Many-body phenomena

J. P. Perdew and M. Levy, in Many-Body Phenomena at Surfaces (eds D. Langreth and H. Suhl), Academic Press, Orlando, 1984, p. 71. 

Adopting the three choices for the extended states y ) from the beginning of this Chapter, we get three different types of two-particle self energies. Before we will concentrate on discussing in how far these self energies are useful for an effective two-particle description of diverse many-body phenomena in the remaining Chapters of this paper, we will briefly touch an alternative formal approach. 

Y. Ohm, Int J. Quantum Chem., Quantum Chem. Symp., 1985, 39-50, from conference Proceedings of the International Symposium on Atomic, Molecular and Sohd-State Theory, Scattering Problems, Many Body Phenomena, and Computational Quantum Chemistry, 18-23 March 1985. 

This lecture is intended to demonstrate qualitative aspects of various many-body phenomena like deposition, fracturing, aggregation, crystallization, melting and vortices using model systems of uniform microparticles dispersed in water or ferrofluid. The particles are confined to monolayers between glass plates allowing direct microscopic observations of local structure and movement of individual particles. 

Kondo (1964, 1969) showed that the behavior of a single magnetic impinity in a nonmagnetic metallic host at low temperatures cannot be understood in terms of the electronic states of the impurity ion alone, but must be treated as a many body phenomenon. Around the inqiurity a screening cloud of spin-polarized ce develops when... 

Superconductivity was discovered in 1911 by Kamerling Onnes [102] and remains one of the most actively studied aspects of the behavior of solids. It is a truly remarkable phenomenon of purely quantum mechanical nature it is also an essentially many-body phenomenon which cannot be described within the single-particle picture. Because of its fascinating nature and of its many applications, superconductivity has been the focus of intense theoretical and experimental investigations ever since its discovery. Studies of superconductivity have gained new vigor since the discovery of high-temperature superconductors in 1987. 

Constraint release (CR). This takes place if a confining chain moves out of the way of a given chain and thus opens some freedom for lateral motion. This phenomenon is an intrinsic many-body effect and for monodisperse polymer melts becomes significant mainly in the creep regime. 

In Chap. 2, Sect. 6.6 and Chap. 6, Sect. 2.3, the phenomenon of hydro-dynamic repulsion was referred to, but not discussed in any detail. While this effect is strictly a many-body effect, it can be approximated very well by a simple model. The motion of one solute, A, necessarily requires that the surrounding solvent moves aside to let the A molecule pass. The motion of the solvent near A in turn requires more distant solvent molecules to move. This action is transmitted by collision, but effectively the solute A entrains solvent molecules to move in the same direction as it is doing itself. The degree of the entrainment of solvent decreases as the... 

Later studies showed the same phenomena in deuterium and deuterium-rare gas mixtures [335, 338, 305], and also in nitrogen and nitrogen-helium mixtures [336] in nitrogen-argon mixtures the feature is, however, not well developed. The intercollisional dip (as the feature is now commonly called) in the rototranslational spectra was identified many years later see Fig. 3.5 and related discussions. The phenomenon was explained by van Kranendonk [404] as a many-body process, in terms of the correlations of induced dipoles in consecutive collisions. In other words, at low densities, the dipole autocorrelation function has a significant negative tail of a characteristic decay time equal to the mean time between collisions see the theoretical developments in Chapter 5 for details. 

The phenomenon of phase behavior is the organization of many-body systems into forms which reflect the interplay between constraints imposed macro-scopically (through the prevailing external conditions) and microscopically (through the interactions between the elementary constituents). In this article we focus on generic computational strategies needed to address the problems of phase behavior, or more specifically the task of mapping equilibrium phase boundaries. 

To describe quantitatively the disorder present in a material, it is often convenient to introduce a structural order parameter. This term refers to a metric that can detect the development of order in a many-body system, perhaps by employing the tools of pattern recognition (Brostow et al., 1998). In many cases, such a measure is constructed to serve as a reaction coordinate for a thermodynamic phase transition (van Duijneveldt and Frenkel, 1992). However, since the form of the order parameter clearly depends on the phenomenon of interest, the development of such measures can be a difficult and subtle matter. 

Since many-body optical transitions in zero-dimensional objects was demonstrated experimentally, it is important to assess this phenomenon from the perspective of the well established field of many-body luminescence. This is accomplished in the present chapter. Below we review the many-body luminescence in various systems studied to date experimentally and theoretically. We then demonstrate that many-body luminescence from highly excited zero-dimensional objects has unique features due to large number of discrete lines. This discreteness unravels the many-body correlations that are otherwise masked in the continuous spectrum of luminescence from infinite systems. We describe in detail the emergence of such correlations for a particular nanostructure geometry - semiconductor nanorings - using the Luttinger liquid approach for quasi-one-dimensional finite-size systems. 

The phenomenon of core penetration is evidently a many-body effect, and its treatment is far beyond the scope of the present work. Thus we only note that since core penetration effects reflect the probability of finding the valence electron at the ionic core, the center of the atom, they scale as n reflecting the normalization of the wave function of the valence electron at the core. 

The electrical excitability phenomenon, inherent to neural tissues, provides an opportunity to effect external control over many body systems paralyzed limbs can be made to move, the blind can experience visual sensations, the deaf people can experience the voice of others close by or by phone, pain can be alleviated, tremors suppressed, and mental disorders treated. Devices, often referred to as neuroprostheses, that perform these functions can be sold. Companies that make devices that provide the most function with the smallest, safest devices that also have long battery lifetimes usually have the market advantage. Function is directly related to electrode placement improperly placed electrodes don t work or have undesirable side effects. The remedy has been reimplantation, but tunable electrodes, structures with multiple small contacts, are making it possible to avoid additional surgery by providing pathways to manipulate the shape of the excitatory fields. 

Although continuum models have been quite sueeessful in assessing macroscopic optical response, they have intrinsie limitations for probing microscopie optical properties, such as molecular polarizability and photoconductivity. The limitations stem from the faet that eontinuum eleetrodynamies, as applied to metal nanostructures, are intended to deseribe the eolleetive motions of the electrons and are thus not applieable to any physieal phenomenon that occurs at small length scales (typieally a few nanometers for typieal eondensed-phase systems). For small length seales, many-body theories need to be applied to account for the quantum eharaeteristies of individual eleetronie transitions, for example, light absorption by an organie sensitizer and subsequent electron injection to semiconductor layer. 

Recalling the quantum mechanical interpretation of the wave function as a probability amplitude, we see that a product form of the many-body wave function corresponds to treating the probability amplitude of the many-electron system as a product of the probability amplitudes (orbitals) of individual electrons. Mathematically, the probability of a composed event is the product of the probabilities of the individual events, provided the individual events are independent of each other. If the probability of a composed event is not equal to the probability of the individual events, these individual events are said to be correlated. Correlation is thus a general mathematical concept describing the fact that certain events are not independent. It can also be defined in classical physics, and in applications of statistics to problems outside science. Exchange, on the other hand, is due to the indistinguishability of particles, and is a tme quantum phenomenon, without any analogue in classical physics. 

There are many other examples of changes in which a solid passes into a liquid, or a liquid into a gas, with absorption of heat at constant temperature. The constant temperature may be called the transition temperature the heat absorbed is called the latent heat of the transition. The latter name is due to Joseph Black, the discoverer of the phenomenon (1757) he appears to have regarded the heat as existing latent in the body in some sort of chemical combination, just as fixed air exists latent in chalk. In both cases the entity has lost its properties by chemical combination, but may be set free again in a suitable way. 

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