Quantum dispersion

The quantum generalization of the APR Hamiltonian results after supplementing this classical Hamiltonian with a non-commuting angular momentum part [Lj, p] = -ihSji which introduces quantum dispersion and thus qualitatively new effects due to additional fluctuations and tunnehng. 

In addition to the static induction effects included in I/scf, the hot Drude oscillators give rise to a 1/r6, temperature-dependent, attractive term. This jkg Ta2/r6 term is the classical thermodynamic equivalent of the London quantum dispersive attraction IEa2/r6. It corresponds to a small perturbation to the London forces, because k T is at least two orders of magnitude smaller than the typical ionization energy IE. The smaller the temperature of the Drude motion, the closer the effective potential is to the SCF potential, making Eq. (9-57) independent of mo, the mass of the oscillators. 

Dispersional Interaction between Molecules. We still wish to consider briefly energies due to interaction between fluctuating induced electric charge distributions of atoms and molecules. In constrast to electrostatic and induced interactions, these are present even when the molecules do not possess permanent electric moments. These dispersional interactions cannot be dealt with on a classical electrostatics level owing to their relation to London s quantum dispersion theory, they have been termed London dispersional interactions. 

The inconsistency is eliminated by the introduction of the hypothesis of existence of broad quantum dispersions discussed earlier. This hypothesis allows the unification of mechanics and thermodynamics. The unified theory was formally presented in a series of papers (7) in the "Foundations of Physics," and is briefly summarized below. 

Regarding the squared average in quantum dispersion one also successively obtains ... 

The integration of Equations 9.49 and 9.51 is carried out using the second-order Heun s algorithm, with a very small time step of 0.001. These equations differ from the corresponding classical equations in two ways First, the noise correlation of c-number spin-bath variables r t) are quantum mechanical in nature, as evident from the correlation function in Equation 9.42, which is numerically fitted by the superposition of exponential functions with D, and X . Second, the knowledge of Q requires the quantum correction equations that yield quantum dispersion around the quantum mechanical mean values q and p for the system. Statistical averaging over noise is... 

Using the checkerboard decomposition, the stability of the distorted Peierls phase has been examined. It was found that for spin-1 electrons, the distorted phase is always robust, even in the presence of nuclear tunneling of the C atoms, which tends to increase the quantum dispersion and destablize the distorted phase. 

The continuum treatment of dispersion forces due to Lifshitz [19,20] provides the appropriate analysis of retardation through quantum field theory. More recent analyses are more tractable and are described in some detail in several references [1,3,12,21,22],... 

If the long-range mteraction between a pair of molecules is treated by quantum mechanical perturbation theory, then the electrostatic interactions considered in section Al.5.2.3 arise in first order, whereas induction and dispersion effects appear in second order. The multipole expansion of the induction energy in its fill generality [7, 28] is quite complex. Here we consider only explicit expressions for individual temis in the... 

Meath W J and Kumar A 1990 Reliable isotropic and anisotropic dipole dispersion energies, evaluated using constrained dipole oscillator strength techniques, with application to interactions involving H2, N2 and the rare gases Int. J. Quantum Chem. Symp. 24 501... 

Valdmanis J A and Fork R L 1986 Design considerations for a femtosecond pulse laser balancing self phase modulation, group velocity dispersion, saturable absorption, and saturable gain IEEE J. Quantum. Electron. 22 112-18... 

Clusters are intennediates bridging the properties of the atoms and the bulk. They can be viewed as novel molecules, but different from ordinary molecules, in that they can have various compositions and multiple shapes. Bare clusters are usually quite reactive and unstable against aggregation and have to be studied in vacuum or inert matrices. Interest in clusters comes from a wide range of fields. Clusters are used as models to investigate surface and bulk properties [2]. Since most catalysts are dispersed metal particles [3], isolated clusters provide ideal systems to understand catalytic mechanisms. The versatility of their shapes and compositions make clusters novel molecular systems to extend our concept of chemical bonding, stmcture and dynamics. Stable clusters or passivated clusters can be used as building blocks for new materials or new electronic devices [4] and this aspect has now led to a whole new direction of research into nanoparticles and quantum dots (see chapter C2.17). As the size of electronic devices approaches ever smaller dimensions [5], the new chemical and physical properties of clusters will be relevant to the future of the electronics industry. 

M. E. Perel man, Kinetical Quantum Theory of Optical Dispersion, Mezniereba, Tblisi, 1989 (in Russian). 

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