Nonstationary states

Experience profound compositional shifts in use May experience phases changes in use Site in the disease s location Operate at variable drug activity Highly nonstationary state kinetics Application technique and amount are highly individualized Applications short-acting Local tissue levels tied to efficacy Used on diseased, damaged skin No easy bioequivalency endpoint Systemic absorption absolutely undesirable, but some unavoidable... 

The above theory is usually called the generalized linear response theory because the linear optical absorption initiates from the nonstationary states prepared by the pumping process [85-87]. This method is valid when pumping pulse and probing pulse do not overlap. When they overlap, third-order or X 3 (co) should be used. In other words, Eq. (6.4) should be solved perturbatively to the third-order approximation. From Eqs. (6.19)-(6.22) we can see that in the time-resolved spectra described by x"( ), the dynamics information of the system is contained in p(Af), which can be obtained by solving the reduced Liouville equations. Application of Eq. (6.19) to stimulated emission monitoring vibrational relaxation is given in Appendix III. 

Interaction with light changes the quantum state a molecule is in, and in photochemistry this is an electronic excitation. As a result, the system will no longer be in an eigenstate of the Hamiltonian and this nonstationary state evolves, governed by the time-dependent Schrodinger equation... 

Pollard, W. T., and Mathies, R. A. (1992), Analysis of Femtosecond Dynamic Absorption Spectra of Nonstationary States, Ann. Rev. Phys. Chem. 43,497. 

In this book we shall write the Hamiltonian as an (algebraic) operator using the appropriate Lie algebra. We intend to illustrate by many applications what we mean by this cryptic statement. It is important to emphasize that one way to represent such a Hamiltonian is as a matrix. In this connection we draw attention to one important area of spectroscopy, that of electronically excited states of larger molecules,4 which is traditionally discussed in terms of matrix Hamiltonians, the simplest of which is the so-called picket fence model (Bixon and Jortner, 1968). A central issue in this area of spectroscopy is the time evolution of an initially prepared nonstationary state. We defer a detailed discussion of such topics to a subsequent volume, which deals with the algebraic approach to dynamics. 

The nonequilibrium aging state (NBAS, see Section III.A) is a nonstationary state characterized by slow relaxation and a very low rate of energy dissipation to the surroundings. Aging systems fail to reach equilibrium unless one waits an exceedingly large amount of time. For this reason, the NEAS is very different from either the nonequilibrium transient state (NETS) or the nonequilibrium steady state (NESS). 

It is impossible to read much of the literature on viscosity without coming across some reference to the equation of motion. In the area of fluid mechanics, this equation occupies a place like that of the Schrodinger equation in quantum mechanics. Like its counterpart, the equation of motion is a complicated partial differential equation, the analysis of which is a matter for fluid dynamicists. Our purpose in this section is not to solve the equation of motion for any problem, but merely to introduce the physics of the relationship. Actually, both the concentric-cylinder and the capillary viscometers that we have already discussed are analyzed by the equation of motion, so we have already worked with this result without explicitly recognizing it. The equation of motion does in a general way what we did in a concrete way in the discussions above, namely, describe the velocity of a fluid element within a flowing fluid as a function of location in the fluid. The equation of motion allows this to be considered as a function of both location and time and is thus useful in nonstationary-state problems as well. 

The decay constant of the transient species can be measured directly by using nonstationary state methods. In these methods the system is irradiated intermittently so that transients are created in the light period and decay in the dark period. The simplest form of the arrangement is the use of sector wheel in which a number of sectors are cut (Figure 10.9). The cut and uncut portions can be of equal size or may vary in a definite... 

It is very important, in the theory of quantum relaxation processes, to understand how an atomic or molecular excited state is prepared, and to know under what circumstances it is meaningful to consider the time development of such a compound state. It is obvious, but nevertheless important to say, that an atomic or molecular system in a stationary state cannot be induced to make transitions to other states by small terms in the molecular Hamiltonian. A stationary state will undergo transition to other stationary states only by coupling with the radiation field, so that all time-dependent transitions between stationary states are radiative in nature. However, if the system is prepared in a nonstationary state of the total Hamiltonian, nonradiative transitions will occur. Thus, for example, in the theory of molecular predissociation4 it is not justified to prepare the physical system in a pure Born-Oppenheimer bound state and to force transitions to the manifold of continuum dissociative states. If, on the other hand, the excitation process produces the system in a mixed state consisting of a superposition of eigenstates of the total Hamiltonian, a relaxation process will take place. Provided that the absorption line shape is Lorentzian, the relaxation process will follow an exponential decay. 

