Quasi-electrons

Away from the charged stripes, creation operators of approximate fermion basis states of coupled holon-spinon and excession-spinon pairs are constructed [2], Together with the small-U states they form, within the auxiliary space, a basis to quasi-electron (QE) states, created by (/ (k). The bare QE energies ef (k) form quasi-continuous ranges of bands within the BZ. 

Spin-up quasi-electron 2 - Spin-down quasi-eiectron 4- 0 t 1 i 2 T i i... 

Numerous studies have been performed in order to elucidate the structure and the dynamics of confined water using a variety of experimental techniques — NMR, quasi-electron neutron diffraction, IR absorption spectroscopy, or molecular dynamics simulation. Most of these studies use model porous media such as clays, polymer membranes, different types of silica and zeolites. Some of these systems (cf Fig. 2) may be used to study water radiolysis in nanoporous media. 

Figure 5. The Chemical Sensor 4440 manufactured by Agilent Technologies as a type of quasi-electronic nose based upon an automated headspace sampler and an MS.

Another example of a quasi-electronic nose is the use of a reconfigured GC column. One commercial example is the z-Nose which is a portable instrument based upon a short Im GC column with an uncoated SAW detector. The instrument is calibrated using compounds similar to the target analyte and shows some promise in detecting explosives [7]. 

Note that the study of molecular aspects in confined systems has become possible only in recent years. These studies require the development of time domain techniques such as quasi-electron neutron scattering (QNS) and laser spectroscopy, on one hand, and the potential of computer simulation on the other. As we articulated in this chapter, the synergy between theories and experiments played a key role in the development of our understanding of this area. 

Quasi-electrons are electrons in solids with properties other than those in vacuum. In a condensed phase electrons interact with each other and with the nuclei. In order to deal with them as independent free units their interactions with the environment must be eliminated (or at least substantially reduced). This is done by transforming the interactions into novel particle properties. For example, when the motion of an electron in a solid is impeded by atoms the electron seems to be heavier, and as a result the electron is transformed into a free quasi-electron with a higher mass. The properties have changed under the transformation from those of free electrons in vacuum to those of quasi-electrons in a solid and so have their identities. 

The quantum electrodynamic procedure replaces electrons and photons by quasi-particles. The quasi-electrons are renormalized with respect to terms quadratic in the electron-photon coupling operator. They differ from Fermi statistics with respect to fourth order terms. Similarly, the quasi-photons are renormalized with respect to terms quadratic in the electron-photon coupling operator. They differ from Bose statistics with respect to fourth order terms. 

In spite of considering two-photon processes, we still find the energy levels (8.17) to be equidistant with respect to the photon occupation numbers n, -I- i. This suggests that it is permissible to neglect the effect of the electron-photon interaction on statistics and to occupy the electron states and the photon states according to Fermi statistics and to Bose statistics. We shall check this question in Section 8.4 by studying the creation and annihilation operators of the resulting quasi-electrons and quasi-photons. 

The perturbed states (8.9) arise from the unperturbed states (8.7) by a one-to-one correspondence, i.e. they are characterized by the occupation numbers / and n, of the electron states i and of the photon states q in the same way as the unperturbed states. Accordingly, we may introduce quasi-electron creation and annihilation operators and C, and quasiphoton creation and annihilation operators and A, in a fully analogous manner to the unperturbed case. We require... 

Each electron creation or atmihilation in state i is coupled to electron creations and atmihilations in other states k via photon emission and absorption. The operators C, Ci create and annihilate quasi-electrons. Similarly, each photon emission or absorption in state q is coupled to an electron transition from state i to state L The operators A, emit and absorb quasi-photons. The brackets in Eqs. (8.26)-(8.29) denote the commutators. We distinguish two different terms of order two in the interaction parameters. The second order processes leading to the same... 

However, each quasi-photon transition still affects the energy of the quasi-electrons, and each quasi-electron transition still affects the energy of the quasi-photons. We may not simultaneously occupy the quasielectron states according to the Fermi distribution and quasi-photon states according to the Bose distribution. This is permissible only after renormalization of the quasi-particles considered. 

We have to sum over all possible distributions of the quasi-electrons among the electron states i and over all quasi-photon occupation numbers n. Using the fact that the energy levels. ..) are... 

The renormalization of the quasi-photon energies entails a renormalization of the quasi-electron energies. The renormalized quasi-electron Hamiltonian results from the total Hamiltonian (8.31) by replacing the photon occupation numbers + i by coth hcoJ2kT). These are just the average occupation numbers given by the Bose distribution (16). 

The quasi-electron transitions, in contrast to the quasi-photons, are strongly interdependent. The energy necessary for creation or annihilation of an electron in state i depends explicitly on the occupation of the remaining electron states The summation over a particular... 

We obtain the free energy of attraction between particles 1 and 2 by occupying the quasi-electron states of the single particles 1 and 2 according to the ffibbs distribution. 

Up to this point, we have considered the transport properties at T=0. When T>0, the entropy contributions must be added to the energy of the quasi-electron assembly. The resulting free energy per itinerant quasi-particle is then specified as the energy plus the entropic contribution that includes both occupied and unoccupied states,... 

This will be discussed in more detail in Sections 2.2.1 and 2.2.5. In the molecular orbital picture many more nearest neighbours are bonded (Na 8), than valence atom orbitals (4) and, in particular, many more than there are valence electrons (1) available. The bond formation in the metal is determined by ionization potential and the energy contributions (Ae ) required to condense the isolated charged particles to a solid and to delocalize the electrons (in the form of a quasi electron gas) in this structure ... 

As a result the curve E(k) looks like that given in Fignre 9.8 on a background of classical parabolic dependence in the places determined by expression (9.2.3) the curve has breaks. The forbidden energy gap, which we met above, is formed. We are unable now to call the particles as electrons we must call them quasi-particles (quasi-electrons). 

Because of mutual influence, some atomic electrons are generalized forming a gas of quasi-electrons in crystals. These electrons preserve some properties of free electrons (e.g., each of them possesses a classical momentum) but, at the same time, also possess properties that distinguish them from really free particles (e.g., they have a mass different from the classical electron mass). Some well-known electric properties of metals are caused by this gas. However, it appears that in a model of free electron gas theoretical calculations strongly overestimate experimentally known characteristics only a small part of the generalized electrons can take part in the formation of these properties. 

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