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

• URL: http://arxiv.org/abs/2005.13611v1
• Date: Wed, 27 May 2020 19:43:55 GMT
• Title: Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method
• Authors: Arnaud Leclerc and Georges Jolicard
• Abstract summary: 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. 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. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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