Quasiparticles, Landau

Properties of the condensed matter are often described in terms of elementary excitations. Various physical quantities (energy, momentum, etc.) can be assigned to these excitations which justifies to consider them as quasiparticles (Landau et al. 1980). Though these quasiparticles carry some physical information, they cannot be identified with the real particles (electrons, atoms, molecules) of the system. Discussion of the physics of quasiparticles is out of the scope of the present book. Mathematical description of quasiparticles is inherently connected to second quantization this point will be considered below. 

Landau-Fermi liquid, 23 840 Landau quasiparticle model, 23 840 Land cost, 9 527 Landering, 8 438-439 Land-farming, 3 768 defined, 3 759t Landfill gas, 25 880 Landfill leachate treatment, reverse osmosis in, 21 646-647 Landfill liners, 25 877-878... 

The local ground-state correlation potential is defined in RDFT as the functional derivative of Eq.(7) with respect to p. When infinitesimal variation of occupation numbers is allowed, a more practical definition follows from the fact that the unsymmetrical energy formuala used to construct Eq.(7) is itself a Landau functional of the occupation numbers [19]. Correlation energies of Landau quasiparticles, expressed as diagonal elements of a one-electron Hamiltonian matrix, are defined by differentiating with respect to occupation numbers to give... 

Calculations for finite nuclei will be discussed which demonstrate that the distribution of sp strength in the experimentally accessible energy region can be qualitatively understood. In addition, it becomes possible to interpret both theoretical and experimental results in terms of quasiparticle excitations, the basic concept of Landau s theory of Fermi liquids [19-21]. In contrast to an infinite liquid, the sp basis must be appropriate for the finite system under study and is not composed of the sp momentum states. Apart from this obvious requirement, most notions carry over rather straightforwardly. The ability to calculate the sp strength distribution and compare to experimental data presents an advantage over the approach initiated by Migdal [22,23]. 

Interaction effects must be accounted for in considering those situations where the quasiparticle distribution function deviates from that of the equilibrium case. In the phenomenological Landau-FL theory the characteristic properties of the qnasiparticles, which can hardly be calculated microscopically, are expressed in terms of parameters which are determined from... 

The influence of the quasiparticle interactions on observable quantities is usually described in terms of a small set of interaction parameters. According to Landau, the compressibility Ke and susceptibility Xs are given by... 

The ratio of fourth order Landau coefficients Pi IP2 — 2 was taken as evidence for the weak coupling nature of superconductivity. Therefore the question arises whether it is possible to calculate the synunetry of the order parameter within a microscopic weak coupling Hamiltonian starting from an on-site effective quasiparticle interaction which is repulsive. Such... 

Mixing of the above two limiting cases can sometimes be useful, too. One of the most important quasiparticle transformations of this type is the so-called Boguliubov transformation applied in the standard theory of superfluidity and superconductivity. These theories are out of the scope of this book but we shall make an exception below to explain the merit of the Boguliubov transformation (Landau et al. 1980). 

Here d,e is the classic Poisson bracket, e is the total energy with the accoimt of self-consistent field, l(p) is the collision integral of Boltzmann-Landau type, the kernel r(p,pf) and the collision cross-section in l( ) are expressed through the amplitude of binary quasiparticle scattering. 

---