Dressed Hamiltonians formulation

The theoretical description of any many body system is usually approached in two distinct stages. First, the solution of some independent particle model yielding a set of quasi-particles, or dressed particles, which are then used to formulate a systematic scheme for describing the corrections to the model. Perturbation theory, when developed with respect to a suitable reference model, affords the most systematic approach to the correlation problem which today, because it is non-iterative and, therefore, computationally very efficient, forms the basis of the most widely used approaches in contemporary electronic structure calculations, particularly when developed with respect to a Moller-Plesset zero order Hamiltonian. 

Hamiltonian in an extended space, the direct product of the usual molecular Hilbert space, and the space of periodic functions of f e [0,T]. This extension of the Hilbert space can be made somewhat more transparent by introducing a new time-like variable, to be distinguished from the actual time variable t. This new time variable can be defined through the arbitrary phase of the continuous (periodic) field, as done in Ref. [28, 29]. A variant of the idea is found in the (f, t ) method developed by Peskin and Moiseyev [30] and applied to the photodissociation of HJ [31, 32]. We will continue with the more traditional and simpler formulation of Floquet theory here, as this is sufficient to bring out ideas of laser-induced resonances in the dressed molecule picture. 

Presumably the most straightforward approach to chemical dynamics in intense laser fields is to use the time-independent or time-dependent adiabatic states [352], which are the eigenstates of field-free or field-dependent Hamiltonian at given time points respectively, and solve the Schrodinger equation in a stepwise manner. However, when the laser field is approximately periodic, one can also use a set of field-dressed periodic states as an expansion basis. The set of quasi-static states in a periodic Hamiltonian is derived by a Floquet type analysis and is often referred to as the Floquet states [370]. Provided that the laser field is approximately periodic, advantages of using the latter basis set include (1) analysis and interpretation of the electron dynamics is clearer since the Floquet state population often vary slowly with the timescale of the pulse envelope and each Floquet state is characterized as a field-dressed quasi-stationary state, (2) under some moderate conditions, the nuclear dynamics can be approximated by mixed quantum-classical (MQC) nonadiabatic dynamics on the field-dressed PES. The latter point not only provides a powerful clue for interpretation of nuclear dynamics but also implies possible MQC formulation of intense field molecular dynamics. 

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