Wigner solid

Figure 6. Histograms of the nearest-neighbor mass spacing distribution for hadron states with same quantum numbers. Curves represent the Poisson (dashed) and Wigner (solid) distributions. Taken from Ref. (Pascalutsa, 2003).

Keywords Density matrices, Wigner solid, strongly orthogonal geminals... 

Fig. 2. Schematic phase diagram as proposed by Buchmann et al. [91] for the two-dimensional Wigner electron solidification in a magnetic field perpendicular to electron assembly. Landau filling factor v is the independent variable [88]. The four Wigner solid phases are labelled Cl to C4. t denotes the reduced melting temperature (compare Fig. 1 which, however, is for three dimensions and zero magnetic field)...

Fig. 21 Macrocyclisation equilibrium constants for polydimethylsiloxane. Experimental data are shown as dashed curves as follows I, Brown and Slusarczuk II, Hartung and Camiolo III, Carmichael and Wigner. The solid curve is calculated from Jacobson Stockmayer theory. (Reproduced with permission from Flory, 1969)...

Some LSD calculations for solids are still performed with the MJW (HL), GL, and RPA (VBH) parametrizations, or even with the Wigner (W) [46, 47] approximation of 1934. Tables I and II show the extent to which these parametrizations are not proper LSD input. 

Diatomic hydrogen, H2, also exhibits a rich and remarkable complex soUd phase diagram. At low temperatures, when a H2-based solid is formed, electrons are confined in the H2 molecules and the soUd is thus a large-gap insulator. E. Wigner and H. B. Huntington predicted in 1935 the possibiUty of preparing... 

Wigner, E. (1930). The operation of time reversal in quantum mechanics. Gdttinger Nachrichten, 133-146. See Group Theory and Solid State Physics, edited by P. H. Meijer, Gordon and Breach Science Publishers, 1964, New York, 265-278. 

The behaviour of the transition-metal bands as the atoms are brought together to form the solid may be evaluated within the Wigner-Seitz sphere approximation by imposing bonding, = 0, or antibonding, R, = 0,... 

It was Wigner, Seitz, Pohl, and others who pioneered the solid-state field rather than Polanyi, largely because of their mastery of the new quantum mechanics, in which he never was at ease, and their theoretical application of quantum mechanics to solids. [61] Polanyi s pioneering work on surfaces and solids became part of the background, rather than the foreground of textbook science. Yet his legacy lay, too, not only in the scientific practice about which he wrote from a philosophical and... 

Shannon27 analyzed in some detail the theory as it applies to the thermal decomposition of solids. He found that of the 31 reactions for which he compared experimental rate constants with those calculated from the Polanyi-Wigner equation, only a third showed order-of-magnitude agreement. In Shannon s view, the lack of agreement stems from neglecting rotational and other vibrational degrees of freedom. 

Cellular Method. The cellular method of Wigner and Seitz (1933) assumes that the solid is divided into "cells" with an ionic core at the origin the atomic wavefunction is of the type... 

Fig. 4. Hartree-Fock free atom 4s valence electron orbital for potassium (solid line) and the 4s-like orbital, obeying the Wigner-Seitz boundary condition, appropriate to the bottom of the conduction bands in metallic potassium (dashed line). Both orbitals are normalized, for the metal, integration is limited to the Wigner-Seitz sphere of radius rws...

Fig. 7. The valence Ss and 5p orbital densities of Sn 5s25pz. Shown are free atom densities (solid lines) free atom densities renormalized to the Wigner-Seitz cell of a—Sn (dashed curves) and a schematic plot (dot-dash) of the way in which the 5p conduction band orbital character deviates from simple renormalization. The Wigner-Seitz radii, rws. of a and j8 Sn are indicated...

Wigner, E. P., Seitz, F. Solid State Phys. 1, 97 (1955) (Seitz and Turnbull, Eds.). New York Academic Press. 

Figure 21 shows temperature dependence of electrical conductivity and magnetic susceptibility of MEM(Af-methyl-iV-ethyl-morpholinium)-(TCNQ)2 [70]. At about 335 K it undergoes a metal-insulator transition accompanied by the onset of a two-fold superstructure and a temperature dependent magnetic susceptibility characteristic of localized moments. It is considered as depicted in Fig. 22(a) that a dimerized TCNQ accepts an electron localized by, for example, the Mott transition or the Wigner crystallization. The solid curve shown in Fig. 21(b) denotes the theoretical prediction for the magnetic susceptibility of a one-... 

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