A Generic Formalism

We now describe a generic formalism for active control of a molecule coupled to the radiation field. That is, we examine how the control conditions for a variety of circumstances can be expressed in terms of the phase of the external field and the phase of the relevant dynamical variables. For simplicity, we consider a simple case, namely, when only two electronic states of the molecule play roles in the reaction dynamics we take these to be the ground electronic state and the first excited electronic state. The radiation that couples the two surfaces is the means of control. The internal state of the molecule is defined by the density operators pj, j e g, e, where g and e denote the ground and excited states, respectively. The combined density operator describing the state of the system can be represented as... 

Similarly, q0= 0.9 and qo/0A = 2.25 which is lower than Q =3.0%. Therefore, a generic design of 6 series of 2 determinations was applicable. The formal hand-over statistical data (based on 6 series of 2 determinations per site) are summarised in Table 3 ... 

The formal definitions of the nonlocal operators x ar d e can be expressed in the form of their application to a generic F(r) function ... 

In order to exploit the ideas introduced above, we begin by noting that within the confines of the inner product formalism, a generic evolution equation is written in the form... 

The problem now is to find a generic way to construct the N wave functions that are correct inside the interaction region. An immediate and obvious formal choice for v r/, inspired by, but slightly different from, the work of Kouri, Hoffman, and coworkers [2,11-14), is to write... 

GENERIC tries to formulate a general time evolution equation by which the time evolution (derivative) of a state variable (which can be, e.g., mass density or fraction, momentum, energy) is determined by two potentials the total energy of the system and a dissipation function. Just the latter one introduces the irreversibility (and, in this way, the thermodynamics ) into consideration and description of the system behavior. The dissipation function or potential is a function of derivatives (with respect to the state variables) of a quantity which should have the physical meaning of the entropy of the system and this latter function is minimum at zero state variables, is zero at zero entropy derivatives just mentioned and a concave function. The general evolution equation can be reformulated by means of Poisson brackets. To apply the GENERIC formalism first one has to select suitable state variables for the problem or system which is to be modeled. The next step is to formulate... 

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