Quantum statistical theory

For liquid metals, one has to set up density functionals for the electrons and for the particles making up the positive background (ion cores). Since the electrons are to be treated quantum mechanically, their density functional will not be the same as that used for the ions. The simplest quantum statistical theories of electrons, such as the Thomas-Fermi and Thomas-Fermi-Dirac theories, write the electronic energy as the integral of an energy density e(n), a function of the local density n. Then, the actual density is found by minimizing e(n) + vn, where v is the potential energy. Such... 

As shown above, classical unimolecular reaction rate theory is based upon our knowledge of the qualitative nature of the classical dynamics. For example, it is essential to examine the rate of energy transport between different DOFs compared with the rate of crossing the intermolecular separatrix. This is also the case if one attempts to develop a quantum statistical theory of unimolecular reaction rate to replace exact quantum dynamics calculations that are usually too demanding, such as the quantum wave packet dynamics approach, the flux-flux autocorrelation formalism, and others. As such, understanding quantum dynamics in classically chaotic systems in general and quantization effects on chaotic transport in particular is extremely important. 

The work of other authors cannot be clearly classified as belonging to one of these three main families. A quantum-statistical theory of longitudinal magnetic relaxation based on a continued fraction expansion has been given by Sauermann, who also pointed out the equivalence between his continued fraction approach (based on the Mori scdar product) and the [AA AT] Pad6 approximants. 

B. Consequences of the Finite Size II. A Quantum Statistical Theory... 

Agarwal G. S., Quantum Statistical Theories of Spontaneous Emission, (Springer, Berlin, 1974). Aharonov Y. and Bohm D., Phys. Rev. 115, 485 (1959). 

The introduction of statistical features in the basic molecular models is considered in Section II,E,2. It is argued that, in most cases, at least one part of the nonradiant molecular manifold is unknown and should be treated under statistical assumptions. By means of a partially random representation of the zero-order Hamiltonian, of the kind introduced by Wigner and others in statistical nuclear theory (see Bloch, 1966, 1969), we define a general dynamical model in which both the quantal and statistical properties of the molecular excitations are combined. Special attention is given to the nature of the statistical limit and irreversible radiationless transitions for the molecular excited states. We also discuss the relationship between this concept and similar concepts in quantum statistical theory of relaxation and master equations (Zwanzig, 1961). 

Agarwal,G.S. Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches (Vol. 70)... 

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