N identical particles under quantum confinement: A many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrodinger equation, the spatial dimension D -> infinity equilibrium (D^0) structure, and the normal-mode (D^{-1}) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose-Einstein condensate with a repulsive hardcore potential

Raman Scattering versus Infrared Conductivity: Evidence for one-dimensional Conduction in La_{2-x}Sr_{x}CuO_{4}

Raman and Infrared (IR) spectra of an underdoped La_{1.90}Sr_{0.10}CuO_{4} single crystal have been measured as a function of temperature. Both techniques provide unconventional low-energy spectra. The IR conductivity exhibits features peaked at finite frequencies which do not have a counterpart in the Raman response. Below approximately 100 K a transfer of both Raman and IR spectral weight towards lower energies is found and a new component in the Raman response builds up being characterized by a very long lifetime of electrons propagating along the Cu-O bonds.Comment: 4 pages, 3 eps figure

Doping dependence of the superconducting gap in Bi2Sr2CaCu2O{8 + delta}

Bi2Sr2CaCu2O{8 + \delta} crystals with varying hole concentrations (0.12 < p < 0.23) were studied to investigate the effects of doping on the symmetry and magnitude of the superconducting gap. Electronic Raman scattering experiments that sample regions of the Fermi surface near the diagonal (B_{2g}) and principal axes (B_{1g}) of the Brillouin Zone have been utilized. The frequency dependence of the Raman response function at low energies is found to be linear for B_{2g} and cubic for B_{1g} (T< T_c). The latter observations have led us to conclude that the doping dependence of the superconducting gap is consistent with d_{x^2-y^2} symmetry, for slightly underdoped and overdoped crystals. Studies of the pair-breaking peak found in the B_{1g} spectra demonstrate that the magnitude of the maximum gap decreases monotonically with increasing hole doping, for p > 0.12. Based on the magnitude of the B_{1g} renormalization, it is found that the number of quasiparticles participating in pairing increases monotonically with increased doping. On the other hand, the B_{2g} spectra show a weak "pair-breaking peak" that follows a parabolic-like dependence on hole concentration, for 0.12 < p < 0.23.Comment: 9 pages REvTex document including 8 eps figures; new table II; changes to Fig. 5 and tex

Theory of Kondo lattices and its application to high-temperature superconductivity and pseudo-gaps in cuprate oxides

A theory of Kondo lattices is developed for the t-J model on a square lattice. The spin susceptibility is described in a form consistent with a physical picture of Kondo lattices: Local spin fluctuations at different sites interact with each other by a bare intersite exchange interaction, which is mainly composed of two terms such as the superexchange interaction, which arises from the virtual exchange of spin-channel pair excitations of electrons across the Mott-Hubbard gap, and an exchange interaction arising from that of Gutzwiller's quasi-particles. The bare exchange interaction is enhanced by intersite spin fluctuations developed because of itself. The enhanced exchange interaction is responsible for the development of superconducting fluctuations as well as the Cooper pairing between Gutzwiller's quasi-particles. On the basis of the microscopic theory, we develop a phenomenological theory of low-temperature superconductivity and pseudo-gaps in the under-doped region as well as high-temperature superconductivity in the optimal-doped region. Anisotropic pseudo-gaps open mainly because of d\gamma-wave superconducting low-energy fluctuations: Quasi-particle spectra around (\pm\pi/a,0) and (0,\pm\pi/a), with a the lattice constant, or X points at the chemical potential are swept away by strong inelastic scatterings, and quasi-particles are well defined only around (\pm\pi/2a,\pm\pi/2a) on the Fermi surface or line. As temperatures decrease in the vicinity of superconducting critical temperatures, pseudo-gaps become smaller and the well-defined region is extending toward X points. The condensation of d\gamma-wave Cooper pairs eventually occurs at low enough temperatures when the pair breaking by inelastic scatterings becomes small enough.Comment: 15 pages, 14 figure

Carrier relaxation, pseudogap, and superconducting gap in high-Tc cuprates: A Raman scattering study

We describe results of electronic Raman-scattering experiments in differently doped single crystals of Y-123 and Bi-2212. The comparison of AF insulating and metallic samples suggests that at least the low-energy part of the spectra originates predominantly from excitations of free carriers. We therefore propose an analysis of the data in terms of a memory function approach. Dynamical scattering rates and mass-enhancement factors for the carriers are obtained. In B2g symmetry the Raman data compare well to the results obtained from ordinary and optical transport. For underdoped materials the dc scattering rates in B1g symmetry become temperature independent and considerably larger than in B2g symmetry. This increasing anisotropy is accompanied by a loss of spectral weight in B2g symmetry in the range between the superconducting transition at Tc and a characteristic temperature T* of order room temperature which compares well with the pseudogap temperature found in other experiments. The energy range affected by the pseudogap is doping and temperature independent. The integrated spectral loss is approximately 25% in underdoped samples and becomes much weaker towards higher carrier concentration. In underdoped samples, superconductivity related features in the spectra can be observed only in B2g symmetry. The peak frequencies scale with Tc. We do not find a direct relation between the pseudogap and the superconducting gap.Comment: RevTeX, 21 pages, 24 gif figures. For PostScript with embedded eps figures, see http://www.wmi.badw-muenchen.de/~opel/k2.htm

The nature of monomer inversion in the ammonia dimer

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