Almost quantum adiabatic dynamics and generalized time-dependent wave operators

作者：Viennot David^*

来源：Journal of Physics A-Mathematical and Theoretical, 2014, 47(6): 065302.

DOI：10.1088/1751-8113/47/6/065302

• geometric
• dynamic or topological
• solutions of wave equations: bound states
• algebraic methods

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 generalization 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 generalization 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 imperfect in this situation.

• 出版日期2014-2-14