Many-body collective effects

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

One of the necessary conditions for a many-body description is the validity of the decomposition of the system under consideration on separate subsystems. In the case of very large collective effects we cannot separate the individual parts of the system and only the total energy of the system can be defined. However, in atomic systems the inner-shell electrons are to a great extent localized. Therefore, even in metals with strong collective valence-electron interactions, atoms (or ions) can be identified as individuals and we can define many-body interactions. The important role in this separation plays the validity for atom- molecular systems the adiabatic or the Born-Oppenheimer approximations which allow to describe the potential energy of an N-atom systeni as a functional of the positions of atomic nuclei. 

Jump rate and diffusivity scale inversely with the square root of atomic mass. However, if migration involves many-body effects and collective motion, the assumptions leading to Eq. 8.31 are no longer valid and this model must be discarded. 

As in the case of the collective dipole moment, the many-body polarizability of the liquid can be broken up into two distinct contributions, one from single molecules and one from DID effects ... 

This means that potential models for water and solute-water interactions will be discussed. This choice, however, is much less restrictive than it might appear. In fact, due to its nature, water and aqueous solutions perfectly serve to illustrate far more general issues in the development of realistic potentials also beyond that sufficient to simple systems, e.g. the treatment of many-body effects and phase, or thermodynamic state, transferability. Moreover, water being water, the model proposed can be readily tested against a wealth of accurate experimental data, probably the largest collection for a single molecular liquid. 

This approach has been proven able to describe successfully the structural features of the hydration complex of several cations [129-132,215,216]. Table 5 collects some results relevant to the first and second hydration shell, for those metal ions where the latter can be clearly identified. It is also possible to note in Table 5 the effect of including many-body terms in the average way allowed by PCM-based potentials. 

Finally, we would like to point out that the kinematic effects of DCF inducing an asymmetry in mass balance in a many-body system should be of universal significance not only in molecular systems but also in a wide variety of many-body systems. This is because the DCF originates not from the interaction potential but from the intrinsic metric of internal space, which is uniquely determined from the shape and mass balance of a system. It is therefore anticipated that the DCF should be an important factor not only in molecular dynamics but in collective motions in nuclear, celestial, and biological many-body systems. 

Some most impressive computer simulations have been made in efforts to model the structure of liquid water. Yet, because these calculations usually are based on pair additivity of the potentials for the H-bonded water molecules, the possibility exists that subtle effects may escape the theoretician, as no means are provided to incorporate the possibility of extensive cooperativity—an aspect that Henry Frank (1972) has so eloquently stressed. Very likely, this is the crux of the problem of interfacially modified water if nothing else, the thermal anomalies (discussed below) in the properties of vicinal water strongly implicate cooperativity on a large scale—a collective behavior of water molecules that no existing potential function is able to reproduce. The cooperativity reflects nonpair additivity, and it does not seem plausible that effective potential energy functions can be devised that will remedy the specific lack of a detailed understanding of many-body interactions in water. Attempts to allow for cooperativity have been made by Finney, Barnes, and co-workers, notably Quinn and Nicholas (see Barnes et al., 1979). 

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]. 

Carsky. P., Hrouda, V., Sychrovsky, V., Hubac= I., Babinec, P.. Mach. P., Urban, J., Masik, J. Brillouin-Wigner Perturbation-Theory as a fxrssible more effective alternative to many-body Rayieigh-Schrodinger perturbation theory and coupled cluster theory Collection of Czechoslovak Chemical Communications 60,1419 (1995)... 

Whereas the full density-density correlation function contains many-body effects (as collective excitations (as poles)), xo does not contain these features. It is by construction an independent particle function. As such it is the response function to the total perturbing effective field,... 

COLLECTIVE EFFECTS IN ISOLATED ATOMS (MANY-BODY ASPECTS OF PHOTOIONIZATION PROCESS)... 

---