Electron fluid

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Metals. A review of the published predictions of the 7 of metals was published, for instance, in Ref.14. In that article, the idea of an uniform electron fluid in which metal cations are embedded is rejected the electrons are concentrated in the spaces of the most intense electric field between the cations and thus form something like a second lattice. This remark seems to be disregarded by the later investigators. 

Actually this is more rigorous than the energy analysis of (4)). Notice that the system looks like a mixture of two electronic fluids, one composed of the (spd) electrons and the other of the 5f electrons. 

Metal ions are held together by freely flowing electrons. These loose electrons form a kind of electronic fluid that flows through the lattice of positively charged ions. 

Simple cavity models have been used to study solvated electrons in liquid ammonia. In that case the dominant interactions arise from long range polarization effects, so that the energy of the localized state is not very sensitive to the fluid deformation in the vicinity of the localized charge. In the case of an excess electron in liquid helium, however, the electron-fluid interaction arises mainly from short range electron-atom interactions, and we shall show that the localized excess electron in a cavity in liquid helium lies lower in energy than the quasi-free electron. 

In the case of angular momentum there is no conflict between the classical and quantum descriptions for an electron fluid and continuity across the classical/quantum limit presents no problem. 

It will now be shown that the existence of quantum potential energy eliminates the need to allow for repulsion between sub-electronic charge elements in an extended electron fluid. An electron, whatever its size or shape is described by a single wave function that fixes the electron density at any point... 

The two potential wells are so close together that the electron fluid tunnels through, filing each well equally. The fluid level in each well is now lower, corresponding to a lowe r potential ene rgy of the system as a whole. The fall in energy corresponds to the energy of the chemical bond in H2+... 

Malleability and ductility These terms refer respectively to how readily a solid can be shaped by pressure (forging, hammering, rolling into a sheet) and by being drawn out into a wire. Metallic solids are known and valued for these qualities, which derive from the non-directional nature of the attractions between the kernel atoms and the electron fluid. The bonding within ionic or covalent solids may be stronger, but it is also directional, making these solids subject to fracture (brittle) when struck with a hammer, for example. A metal, by contrast, is more likely to be simply deformed or dented. 

The conductivity of an electrolytic solution decreases as the temperature falls due to the decrease in viscosity which inhibits ionic mobility. The mobility of the electron fluid in metals is practically unaffected by temperature, but metals do suffer a slight conductivity decrease (opposite to ionic solutions) as the temperature rises this happens because the more vigorous thermal motions of the kernel ions disrupts the uniform lattice structure that is required for free motion of the electrons within the crystal. Silver is the most conductive metal, followed by copper, gold, and aluminum. 

Thermionic effect The electrons within the electron fluid have a distribution of velocities very much like that of molecules in a gas. When a metal is heated sufficiently, a fraction of these electrons will acquire sufficient kinetic energy to escape the metal altogether some of the electrons are essentially boiled out of the metal. This thermionic effect, which was first observed by Thomas Edison, was utilized in vacuum tubes which served as the basis of electronics from its beginning around 1910 until semiconductors became dominant in the 1960 s. 

The unknown exchange-correlation energy functional Exc[p] is thereby approximated in terms of the exchange-correlation energy for the particle, Xc(po) of the electron fluid discussed above at uniform density po. xc(po) is accurately known, as referenced earlier. 

In the investigation of Ortiz et al. [104], a stochastic method is presented which can handle complex Hermitian Hamiltonians where time-reversal invariance is broken explicitly. These workers fix the phase of the wave function and show that the equation for the modulus can be solved using quantum Monte Carlo techniques. Then, any choice for its phase affords a variational upper bound for the ground-state energy of the system. These authors apply this fixed phase method to the 2D electron fluid in an applied magnetic field with generalized periodic boundary conditions. 

Dielectric Screening. The dielectric function e corrects the bare potentials for the current flows and the polarization of the electronic fluid. In the calculation of a screened two-body interaction Ug and of the relaxation time r, one uses 1/c ... 

For a system formed fi om a single chemical species (the electronic fluid evolves under the same potential generated by the system nuclei for a fixed coupling constant) the construction of the operator with chemical potential includes the following ingredients ... 

As the thermal coupling between the electron and ion fluids is relatively loose and losses through the electron fluid can be high (Doyle et al. 2007) ECRH is not the most efficient way of heating the ions. This task can be more efficiently done by waves resonating in the ion cyclotron... 

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The second main theoretical approach is developed from the theories of electronic structure and properties of the condensed state. One assumes a basic arrangement of the atoms and calculates the electronic and thermodynamic properties using various approximations. The assumed structure may be completely specified, as a crystal for example, or may be statistical in nature. The lattice gas which we discuss shortly is an example of the latter. Most theories of this type make use of model Hamiltonians and yield results in terms of the model parameters. Model Hamiltonians are very instructive and the calculations provide insight into the interplay between electronic structure and fluid structure. The models, however, are generally too artificial to provide quantitative predictions of the measured properties of real electronic fluids. 

It is clear that an explanation based on superposition of electrons and nuclei of the atoms involved in the formation of a molecule is full of naivety and practically eludes the essence of the private transfers of particles and properties that define a new assembly of electronic fluid and nuclei, found in an external and d5mamic interaction. 

Even with non-polar liquids, the local environment of, and interaction between, the outer electron shells of atoms or molecules in the surface is different from that in the bulk phase, so that an electrical inhomogeneity can still arise, but is less marked than with dipolar or free electron fluids. 

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