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Only those quasienergy states whose dominant components are from 1 g and 1 u states are included. Two di erent groups of quasienergy states can be identiÿed. The two solid lines indicate one representative quasienergy level from each group (adapted from Ref. [29]). Fig. 25. The imaginary parts of the complex quasienergies vs. R from the lower and upper groups of quasienergy levels (adapted from Ref. [29]). A. Telnov / Physics Reports 390 (2004) 1 – 131 the quasienergy levels. Two di erent groups, called the “lower” and “upper” groups of quasienergy states can be identiÿed.

A. Telnov / Physics Reports 390 (2004) 1 – 131 51 Fig. 22. Same as Fig. 20 except for the intensity I = 5 × 1013 W=cm2 (strong ÿeld case) (adapted from Ref. [50]). molecules become more unstable in stronger ÿelds, a phenomenon known as “bond softening” [140]. What is more intriguing here is the unexpected behavior of the upper group resonances. A comparison of Figs. 20(b) and 21(b) reveals that the photodissociation rates of these high-lying VQE resonances actually decrease with increasing laser intensity!

In the prolate spheroidal coordinates, however, only the coordinate needs to be complex rotated, namely, → exp(i ), where is the rotation angle. Consider, for example, the dc ÿeld ionization of H2+ . 45) where F is the electric ÿeld amplitude. 3. 7. Applications of non-Hermitian Floquet methods: atomic multiphoton processes in strong ÿelds In this section, we present several applications of non-Hermitian Floquet formalisms and complex quasienergy methods for nonperturbative studies of atomic MPI/ATI in intense monochromatic laser ÿelds.