Sudden perturbations, theory

Here AEdiscr and A on are, respectively, the average energies of all the transitions into the discrete and continuous spectra E is the energy of the transition into the continuous spectrum and is the first ionization potential. The sudden-perturbation theory Eqs. (68) and (69) especially convenient for calculating A and A , since they involve only the ground-state wave function, allowing one to avoid the calculation of the spectrum of exited states. 

The perturbation theory presented in Chapter 2 implies that orientational relaxation is slower than rotational relaxation and considers the angular displacement during a free rotation to be a small parameter. Considering J(t) as a random time-dependent perturbation, it describes the orientational relaxation as a molecular response to it. Frequent and small chaotic turns constitute the rotational diffusion which is shown to be an equivalent representation of the process. The turns may proceed via free paths or via sudden jumps from one orientation to another. The phenomenological picture of rotational diffusion is compatible with both... 

The onset of sudden variations in vibrational fine structure is one of the most sensitive indicators of a change in resonance structure. The magnitudes of fine-structure parameters are determined by second-order perturbation theory (a Van Vleck or contact transformation) [17]. The energy denominators in these second-order sums over states are approximately independent of vib as long as the <01 <02 - 3/v-6 resonance structure is conserved. 

Note that in a sudden transition, eq. 3 is a more general relation than the Golden role (see, e.g., reference 15). In that circumstance the Golden rule appears as a special case of the FC factor, corresponding to small V and the applicability of perturbation theory. In order to evaluate the FC factor, Berry used the dressed oscillator model which, in principle, coincides with the previously described quasi-diatomic method. 

Near the TS things change. The rapid evolution of the light components of the system (electrons and H atoms involved in a transfer process) makes the adiabatic approximation questionable. Also the sudden time dependent perturbation we introduced in Section 1.1.3 to describe solvent effects on electronic transitions is not suitable. We are considering here an intermediate case for which the time dependent perturbation theory does not provide simple formulae to support our intuitive considerations. Other descriptions have to be defined. 

As will be shown below, jthe average chemical shift is always positive. It is convenient to calculate A using Migdal s (1941) theory of sudden perturbations. According to this theory, the electron wave function does not manage to change within the /1-decay time, and so the average chemical shift... 

The time-dependent perturbation theory developed in Section 1.4 is useful for small perturbations, and is widely applied in spectroscopy. The contrasting situation in which the perturbation is not small compared to the energy separations between unperturbed levels is often more difficult to treat. A simplification occurs when the Hamiltonian changes suddenly at t = 0 from J ,... 

There also exist a wide variety of approximate quantum mechanical and semiclassical theories [72]. In various limits some of the degrees of freedom can be treated as slow or fast compared to others, leading to sudden or adiabatic approximations, and in some cases the coupling between translational and internal motion can make perturbation theory a useful approximation. 

Adiabatic energy transfer occurs when relative collision velocities are small. In this case the relative motion may be considered a perturbation on adiabatic states defined at each intermolecular position. Perturbed rotational states have been introduced for T-R transfer at low collision energies and for systems of interest in astrophysics.A rotational-orbital adiabatic basis expansion has also been employed in T-R transfer,as a way of decreasing the size of the bases required in close-coupling calculations. In T-V transfer, adiabatic-diabatic transformations, similar to the one in electronic structure studies, have been implemented for collinear models.Two contributions on T-(R,V) transfer have developed an adiabatical semiclassical perturbation theory and an adiabatic exponential distorted-wave approximation. Finally, an adiabati-cally corrected sudden approximation has been applied to RA-T-Rg transfer in diatom-diatom collisions. 

In summary, the model allows for two types of interactions between the mirror spaces, the weak kinematical perturbation and the adiabatic and sudden limits equivalent to Eq. (17) or Eqs. (29)-(34). The overwhelming rate of particles over antiparticles in the Universe is inferred in this picture once the particular particle state has been selected. The Minkowski metric of the special theory of relativity is represented here by a non-positive definite metric, Eq. (8), bringing about a quantum model with a complex symmetric ansatz. Although the latter permits general symmetry violations, it is nevertheless surprising that fundamental transformations between complex symmetric representations and canonical forms come out unitary. 

Virtually all non-trivial collision theories are based on the impact-parameter method and on the independent-electron model, where one active electron moves under the influence of the combined field of the nuclei and the remaining electrons frozen in their initial state. Most theories additionally rely on much more serious assumptions as, e.g., adiabatic or sudden electronic transitions, perturbative or even classical projectile/electron interactions. All these assumptions are circumvented in this work by solving the time-dependent Schrodinger equation numerically exact using the atomic-orbital coupled-channel (AO) method. This non-perturbative method provides full information of the basic single-electron mechanisms such as target excitation and ionization, electron capture and projectile excitation and ionization. Since the complex populations amplitudes are available for all important states as a function of time at any given impact parameter, practically all experimentally observable quantities may be computed. 

Water is the main natural explosive agent on the Earth. This fact is well demonstrated by all forms of volcanic and hydrothermal explosive manifestations, characterized by a sudden and brutal vaporization of water and other dissolved volatiles from a condensed state, either from aqueous solutions or from supersaturated magmas. This paper is mainly devoted to the first case, i.e. the explosivity of aqueous solutions. Explosions can be defined as violent reactions of systems, which have been perturbed up to transient and unstable states by physico-chemical processes. As such, the traditional approach to such problems is to rely on kinetic theories of bubble nucleations and growths, and this topic has been already the subject of an abundant literature (see references therein ). We apply here an alternative and complementary method by... 

A further method relies on the fact that the natural drop time of a dropping mercury electrode is proportional to the interfacial tension [18]. Again, drop birth can be detected electrically by the sudden change in impedance, so the method is easily automated. Unlike the other methods there is no adequate theory describing the mechanism of drop detachment, so the proportionality constant is again obtained by calibration with a solution of known properties. The method is extremely sensitive to vibrations and impurities, and consequently it is difficult to obtain results better than 1%. Also as a dropping mercury electrode is used, the system is dynamic and may not be in equilibrium if the rate of adsorption is slow. Similarly, capacitance measurements will be frequency dependent if adsorption is slow compared with the period of a.c. perturbation, and this provides a useful check of whether equilibrium is obtained. 

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