Tunneling nonadiabatic

The problem of nonadiabatic tunneling in the Landau-Zener approximation has been solved by Ovchinnikova [1965]. For further refinements of the theory beyond this approximation see Laing et al. [1977], Holstein [1978], Coveney et al. [1985], Nakamura [1987]. The nonadiabatic transition probability for a more general case of dissipative tunneling is derived in appendix B. We quote here only the result for the dissipationless case obtained in the Landau-Zener limit. When < F (Xe), the total transition probability is the product of the adiabatic tunneling rate, calculated in the previous sections, and the Landau-Zener-Stueckelberg-like factor... 

The problem of nonadiabatic tunneling has been already formulated in section 3.5, and in this subsection we study how dissipation affects the conclusions drawn there. The two-state Hamiltonian for the system coupled to a bath is conveniently rewritten via the Pauli matrices... 

When Va varied within the interval 1-8 cm the tunneling splitting was found to depend nearly linearly on Fj, in agreement with the semiclassical model of section 3.5 [see eq. (3.92)], and the prefactor AjA ranged from 0.1 to 0.3, indicating nonadiabatic tunneling. Since this model is one-dimensional, it fails to explain the difference between splittings in the states with the [Pg.127]

In this appendix we shall show how the quasienergy ideas developed in section 5 can be applied to the problem of nonadiabatic tunneling. We use the Imf approach of section 3.3 for the multidimensional system with Hamiltonian... 

The method is composed of the following algorithms (1) transition position is detected along each classical trajectory, (2) direction of transition is determined there and the ID cut of the potential energy surfaces is made along that direction, (3) judgment is made whether the transition is LZ type or nonadiabatic tunneling type, and (4) the transition probability is calculated by the appropriate ZN formula. The transition position can be simply found by... 

Figure 7. Two-dimensional (2D) H2O system in the laser field, (a)excited and (b) ground adiabatic potentials. Filled circles nonadiabatic tunneling-type region. Open circles LZ-type region. Taken from Ref. [19].

Figure 45. Schematic picture representing the nonadiabatic tunneling-type transition.

Figure A.l. Schematic adiabatic potentials and various parameters used in the ZN formulas, (a) Landau-Zener type, (b) Nonadiabatic tunneling type. Taken from Ref. [9].

The formulas derived in the time-independent framework can be easily transferred into the corresponding time-dependent solutions. The formulas in the time-independent linear potential model, for example, provide the formulas in the time-dependent quadratic potential model in which the two time-dependent diabatic quadratic potentials are coupled by a constant diabatic coupling [1, 13, 147]. The classically forbidden transitions in the time-independent framework correspond to the diabatically avoided crossing case in the time-dependent framework. One more thing to note is that the nonadiabatic tunneling (NT) type of transition does not show up and only the LZ type appears in the time-dependent problems, since time is unidirectional. 

---