Householder Transformations for the Complex Symmetric Eigenvalue Problem
• Tachyonic Field Theory and Neutrino Mass Running
• Experimental demonstration of the dynamics of quantum coherence evolving under a PT-symmetric Hamiltonian on an NMR quantum processor
• Generalized Nonanalytic Expansions, PT-Symmetry and Large-Order Formulas for Odd Anharmonic Oscillators
• Calculation of the Characteristic Functions of Anharmonic Oscillators