Quasi-particle excitations

It is instructive to start with the excitation spectrum in the case of the ordinary 2SC phase when dfi = 0. With the conventional choice of the gap pointing in the anti-blue direction in color space, the blue quarks are not affected by the pairing dynamics, and the other four quasi-particle excitations are linear superpositions of ur>g and dr(J quarks and holes. The quasi-particle is nearly identical with a quark at large momenta and with a hole at small momenta. We represent the quasi-particle in the form of Q(quark, hole), then the four quasiparticles can be represented explicitly as Q(ur,dg), Q(ug, dr), Q(dr,ug) and Q(dg,ur). When S/i = 0, the four quasi-particles are degenerate, and have a common gap A. 

The experimental 5s XPS spectrum in Xe7,8 (Fig. 32a) looks quite similar to the 4p spectrum in Ba, suggesting that the 5 s level lies just below the 5 1 level structure, forming a well-defined 5 s1/2 quasi-particle excitation and giving considerable strength to a prominent satellite spectrum, mainly 5 p25 d94, 95. The basic process is again giant Coster-Kronig fluctuation of the core hole... 

To many, the liigh-T, superconductors represent perhaps the most striking example to date of the breakdown of Landau s Fermi-liquid description of metals. One of the fundamental signatures of a Fermi-liquid is a Fermi surface, the locus in reciprocal space of long-lived quasi-particle excitations that govern the electronic properties at low temperatures. In conventional metals, these excitations have well-defined momenta with components in all three dimensions. The failure to unambiguously observe such an entity in the... 

The conclusion that there are extended quasi-particle excitations along nodal arcs is in good agreement with the STM observations by the group of... 

The dark states of the /V-atom system can be identified as quasi-particle excitations of the so-called dark-state polaritons l> in the space of atoms and cavity mode [Fleischhauer 2000]... 

The Andreev reflection is the second-order quantum mechanical process by which an electron-like particle incident on a superconductor with a quasi-particle excitation energy E above the Fermi energy may be transmitted as a Cooper pair in the superconductor, if a hole-like particle (-E) is reflected along the path of the incoming electron [12], For a superconductor-semiconductor interface with low contact resistance (high transparency) and with a negligible Schottky barrier, the Andreev scattering leads to an increased conductance. 

For the actual quasi-particle excitations E one has to solve the Dyson equation (2.1) or p.2) with a non-local energy-dependent self-energy 2. sham and Kohn have suggested LDA approximations for which is also a functional of density. To this they split 2 into a local and non-local component... 

If there is a small mismatch (dp < A) between the Fermi surfaces of the pairing u and d quarks, the excitation spectrum will change. For example, we show the excitation spectrum of Q(ur, dg) and Q(dg,ur) in the left panel of Figure 3. We can see that 5p induces two different dispersion relations, the quasi-particle Q(dg,ur) has a smaller gap A — p, and the quasi-particle Q(ur,dg) has a larger gap A //. This is similar to the case when the mismatch is induced by the mass difference of the pairing quarks [16]. 

AEAt ft) we have here well-defined excited levels in the quasi-particle picture. There is no contradiction as the superposition of both processes, Eqs. (55) and (56), gives to the total cross section a finite line width which is in agreement with the uncertainty principle. 

The conduction electrons move independently in the liquid. This latter assumption raises some difficulties, since the Coulomb interaction between the electrons is large. The difficulty is overcome by realizing that we need not consider the motions of electrons which are strongly correlated, but only the motions of Landau quasi particles (25), each electron being surrounded by a correlation hole. In more formal language, we may say that the quasi particles stand in one-to-one correspondence with the electrons and represent the elementary excitations of the Fermi liquid. 

The low quantized excitation levels or elementary excitations of the material system are also called quasi-particles in solid state physics by analogy with the elementary particles in quantum-field theory 2-3>. 

The elementary excitations mentioned so far are not related in any special way to the solid state and will therefore not be treated in this article. We will discuss here the following low-lying quantized excitations or quasi-particles which have been investigated by Raman spectroscopic methods phonons, polaritons, plasmons and coupled plasmon-phonon states, plasmaritons, mag-nons, and Landau levels. Finally, phase transitions were also studied by light scattering experiments however, they cannot be dealt with in this article. 

The use of lasers for the excitation of Raman spectra of solids has led to the detection of many new elementary excitations of crystals and to the observation of nonlinear effects. In this review we have tried to lead the reader to a basic understanding of these elementary excitations or quasi-particles, namely, phonons, polaritons, plasmons, plasmaritons, Landau levels, and magnons. Particular emphasis was placed upon linear and stimulated Raman scattering at polaritons, because the authors are most familiar with this part of the field and because it facilitates understanding of the other quasi-particles. 

Recently, Connerade59 has pointed out this and other cases of level crossing and given experimental evidence for the breakdown of the quasi-particle picture for a 4 d-core hole in In. The situation is complicated by the fact that the experiment concerns 4d-threshold photoabsorption and therefore involves the participation of a bound or very slow photoelectron which perturbs the picture of an interacting core hole. One therefore has to consider interactions between discrete nd continuous single and double excitations. 

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