Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method

Abstract

We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters, using adaptative projectors which follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-hermitian hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive, it converges within a few dozen iterations at constant memory cost. We first illustrate the abilities of the method on a 4-D coupled oscillator model hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H${}_2^{+}$ in the vicinity of exceptional points are calculated as an illustrative example.

arXiv comment30 pages, 4 figures

References in corpus (5)

• Exotic states in the strong field control of H${}_2^{+}$ dissociation dynamics: From exceptional points to zero-width resonances
• Controlling vibrational cooling with Zero-Width Resonances: An adiabatic Floquet approach
• Clusters of Exceptional Points for a Laser Control of Selective Vibrational Transfer
• Almost quantum adiabatic dynamics and generalized time dependent wave operators
• Global integration of the Schrödinger equation within the wave operator formalism: The role of the effective Hamiltonian in multidimensional active spaces