The simplest example of a compound state is encountered when we imagine that at time t = 0 it is somehow possible to prepare the system in the nonstationary state... 

This nonstationary state may be represented as a superposition of the eigenfunctions of the total Hamiltonian, i.e.,... 

Finally, it should be pointed out that Tjh represents the half width of the energy distribution. From eq. (2-7) we see that V is also the reciprocal of the lifetime of the initial nonstationary state. Of course, the width and the lifetime of the metastable level are related by the uncertainty principle. 

In what follows we shall consider an excitation process which is short lived on the time scale of the resulting excited state. This excitation process may involve an electron-molecule collision or absorption of a light pulse. We start with the system in the ground state (f>0. The excitation process introduces a time-dependent perturbation Tx(t) for a duration of time r. An excited nonstationary state is thereby produced which can be represented as a superposition of molecular eigenstates (see eq. 6-2)... 

We shall later assume, in Section XI-B, that the zero-order states are BO states, that the ground state is adequately represented as a BO state, and that the ground state is connected, via a dipole transition matrix element, only to the state or fB. Absorption of a photon by a molecule will then lead to the creation of the nonstationary state [Pg.257]

To obtain the probability of finding the molecule in the nonstationary state corresponding to one of the zero-order components we need merely determine the squares of the absolute magnitudes of the corresponding expansion coefficients, e.g.,... 

We next examine the amplitudes of the states excited state of the system. These are obtained from the projections (overlaps) <9>a f(0) and <9>n T(0>. Clearly, the probability of finding a molecule in the nonstationary state [Pg.261]

Similarly, the probability of finding the molecule in the nonstationary state [Pg.262]

One of the interesting consequences of eqs. (11-25) and (11-26) is the dependence of the probability of the molecule being in a given nonstationary state on the time correlations in the coupled radiation field. In most experimental studies the radiation field employed consists of a superposition of many frequencies with random phases. It is convenient to represent that form of field in terms of a correlation function d>(t, t"), which is defined in eq. (6-16). Introducing, because of the polychromaticity of the radiation field, the averages of eqs. (11-25) and (11-26), choosing the same representation for the field correlation function as did Bixon and Jortner, and using the conservation of probability, we find for the probability of dissociation of the molecule the relation ... 

Using first-order, time-dependent perturbation theory it can be shown15 that one can rigorously speak of the excited system, eqs. (12-1)— (12-7), as being in the initial nonstationary state, 5>. With this preparation of our molecule assured, then, we shall, for the time being, neglect the... 

A different type of nonstationary state experiment that has been reported by Bonzel and co-workers (193, 194) is illustrated in Fig. 44. A Pt(110) surface was initially exposed to a mixture of CO and 02. At the substrate temperature and pc0 and p0l, 0CO > 0 o and the sticking coefficient for Oz is drastically reduced. If pco is suddenly reduced, it is seen that after an induction period which is strongly temperature dependent the rate of C02 production passes through a maximum before decreasing sharply. A similar experiment in which the surface was initially covered with oxygen after pco was... 

T. Mercouris, C.A. Nicolaides, Time dependence and properties of nonstationary states in the continuous spectrum of atoms, J. Phys. B 30 (1997) 811. 

An advantage of the local control method described above is that it can be applied to wave packet propagation starting from an initial, nonstationary state, in contrast to ordinary wave packet control, which begins with the initial condition of a stationary state. An example where starting from such an initial condition is useful is the control of a localized state of a double-well potential. In this case, by propagating the final-state wave packet backward to the initial state, pulses that are optimized for forward... 

Femtosecond time-resolved methods involve a pump-probe configuration in which an ultrafast pump pulse initiates a reaction or, more generally, creates a nonstationary state or wave packet, the evolution of which is monitored as a function of time by means of a suitable probe pulse. Time-resolved or wave... 

In Section 2.2 we mentioned the impossibility to strictly substantiate the equilibrium descriptions for all cases of life and the need to apply equilibrium approximations in some situations. The vivid examples of the cases, where the strongly nonequilibrium distributions of microscopic variables are established in the studied system and the principal difficulties of its description with the help of intensive macroscopic parameters occur, are fast changes in the states at explosions, hydraulic shocks, short circuits in electric circuits, maintenance of different potentials (chemical, electric, gravity, temperature pressure, etc.) in some spatial regions or components of physicochemical composition interaction with nonequilibrium and sharply nonstationary state environment. 

These complications notwithstanding, molecular geometries can be derived solely from wavefunctions of spectroscopic states (or even nonstationary states with zero linear momentum) under favorable conditions. This can be accomplished in principle [21] by constructing the functions... 

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