Lifshitz limit

To summarize, if p(ej ) is unbounded the energy band is unbounded. If the band is bounded and there is sufficient symmetry remaining, the bound is a normal band edge. Otherwise, it is a Lifshitz limit. 

Note that the paper [ 1 ] by I.M. Lifshitz forestalled the corresponding experiments by at least 10 or rather 20 years. Experimental observation of such transitions is even now far from a routine procedure. Here we shall limit the discussion to mentioning several studies, which are in our opinion the most important achievements in this field [31-34]. We shall also refer to very informative reports on computer simulation of the coil-globule transition, namely, recent paper [35], and a very good reference list therein. 

Ya.B. applied formal perturbation theory to the interaction of an atom with the electrons of a metal, where the latter are assumed to be free. Meanwhile, Casimir and Polder and Lifshitz neglected the spatial dispersion of the dielectric permittivity of the metal. Therefore, in the region of small distances, frequencies of order ui0 are important at small distances in the sense indicated above, as are arbitrarily small frequencies at large distances. In both limits the dielectric permittivity of the metal is not at all close to one. Meanwhile, the perturbation theory used by Ya.B. corresponds formally to an expansion in powers of e - 1. and is therefore not applicable in this case. Neglecting the spatial dispersion is valid, however, only at distances r > a (a is the Debye radius in the metal) of the atom from the surface. At the opposite extreme, r a, the wave vectors kj 1/r > a vF/u>0 Me of importance (vF is the electron speed at the Fermi boundary). In this region of strong spatial dispersion perturbation theory can be applied, and the (--dependence satisfies Zeldovich s law. 

These results show that the two gaps behaviour is present over all the range of the reduced Lifshitz parameter -0.8< z <+0.8. These results support the predictions that the doped materials remain in the clean limit for interband pairing although the large number density of impurity centres. This results falsifies the predictions of the multigap suppression because of impurity scattering due to substitutions. 

Both formulations stumble when the materials are real conductors such as salt solutions or metals. In these cases important fluctuations can occur in the limit of low frequency where we must think of long-lasting, far-reaching electric currents. Unlike brief dipolar fluctuations that can be considered to occur local to a point in a material, walls or discontinuities in conductivity at material interfaces interrupt the electrical currents set up by these longer-lasting "zero-frequency" fields. It is not enough to know finite bulk material conductivities in order to compute forces. Nevertheless, it is possible to extend the Lifshitz theory to include events such as the fluctuations of ions in salt solutions or of electrons in metals. 

When there are small differences in dielectric polarizability and also in the limits of very small and very large separation, the general Lifshitz formula reduces to simpler, power-law forms. 

Rather than think in terms of joining the two formulations in the dilute-gas limit, it is possible to reduce the general form to one that superficially looks like that limit. Recall that when retardation and magnetic susceptibilities are ignored the Lifshitz result (omitting magnetic terms) becomes... 

Derjaguin transform from full Lifshitz result, including retardation C.l.a. Force per unit length C.l.b. Free energy of interaction per unit length C.l.c.l. Nonretarded (infinite light velocity) limit C.l.c.2. Cylinders of equal radii C.l.c.3. Cylinder with a plane... 

C.2.b. Free energy per interaction C.2.c. Nonretarded (infinite light velocity) limit C.2.d. Light velocities taken everywhere equal to that in the medium, small Aji, Aji, q = 1 C.2.e. Hamaker-Lifshitz hybrid form C.3. Two parallel cylinders... 

Although our military experience managing toxicity from nerve agent exposure is limited, exposures to related chemicals such as the OP class occur commonly each year in the USA. In 2006, there were a total of approximately 5,400 OP exposures across the USA (Bronstein et al, 2007). OPs, such as malathion, are commonly used as pesticides. OP toxicity manifests in a similar fashion as toxicity from nerve agents however, this chemical class is considerably less toxic. One case series of 16 children who experienced poisonings with OPs confirmed that pediatric patients present with toxicity differently than adults (Lifshitz et al, 1999). These children often did not manifest the classic muscarinic effects (such as salivary secretions and diarrhea) seen in adults. 

For K-(ET)2l3 no beating of the SdH or dHvA signal was observed even for the lowest fields where oscillations were seen. This proves the extremely 2D character of this organic superconductor. As an upper limit for the transfer integral t the extraordinary small value oit/ep < 1/5000 can be estimated. This almost perfectly 2D electronic structure might be the reason for the unusual behavior of the SdH and dHvA oscillations, especially for the field dependence of the effective mass at higher fields where the 3D Lifshitz-Kosevich theory no longer works. 

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