Quasienergy method

S.-I. Chu, D.A. Telnov, Beyond the Floquet theorem Generalized Floquet formalisms and quasienergy methods for atomic and molecular multiphoton processes in intense laser fields, Phys. Rep. 390 (2004) 1. 

Quasienergies from Short Time Cross-Correlation Probability Amplitudes by the Filter-Diagonalization Method. 

In this section we outline the coupled cluster-molecular mechanics response method, the CC/MM response method. Ref. [51] considers CC response functions for molecular systems in vacuum and for further details we refer to this article. The identification of response functions is closely connected to time-dependent perturbation theory [51,65,66,67,68,69,70], Our starting point is the quasienergy and we identify the response functions as simple derivatives of the quasienergy. For a molecular system in vacuum where Hqm is the vacuum Hamiltonian for the unperturbed molecule and V" is a time-dependent perturbation we have the following time-dependent Hamiltonian, H,... 

From the definition of molecular properties (29) and the above discussion it is clear that the proper theoretical framework for the description of molecular properties is variational perturbation theory. An excellent presentation of this approach is provided by Helgaker and Jprgensen [9]. Although they focus on the calculation of geometrical derivatives, the methods and proofs presented are straightforwardly extended to quasienergy derivatives, as shown by Christiansen eta/. [13]. 

In each case, we first studied the laser driven dynamics of the system in the framework of the Floquet formalism, described in Sect. 6.5 of Chap. 6, which provides a geometrical interpretation of the laser driven dynamics and its dependence on the frequency and amplitude of the laser field, through the analysis of the eigenvalues of the Floquet operator, called quasienergies. Various effective models were used for that purpose. This analysis allowed us to explain the shape of the relevant quasienergy curves as a function of the laser parameters, and to obtain the parameters of the laser field that induce the CDT. We then used the MCTDH method to solve the TDSE for the molecule in interaction with the laser field and compare these results with those obtained from the effective Hamiltonian described in Sect. 8.2.3 above. 

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