Quasistationary states

Third, it is often useful to assume that the concentration of one or more of the intermediate species is not changing very rapidly with time (i.e., that one has a quasistationary state situation). This approximation is also known as the Bodenstein steady-state approximation for intermediates. It implies that the rates of production and consumption of intermediate species are nearly equal. This approximation is particularly good when the intermediates are highly reactive. 

Gurvitz SA, Kalbermann G (1987) Decay width and the shift of a quasistationary state. Phys Rev Lett 59 262... 

The quasistationary state (if the system has achieved this state) would have the form [X]st = k 3/k2 and [Y]st = k1[A]o/k2, where [A] = [A]0 in the course of the whole process. To describe the behavior of the system near the quasistationary state, the following variables are introduced ... 

Lichtner PC (1988) The quasistationary state approximation to coupled mass transport and fluid-rock interaction in porous media. Geochim Cosmochim Acta 52 143-65. 

A.M. DyKhne, A.V. Chaplik, Normalization of the wave functions of quasistationary states, JETP 13 (1961) 1002. 

Phase II The authors assume a quasistationary state in which the number of particles Nt containing i radicals does not change with time. The concentrations of these particles must obey the relations... 

E.E.Nikitin, Quasistationary states in a eonieal potential well, Doklady Akad.Nauk SSSR, 183,319(1968)... 

We have proved that in the no-energy-transfer regime, the fundamental mode evolves into a quasistationary state with the super-Poissonian (Ff >1) photocount statistics, whereas the Mh harmonic goes over into a sub-Poissonian (Fx < 1) quasistationary state. We have found that the most suppressed photocount noise is obtained for the third harmonic as described by the quantum Fano... 

The real parts of the eigenvalues, e,., give the energies of the quasista-tionary states, while the negative of the imaginary parts of the eigenvalues give one half the uncertainty widths, hV, of these quasistationary states or the lifetimes from r,. = r . 

The essential step in understanding collisionally induced intersystem crossing processes has been made by Gelbart and Freed. In small molecules, the optical excitation does not prepare pure spin states but the quasistationary states resulting from the intramolecular singlet-triplet coupling. In a simple two-level model... 

K i is thus proportional to i.e., to the /-state content in the initially prepared quasistationary state. This conclusion, which readily follows from... 

The word coherence has also been used in the description of radiationless processes (RP) in molecules in the gasphase. In the so-called molecular eigenstate basis set-description of RP, the initial state prepared after flash excitation can be written as a superposition of quasistationary states ... 

L.A. Khalfin, Contribution to the decay theory of a quasistationary state, Sov. Phys. JETP 6 (1958) 1053. 

S. Kais and D.R. Herschbach, J. Chem. Phys. (1993). Complex scaling, quasistationary states. 

Applications of 1/n expansions to calculations of energies and wave functions are considered, including quasistationary states. As illustrations we have examined the power-law, funnel, and Yukawa potentials. It has been shown that in many cases the method ensures high accuracy, even for small quantum numbers. The connection of these results with the properties of coherent states is briefly discussed. 

In a previous section [1] we considered a version of the 1/n-expansion which is applicable not only in the case of the discrete spectrum, but also for quasistationary states. Here we apply the same method to the energy spectrum of a hydrogen atom in electric and/or magnetic fields that are strong relative to the atomic field at the position of the electron orbit. Note that in the presence of an electric field, all atomic states are not stable, but quasistationary (with complex energy E = Er — r/2) so the appearance of complex equilibrium points is quite natural. 

Assigning in advance a dynamics of the chemical system composition to the pre-quasistationary state of its evolution can be done in two ways. First is the indirect or experimental way due to determination of the concentrations of reacting substances in time. The second is the direct or theoretical way via determination of the rate of an elementary reaction. Both methods assign in advance a phase trajectory a - a(t) and x = x(t) only at well-known starting concentrations of the reacting substances. 

At the quasistationary state of evolution the concentration of intermediate substances is completely determined by the concentration of the composing substances, x = x(a), and does not depend on time. The connection x = x(a) is the third level of correlation in the indignant chemical system. 

Fig. 5.8 Relaxation of distribution function P (t) from initial state to final state via quasistationary state.

---