Two-body Kramers model

E. Two-Body Kramers Model Slowly Relaxing Local Structure... 

Two-Body Fokker-Planck-Kramers Model SRLS case... 

The next model considered in this work is Kramers description of a two-body system, that is, the generalization of model (a) in order to account for inertial effects. The time evolution operator is given by a... 

Fig. 4.4 VDOS calculated from a a two-body potential (VB) derived by Kramer et al. on a quantum-chemical calculation of an H4Si04 cluster [55], b a two-body potential (TS) derived by Tsuneyuki et al. using a Hartree-Fock calculation on SiOJ cluster [9], c a three-body (3B) potential by Sander, Leslie, and Catlow with a shell-model description and with three-body interactions [48] and d a two-body potential (KR) proposed by Kramer et al. using a mixed self-consistent field and empirical procedures [10], Note the KR potential here is the BKS potential. Figure taken from [56]...

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]. 

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