Coherent states conductivity

When the temperature T decreases below the critical temperature Tc BEC starts at first only for a small fraction of all atoms in the magnetic trap, i.e. not all atoms are immediately transferred into the coherent state of BEC. With decreasing temperature the fraction of the condensed atoms increases (Fig. 9.35). The BEC-state is separated from the normal state with T > Tc by an energy gap similar to the energy gap between the Cooper pair state in supra-conductivity and the normal state. One therefore has to pump energy into the condensate in order to convert the assemble into the normal state. Also the energy distribution changes from a Maxwell-Boltzmann distribution above to a distribution... 

The R ions form a periodic lattice, which leads for the 4f electrons together with the conduction electrons to the formation of quasi-particle bands, i.e. the electrons are in a coherent state. Since the magnetic moments either vanish (in the non-magnetic Kondo state) or form themselves a periodic magnetic structure (Kondo systems with magnetic order) there is no elastic scattering of the conduction electrons and therefore Pn,(0) = 0. This is different at high temperatures, where even in a periodic lattice one has disordered moments, which scatter elastically. The coefficient Ai can be calculated analytically. One finds A = j j + with the resistivity in the unitarity limit... 

One more trend in laser control is based on the use of the property of coherence of the laser light. To effect coherent laser control, it is necessary that not only the light, but also the atom (or molecule) should be in a coherent state during the interaction. For atoms in a beam or in a low-pressure gas, the phase relaxation time of their wave functions depends on spontaneous decay or on collisions and can be comparatively long (from 10 to 10 s). It was for precisely this reason that the main experiments on coherent interaction were conducted with atoms. These experiments led in the final analysis to the discovery of new effects, such as coherent population trapping (Arimondo 1996), electromagnetically induced transparency (Harris 1997), and the slow-light effect (Hau et al. 1999 Kash et al. 1999). 

If the target is a pure electronic state (or coherent superposition state) in the conduction band, c)) the target operator can be written as... 

ANG AO ATA BF CB CF CNDO CPA DBA DOS FL GF HFA LDOS LMTO MO NN TBA VB VCA WSL Anderson-Newns-Grimley atomic orbital average t-matrix approximation Bessel function conduction band continued fraction complete neglect of differential overlap coherent-potential approximation disordered binary alloy density of states Fermi level Green function Flartree-Fock approximation local density of states linear muffin-tin orbital molecular orbital nearest neighbour tight-binding approximation valence band virtual crystal approximation Wannier-Stark ladder... 

Technically important electrochemical reactions of pyrrole and thiophene involve oxidation in non-nucleophilic solvents when the radical-cation intermediates react with the neutral molecule causing polymer growth [169, 191], Under controlled conditions polymer films can be grown on the anode surface from acetonitrile. Tliese films exhibit redox properties and in the oxidised, or cation doped state, are electrically conducting. They can form the positive pole of a rechargeable battery system. Pyrroles with N-substituents are also polymerizable to form coherent films [192], Films have been constructed to support electroactive transition metal centres adjacent to the electrode surface fomiing a modified electrode,... 

Symmetry of superconducting state. No Hebel-Slichter coherence peak was observed in either k -(ET)2Cu(NCS)2 or c-(ET)2Cu[N(CN)2]Br in NMR measurements, ruling out a BCS s-wave state. The symmetry of the superconducting state of c-(ET)2Cu(NCS)2 had been controversially described as normal BCS-type or non-BCS type however, scanning tunneling spectroscopy showed f-wave symmetry with line nodes along the direction near ti/4 from k - and Kc-axes [228, 229], and thermal conductivity measurements were consistent with this result [230]. c-(ET)2Cu [N(CN)2]Br showed the same symmetry [231]. 

The conduction electrons are scattered by the alkali atoms, the coherence implicit in the radial distribution function. Unlike the case of the scattering of a single electron in a plane wave state by a liquid, discussed previously, in this case the structure factor S(k) must be known up to the Fermi energy (which is 0.5 e.v. — 1 e.v. in saturated metal ammonia solutions). 

Fig. 15. Pictorial presentation of the physical concept of electron charge transfer in [TCNQ-TTF] as a function of temperature. TR-A each TCNQ resonates between the two harmonic oscillator states at a temperature dependent frequency, co. Electrons on TTF are in an unpaired state (shaded)., TR-B Covalon conduction sets in under the condition, (O v (represented by arrows within TCNQ. TR-C this suggests the diminishing ratio of coherent (straight lines) to incoherent (wavy) parallel lines) with the temperature increase.

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