Almost quantum adiabatic dynamics and generalized time dependent wave operators

Abstract

We consider quantum dynamics for which the strict adiabatic approximation fails but which do not escape too far from the adiabatic limit. To treat these systems we introduce a generalisation of the time dependent wave operator theory which is usually used to treat dynamics which do not escape too far from an initial subspace called the active space. Our generalisation is based on a time dependent adiabatic deformation of the active space. The geometric phases associated with the almost adiabatic representation are also derived. We use this formalism to study the adiabaticity of a dynamics surrounding an exceptional point of a non-hermitian hamiltonian. We show that the generalized time dependent wave operator can be used to correct easily the adiabatic approximation which is very unperfect in this situation.

This second version contains another example with higher dimensionality (the molecule H2+)

References in corpus (3)

• Geometric Phase for Non-Hermitian Hamiltonians and Its Holonomy Interpretation
• General Adiabatic Evolution with a Gap Condition
• Discussion of the adiabatic hypothesis in control schemes using exceptional points

Cited by in corpus (6)

• General description of quasi-adiabatic dynamical phenomena near exceptional points
• Non-Hermitian dynamics without dissipation in quantum systems
• State Flip at Exceptional Points in Atomic Spectra
• Time Crystals from Minimum Time Uncertainty
• Population transfer at exceptional points in spectra of the hydrogen atom in parallel electric and magnetic fields
• Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method