Quasiparticle

Figure B3.2.1. The band structure of hexagonal GaN, calculated using EHT-TB parameters detemiined by a genetic algorithm [23]. The target energies are indicated by crosses. The target band structure has been calculated with an ab initio pseudopotential method using a quasiparticle approach to include many-particle corrections [194].

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... 

To be a bit more explicit (following [32, 33]), the quasiparticle energies and wavefunctions are given by... 

Bechstedt F 1992 Quasiparticle corrections for energy gaps in semiconductors Adv. Solid State Phys. 32 161... 

Flybertsen M S and Louie S G 1985 First-principles theory of quasiparticles Calculation of band gaps in semiconductors and insulators Phys. Rev. Lett. 55 1418... 

Louie S G 1987 Theory of quasiparticle energies and excitation spectra of semiconductors and insulators Eleotronio Band Struoture and Its Applioations (Leoture Notes in Physios vol 283) ed M Youssouf (Berlin Springer)... 

Massidda S, Continenza A, Posternak M and Baldereschi A 1997 Quasiparticle energy bands of transition-metal oxides within a model GW scheme Phys. Rev. B 55 13 494-502... 

This idea that the heat was transfered by a random walk was used early on by Einstein [21] to calculate the thermal conductance of crystals, but, of course, he obtained numbers much lower than those measured in the experiment. As we now know, crystals at low enough T support well-defined quasiparticles—the phonons—which happen to carry heat at these temperatures. Ironically, Einstein never tried his model on the amorphous solids, where it would be applicable in the / fp/X I regime. 

Straightforward analytical models, however, receive particular attention in the present book, as they are of unique significance in the comprehension of physical phenomena and, moreover, provide the very language to describe them. To exemplify, recall the effect caused on the phase transition theory by the exactly soluble two-dimensional Ising model. Nor can one overestimate the role of the quasiparticle concept in the theory of electronic and vibrational excitations in crystals. As new experimental evidence becomes available, a simplistic physical picture gets complicated until a novel organizing concept is created which covers the facts known from the unified standpoint (thus underlying the aesthetic appeal of science). 

Silicon is a model for the fundamental electronic and mechanical properties of Group IV crystals and the basic material for electronic device technology. Coherent optical phonons in Si revealed the ultrafast formation of renormalized quasiparticles in time-frequency space [47]. The anisotropic transient reflectivity of n-doped Si(001) featured the coherent optical phonon oscillation with a frequency of 15.3 THz, when the [110] crystalline axis was parallel to the pump polarization (Fig. 2.11). Rotation of the sample by 45° led to disappearance of the coherent oscillation, which confirmed the ISRS generation,... 

The fermionic determinant Detiow averaged over instanton anti-instanton positions, orientations and sizes leads to a partition function of light quarks Z. Then the properties of the hadrons and their interactions are concentrated in the QCD effective action written in terms of the quasiparticles. This approach leads to the Diakonov-Petrov(DP) effective action (D.I. Diakonov et.al., 1996). It was shown that DP effective action is a good tool in the chiral limit but fails beyond this limit, checked by the calculations of the axial-anomaly low energy theorems (M.M. Musakhanov et.al., 1997 E. Di Salvo et.al., 1998). 

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... 

Abstract We review our quasiparticle model for the thermodynamics of strongly interacting matter at high temperature, and its extrapolation to non-zero chemical potential. Some implications of the resulting soft equation of state of quark matter at low temperatures are pointed out. 

Keywords QCD equation of state, quasiparticles, quark stars... 

In the following we will outline a thermodynamical quasiparticle model, which can be derived in a series of approximations. 

HTL quasiparticle model. In QCD, the truncation of a resummation scheme based on 2-point functions is delicate because of gauge invariance. 

Figure 2. Comparison of the pressure, in units of the free pressure, of the SU(3) plasma from the HTL quasiparticle approximation (7) vs. lattice data [6].

Phenomenological quasiparticle model. Taking into account only the dominant contributions in (7), namely the quasiparticle contributions of the transverse gluons as well as the quark particle-excitations for Nj / 0, we arrive at the quasiparticle model [8], The dispersion relations can be even further simplified by their form at hard momenta, u2 h2 -rnf, where m.t gT are the asymptotic masses. With this approximation of the self-energies, the pressure reads in analogy to the scalar case... 

Figure 3. The quasiparticle fit (solid line) of the lattice data [9] (open symbols) for the pressure in QCD with Nj = 2 light flavors. The full symbols, representing data with large quark masses, agree with the results for the pure SU(3) plasma (hatched band) for details see [10].

The phenomenological quasiparticle model can be generalized to non-zero chemical potential, where the quasiparticle masses of the gluons and quarks read... 

It is noteworthy that the correspondence T g/ir holds with a good accuracy even when g is not small. A similar observation was made in the HTL quasiparticle approach [12],... 

The characteristic line emanating from Tc is naturally related to the critical line Tc(fi) enclosing the hadronic phase. The comparison, in Figure 4, of our result for the curvature of the critical line at g - 0, which can be calculated in lattice QCD [13], is a nontrivial and successful test of the extension of the quasiparticle approach to g > 0. 

Finally, as a direct confirmation of our mapping procedure, the quasiparticle model can also successfully describe the available lattice data for p(g. T) with... 

Figure 5. The quark number susceptibility for Nf = 2, calculated from the quasiparticle model with the same parameters as in Figs. 3 and 4, for several chemical potentials compared to the lattice data [14] at /u = 0.

At low temperatures, matter will undergo a transition to a color-superconducting state, with a different quasiparticle structure than presumed in our quasiparticle approach. Nonetheless, pairing affects the thermodynamic bulk properties only at the relative order of 0(A2/fi2), where the estimated gap A < 100 MeV is comfortably smaller than the chemical potential. Therefore, our equation of state is a reasonable approximation even at small temperatures (maybe except for the pressure where it becomes very small). 

---