High-Order Adiabatic Approximation for Non-Hermitian Quantum System and Complexization of Berry's Phase

Abstract

In this paper the evolution of a quantum system drived by a non-Hermitian Hamiltonian depending on slowly-changing parameters is studied by building an universal high-order adiabatic approximation(HOAA) method with Berry's phase ,which is valid for either the Hermitian or the non-Hermitian cases. This method can be regarded as a non-trivial generalization of the HOAA method for closed quantum system presented by this author before. In a general situation, the probabilities of adiabatic decay and non-adiabatic transitions are explicitly obtained for the evolution of the non-Hermitian quantum system. It is also shown that the non-Hermitian analog of the Berry's phase factor for the non-Hermitian case just enjoys the holonomy structure of the dual linear bundle over the parameter manifold. The non-Hermitian evolution of the generalized forced harmonic oscillator is discussed as an illustrative examples.

ITP.SB-93-22,17 pages

Cited by in corpus (22)

• Two-Photon Transport in a Waveguide Coupled to a Cavity with a Two-level System
• Mechanical PT symmetry in coupled optomechanical systems
• Adiabaticity condition for non-Hermitian Hamiltonians
• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• Stochastic pump effect and geometric phases in dissipative and stochastic systems
• Berry Phase of a Resonant State
• Berry connection induced anomalous wave-packet dynamics in non-Hermitian systems
• Quantum Dynamical Approach of Wavefunction Collapse in Measurement Process and Its Application to Quantum Zeno Effect
• Construction of pseudo-bosons systems
• Non-Hermitian dynamics of slowly-varying Hamiltonians
• Topological Microlaser with A non-Hermitian Topological Bulk
• Inverse engineering rigorous adiabatic Hamiltonian for non-Hermitian system
• Pseudo-bosons, so far
• Pump-and-probe optical transmission phase shift as a quantitative probe of the Bogoliubov dispersion relation in a nonlinear channel waveguide
• Geometric phases in neutrino oscillations with nonlinear refraction
• Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions
• Logarithmic perturbation theory for quasinormal modes
• Stability analysis of non-thermal fixed points in longitudinally expanding kinetic theory
• Non-Adiabatic Fluctuation in Measured Geometric Phase
• Accidental Degeneracy and Berry Phase of Resonant States
• Counterdiabatic driving for pseudo- and antipseudo- Hermitian systems
• Non-Hermitian wave-packet dynamics and its realization within a non-Hermitian chiral cavity