Quasi-particle operators

We assume that Rk can be expressed in terms of the operators 0 which are strings of quasi-particle operators Yp, where, by definition, Y° = Xa... 

By substituting the quasi-particle operators (8.26)-(8.29) into the Hamiltonian (8.1), we obtain... 

As mentioned in Section 2, the CPs of solids have to be calculated on the quasi-particle scheme. In order to calculate the quasi-particle states, non-local and energy-dependent self-energy in Equation (13) must be evaluated in a real system. In practice, the exact self-energy for real systems are impossible to compute, and we always resort to approximate forms. A more realistic but relatively simple approximation to the selfenergy is the GWA proposed by Hedin [7]. In the GW A, the self-energy operator in Equation (12) is... 

The discussion of the parity operator can now be repeated verbatim with states, replaced by the molecular states ,, and the understanding that the set, are associated with the quasi-particle solutions of the quantum field theory of the chiral medium. In the next section we discuss some models of these molecular (quasi-particle) states. 

A proper definition of (quasi-)particle-creation and (quasi-)particle-annihilation operators an and a is provided by diagonalization of the (time-independent) unperturbed part Ho = //ext+Z/e-e of the total Hamiltonian. After the iteration is performed (e.g. on the Dirac-Fock level) the latter may be cast into the form... 

We define an operator as closed , if its action on any model function G P produces only internal excitations within the IMS. An operator is quasi-open , if there exists at least one model function which gets excited to the complementary model space R by its action. Obviously, both closed and quasi-open operators are all labeled by only active orbitals. An operator is open , if it involves at least one hole or particle excitation, leading to excitations to the g-space by acting on any P-space function. It was shown by Mukheijee [28] that a size-extensive formulation within the effective Hamiltonians is possible for an IMS, if the cluster operators are chosen as all possible quasi-open and open excitations, and demand that the effective Hamiltonian is a closed operator. Mukhopadhyay et al. [61] developed an analogous Hilbert-space approach using the same idea. We note that the definition of the quasi-open and closed operators depends only on the IMS chosen by us, and not on any individual model function. 

Fig. 4.11 Kinetic Inductance Detector principle of operation. An absorbed photon breaks apeirt a Cooper pair resulting in an excess quasi-particle population (a). The complex impedance of the film is altered by increasing the kinetic inductance and a microwave resonance circuit is used to sense...

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. 

A many-electron method to calculate excitation energies in semiconductors and insulators. It uses a Green s function (G) and a screened Coulomb potential (denoted W) to express the so-called self-energy operator. The self-consistent solution of quasi-particle equations containing the self-energy operator gives quasi-particle energies which can be interpreted as... 

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