Many-body relaxation effect

A model having predictions that are consistent with the aforementioned experimental facts is the Coupling Model (CM) [21-26]. Complex many-body relaxation is necessitated by intermolecular interactions and constraints. The effects of the latter on structural relaxation are the main thrust of the model. The dispersion of structural relaxation times is a consequence of this cooperative dynamics, a conclusion that follows from the presence of fast and slow molecules (or chain segments) interchanging their roles at times on the order of the structural relaxation time Ta [27-29]. The dispersion of the structural relaxation can usually be described by the Kohlrausch-William-Watts (KWW) [30,31] stretched exponential function,... 

P were fixed, the dynamics are reduced entirely to a many-body relaxation problem. None of the theories mentioned in the NY Times article have considered many-body relaxation either at all or directly. Molecular dynamics simulations starting from some interaction potential as well as Monte Carlo simulations of toy models necessarily have captured the effects of many-body relaxation, but these are computer experiments and not theoretical solution of the problem. 

Absorption of the X-ray makes two particles in the solid the hole in the core level and the extra electron in the conduction band. After they are created, the hole and the electron can interact with each other, which is an exciton process. Many-body corrections to the one-electron picture, including relaxation of the valence electrons in response to the core-hole and excited-electron-core-hole interaction, alter the one-electron picture and play a role in some parts of the absorption spectrum. Mahan (179-181) has predicted enhanced absorption to occur over and above that of the one-electron theory near an edge on the basis of core-hole-electron interaction. Contributions of many-body effects are usually invoked in case unambiguous discrepancies between experiment and the one-electron model theory cannot be explained otherwise. Final-state effects may considerably alter the position and strength of features associated with the band structure. 

In early years of NMR, extensive studies of molecular dynamics were carried out using relaxation time measurements for spin 1/2 nuclei (mainly for 1H, 13C and 31P). However, difficulties associated with assignment of dipolar mechanisms and proper analysis of many-body dipole-dipole interactions for spin 1/2 nuclei have restricted their widespread application. Relaxation behaviour in the case of nuclei with spin greater than 1/2 on the other hand is mainly determined by the quadrupolar interaction and since the quadrupolar interaction is effectively a single nucleus property, few structural assumptions are required to analyse the relaxation behaviour. 

Clearly, a general theory able to naturally include other solvent modes in order to simulate a dissipative solute dynamics is still lacking. Our aim is not so ambitious, and we believe that an effective working theory, based on a self-consistent set of hypotheses of microscopic nature is still far off. Nevertheless, a mesoscopic approach in which one is not limited to the one-body model, can be very fruitful in providing a fairly accurate description of the experimental data, provided that a clever choice of the reduced set of coordinates is made, and careful analytical and computational treatments of the improved model are attained. In this paper, it is our purpose to consider a description of rotational relaxation in the formal context of a many-body Fokker-Planck-Kramers equation (MFPKE). We shall devote Section I to the analysis of the formal properties of multivariate FPK operators, with particular emphasis on systematic procedures to eliminate the non-essential parts of the collective modes in order to obtain manageable models. Detailed computation of correlation functions is reserved for Section II. A preliminary account of our approach has recently been presented in two Letters which address the specific questions of (1) the Hubbard-Einstein relation in a mesoscopic context [39] and (2) bifurcations in the rotational relaxation of viscous liquids [40]. 

This chapter describes theoretical and computational studies of surface structure, based on solving the electronic Schrodinger equation. This is done within the framework of density functional theory, in which the complicated many-body motion of all the electrons is replaced by an equivalent but simpler problem of each electron moving in an effective potential. The basis of density functional theory, the way that the Schrodinger equation is solved at surfaces, and how the equilibrium atomic structure is determined are presented. These are used to discuss the energetics, surface relaxation and surface reconstructions of metals, adsorbates on metals, and the surface reconstructions of semiconductors. 

We have presented a relativistically covariant many-body perturbation procedure, based upon the CEO and the GO. This represents a unification of the many-body perturbation theory and quantum electrodynamics. Applied to all orders, the procedure leads in the equal-time approximation to the BSE in the effective-potential form. By relaxing this restriction, the procedure is consistent with the full BSE. The new procedure will be of importance in cases where QED effects beyond first order in combination with high-order electron correlation are significant. 

Costa et al. present results of many-body perturbation theory, coupled cluster and quadratic Cl methods apphed to the calculation of the polarizability and first hyperpolarizability of NaH. It is shown that the nuclear relaxation contribution is substantial for this molecule and that it is appreciably affected by electron correlation effects. 

A direct comparison of the computed DOS curves with the UPS spectrum of a cluster has no theoretical justification since the former does not take into account orbital relaxation and many-body effects. However, this is not too serious a limitation given the relatively small relaxation and the qualitative nature of the comparison. With this in mind, the DOS curves and the UPS spectra of osmium carbonyl clusters have been compared. [261, 296] The positions of the computed ener levels correlate well with the structure of the UPS spectrum (Fig. 2-32). 

Comprehensive theoretical calculations of radiative transition rates as well as Auger and Coster-Kronig transition rates are available. However, uncertainties are large for Coster-Kronig transitions with small excess energy due to the strong influence of several effects (i) many-body interactions in the initial and final atomic systems, (ii) relaxation in the final ionic state, and (iii) exchange interaction between the continuum electron and the final bound-state electrons. For an experimental determination of decay rates, various techniques have been employed, e.g., the use of radioactive sources or coincidence techniques. Most techniques... 

The nucleus in a Mossbauer experiment is part of a many-body system consisting of the surrounding electrons and the quasiparticles corresponding to the various other degrees of freedom of the solid. Relaxation effects result from the various time-dependent processes in the vicinity of the nucleus. The nucleus thus acts as a local microscopic probe, which does not participate directly in the relaxation processes in its environment, but which senses these processes via the hyperfine interactions. Now, in interpreting the relaxation behaviour it is necessary to consider the nature and interrelationship of the important timescales of the problem. Some of these timescales are determined by the nature of the Mossbauer isotope and the interaction being studied, i.e., the mean lifetime of the Mossbauer excited state and the Larmor precession time t,. The other timescales relate to, and are characterised by, the nature of the fluctuations in the nuclear environment. These latter timescales are the inverse of the various relaxation rates and, as mentioned earlier, these can be controlled in the laboratory in various ways. The character of the relaxation spectra obtained obviously depends crucially on the interplay of the various timescales as discussed below. 

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