Resonance field-induced

The first volume contained nine state-of-the-art chapters on fundamental aspects, on formalism, and on a variety of applications. The various discussions employ both stationary and time-dependent frameworks, with Hermitian and non-Hermitian Hamiltonian constructions. A variety of formal and computational results address themes from quantum and statistical mechanics to the detailed analysis of time evolution of material or photon wave packets, from the difficult problem of combining advanced many-electron methods with properties of field-free and field-induced resonances to the dynamics of molecular processes and coherence effects in strong electromagnetic fields and strong laser pulses, from portrayals of novel phase space approaches of quantum reactive scattering to aspects of recent developments related to quantum information processing. 

The models for the control processes start with the Schrodinger equation for the molecule in interaction with a laser field that is treated either as a classical or as a quantized electromagnetic field. In Section II we describe the Floquet formalism, and we show how it can be used to establish the relation between the semiclassical model and a quantized representation that allows us to describe explicitly the exchange of photons. The molecule in interaction with the photon field is described by a time-independent Floquet Hamiltonian, which is essentially equivalent to the time-dependent semiclassical Hamiltonian. The analysis of the effect of the coupling with the field can thus be done by methods of stationary perturbation theory, instead of the time-dependent one used in the semiclassical description. In Section III we describe an approach to perturbation theory that is based on applying unitary transformations that simplify the problem. The method is an iterative construction of unitary transformations that reduce the size of the coupling terms. This procedure allows us to detect in a simple way dynamical or field induced resonances—that is, resonances that... 

This leads to distinguish two types of resonances the resonances induced by the field that occur beyond a threshold of the field, and resonances that occur for an arbitrary small value of the field. These are called, respectively, (i) the dynamical resonances (or equivalently field induced resonances or nonlinear resonances) and (ii) the zero-field resonances. 

The conceptual framework of the treatment of the field-induced resonances of work discussed in this article follows from the one that has proven useful for the solution of the MEP for field-free resonances. Therefore, the... 

The various analyses, examples and applications of the SSA which are presented in the sections that follow, show how reliable wavefunctions of unstable states can be obtained. These have a form which is transparent and usable regardless of whether they describe field-free or field-induced excited state systems of, say, 2, 15, or 30 electrons and of whether there is one or many open channels. In this way, additional properties and good understanding of the interplay between structure and dynamics can be (and indeed have been) obtained. The discussion, in conjunction with the corresponding references, explains how the SSA has formed the framework for the formal and computational treatment—nonperturbatively—of a variety of prototypical problems irwohring field-free as well as field-induced resonance states in atoms and in small molecules. 

The solution, namely the complex eigenvalue of the field-induced resonance state, is a function of the frequency and strength of the field. For normal cases where there are no serious field-induced near-degenaracies, it is connected smoothly to the unperturbed energy Eq ... 

The contribution of fhe open channels is fhen faken info account by appropriate methods that employ different function spaces, symbolized here by X s (as = asymptotic) (Eq. (1)). These methods are based either on K - matrix theory and numerically computed scattering orbitals for atoms and diatomics (real energy-dependent) (see [17, 29, 79-87]), or via diagonalization of fhe non-Hermifian mafrices of fhe CESE-SSA for field-free or field-induced resonances. 

The vibrational progressions can be adequately simulated through the calculation of Franck-Condon factors however the observed spin-orbit branching ratio, along with the intensity distribution, reflects a considerable contribution from both spin-orbit and field-induced resonant autoionization processes. Also, accidental resonances at the two-photon level with ion-pair states further perturb the distribution of peak intensities. 

Fig. 9.5 Illustration of the dipolar interaction. (A and B) The magnetic field induced by spin I adds up to the static magnetic field Bo and leads to a shift of the resonance frequency of the close-by spin S. Since spins parallel and...

The Mbssbauer effect involves resonant absorption of y-radiation by nuclei in solid iron oxides. Transitions between the I = Y2 the I = 72 nuclear energy levels induce resonant absorption (Fig. 7.4). A Mbssbauer spectrum is a plot of the transmission of the rays versus the velocity of their source movement of the source ( Co for iron compounds) ensures that the nuclear environments of the absorber and the source will match at certain velocities (i.e. energies) and hence absorption takes place. In the absence of a magnetite field the Mbssbauer spectrum consists of one (if the absorbing atoms are at a site of cubic symmetry) or two (symmetry distorted from cubic) absorption maxima. When a static magnetic field acts on the resonant nuclei, this splits the nuclear spin of the ground state into two and those of the ex-... 

The nonresonant contributions pertain to electron cloud oscillations that oscillate at the anti-Stokes frequency but do not couple to the nuclear eigenfrequencies. These oscillatory motions follow the driving fields without retardation at all frequencies. The material response can, therefore, be described by a susceptibility that is purely real and does not depend on the frequencies of the driving fields. The resonant contributions, on the other hand, are induced by electron cloud oscillations that are enhanced by the presence of Raman active nuclear modes. The presence of nuclear oscillatory motion introduces retardation effects relative to the driving fields i.e., there is phase shift between the driving fields and the material oscillatory response. 

This general and important relationship, irrespective of the value of /, is called Larmor s equation. It relates the intensity of the magnetic field in which the nuclei are located to the electromagnetic radiation frequency that induces resonance hence, a signal in the spectrum (see Table 9.1 and Fig. 9.1). 

Kitzerow et al. recently demonstrated that temperature-induced phase transitions (Iso-N) and electric field-induced reorientation of a nematic liquid crystal (5CB in this case) can be used to tune photonic modes of a microdisc resonator, in which embedded InAs quantum dots serve as emitters feeding the optical modes of the GaAs-based photonic cavity [332],... 

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