Elementary excitation

Pines D 1963 Elementary Excitations in Solids (New York Benjamin)... 

More advanced teclmiques take into account quasiparticle corrections to the DFT-LDA eigenvalues. Quasiparticles are a way of conceptualizing the elementary excitations in electronic systems. They can be detennined in band stmcture calculations that properly include the effects of exchange and correlation. In the... 

In spite of the absence of periodicity, glasses exhibit, among other things, a specific volume, interatomic distances, coordination number, and local elastic modulus comparable to those of crystals. Therefore it has been considered natural to consider amorphous lattices as nearly periodic with the disorder treated as a perturbation, oftentimes in the form of defects, so such a study is not futile. This is indeed a sensible approach, as even the crystals themselves are rarely perfect, and many of their useful mechanical and other properties are determined by the existence and mobility of some sort of defects as well as by interaction between those defects. Nevertheless, a number of low-temperamre phenomena in glasses have persistently evaded a microscopic model-free description along those lines. A more radical revision of the concept of an elementary excitation on top of a unique ground state is necessary [3-5]. 

Corrected version given in Eq. (3-58) of Pines, D. Elementary Excitations in Solids Benjamin NY, 1964. 

C. Valdemoro, Spin-adapted reduced Hamiltonian. 1 Elementary excitations. Phys. Rev. A 31, 2114 (1985). 

SRPA equations are very general and can be applied to diverse systems (atomic nuclei, atomic clusters, etc.) described by density and current-dependent functionals. Even Bose systems can be covered if to redefine the many-body wave function (25) exhibiting the perturbation through the elementary excitations. In this case, the Slater deterninant for Iph excitations should be replaced by a perturbed many-body function in terms of elementary bosonic excitations. 

Ions in the lattice of a solid can also partake in a collective oscillation which, when quantized, is called a phonon. Again, as with plasmons, the presence of a boundary can modify the characteristics of such lattice vibrations. Thus, the infrared surface modes that we discussed previously are sometimes called surface phonons. Such surface phonons in ionic crystals have been clearly discussed in a landmark paper by Ruppin and Englman (1970), who distinguish between polariton and pure phonon modes. In the classical language of Chapter 4 a polariton mode is merely a normal mode where no restriction is made on the size of the sphere pure phonon modes come about when the sphere is sufficiently small that retardation effects can be neglected. In the language of elementary excitations a polariton is a kind of hybrid excitation that exhibits mixed photon and phonon behavior. 

We must again emphasize, even more strongly than we did at the beginning of this chapter, that surface plasmons and surface phonons are not examples of the failure of the bulk dielectric function to be applicable to small particles. Down to surprisingly small sizes—exactly how small is best stated in specific examples, as in Sections 12.3 and 12.4—the dielectric function of a particle is the same as that of the bulk parent material. But this dielectric function, which is the repository of information about elementary excitations, manifests itself in different ways depending on the size and shape of the system. 

All occupation number vectors in F(m,N) can be obtained from an occupation number vector I n> with N electrons by applying one or several elementary excitation operators on I n>. If a single excitation operator is applied we obtain a single excitation, if two excitation operators are involved, we obtain a double excitation, etc. 

The commutator between two elementary excitation operators is in next section shown to be... 

Feynman developed wave functions to provide an atomistic interpretation of Landau s spectrum of elementary excitations. 

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. 

D. Pines, Elementary Excitations in Solids. Benjamin, New York, 1963. 

Pines, D. Elementary excitations in solids. New York Benjamin Inc. 1963. 

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. 

Such a low-lying excitation is shown on the right. These elementary excitations are called spin waves. The spin vectors precess on cones and successive spins have a constant angle of phase shift. This is shown in the lower part of the figure showing one wavelength of a spin wave in a chain of spins (a) in perspective projection and (b) viewed from above. 

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. 

The investigation of elementary excitations in solids by Raman spectroscopy has developed very quickly in the last few years and will certainly lead to many more new results in the future. For example, the huge class of biaxial crystals has so far been avoided by many workers because of the difficulty of the experimental techniques required, but many interesting effects are to be expected from their study. 

An important prediction of LL theory is that the low-energy elementary excitations of a one-dimensional metal are not electronic quasiparticles, as... 

The conductance for a spacing of 2 /xm between gates g and g2 is shown in Fig. 2. The measured bright and dark curves in the plot can be interpreted as spectral peaks tracing out the dispersions of the elementary excitations in the wires. [3] In the case of noninteracting electrons, the curves are expected to map out parabolas defining the continua of electron-hole excitations across... 

The universality of the relaxation time near the crossover temperature also originates in the dynamic nature of supercooled liquids. The idea here is that supercooled liquids have collective excitations. These elementary excitations have characteristics of phonons [119-122]. Furthermore, there is a unique temperature at which the lifetime for the elementary excitation becomes comparable to the lifetime of hopping dynamics on the potential energy surface [119]. Analysis indicates that the value of crossover relaxation time at this characteristic temperature is < ) x 10-7 5 s, where < ) varies between 1 and [ 119]. 

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