International Journal of Modern Physics B

A tight-binding model of electron dynamics in mesoscopic normal rings is studied using boundary conformal field theory. The partition function is calculated in the low energy limit and the persistent current generated as a function of an external magnetic flux threading the ring is found. We study the cases where there are defects and electron–electron interactions separately. The same temperature scaling for the persistent current is found in each case and the functional form can be fitted, with a high degree of accuracy, to experimental data.

We study the half-filled two-dimensional Hubbard model in the intermediate coupling regime. As temperature is decreased for a two-dimensional half-filled band, two-dimensional critical fluctuations give rise to a strong local maximum in |Im Σ(k_F, ω)| at ω=0, leading to a split peak with a pseudogap inside in the spectral function and the density of states. The calculated energy dispersion is in good agreement with that of spin density wave approximation.

Effects of magnetic impurities on a two-dimensional Hubbard antiferromagnet are treated self-consistently within a numerical Hartree–Fock approximation. Both kinds of impurities — those with spin equal to the host spin (S′=S); and those with spin different from the host spin (S′≠S) — have been studied. In this approach, S′=S impurities lead to momentum (Q) dependent renormalization of the long wavelength magnon energies, unlike in the previous perturbative calculations where the renormalization was found to be Q-independent. S′≠S impurities, however, give Q-dependent logarithmically diverging corrections. Both kinds of impurities leave the gapless Goldstone mode in the spin excitations unaffected.

A study of experimental results on various parameters of underdoped cuprates in the normal state combined with analytic calculation of Hall parameters assuming a two-channel Kondo model for the system leads to the conclusion that the spin and charge pseudogaps are, respectively, a Kondo hybridisation gap and an incipient d-wave "superconducting" gap. The former occurs due to resonant scattering of doped holes by the magnetic Cu²⁺ ions while the latter occurs due to incoherent Cooper pairing of Kondo-compensated quasi-itinerant Cu d-orbitals via exchange of spin excitations. We comment on the essential similarity of the high-T_c and heavy fermion superconductors and a certain crossover at lower temperatures from the two-channel to the one-channel Kondo model. An expression has been derived for the Kondo contribution to the spectral function of the charge pseudogap. We believe this work unravels the long-standing conundrum of the high-T_c cuprates.

The understanding of the spin gap phenomenon in the normal state of the high temperature superconductors can provide the mechanism of the high temperature superconductivity. A specific function of thermal excitation for quasiparticles was introduced based on the experimental relationship between resistivity and temperature. This specific function describes the deviation in resistivity from the T-linear relationship w.r.t. the normal state of the high temperature superconductors. With this function, the spin gap is naturally introduced. Our experimental results indicate that the spin gap behavior is closely related not only to the oxygen deficiency but also to the structural change in the a–b plane. Furthermore, we found that the crossover from anomalous metallic state to spin gap state takes place within a temperature range T_S<T<T*, which depends on the oxygen content and the Ca-doping level. Pressure effects on the spin gap phenomenon in bulk samples of oxygen-deficient YBa₂Cu₃O_6+δ and Ca-doped Y_1-xCa_xBa₂Cu₃O_6+δ were also investigated. Under high hydrostatic pressure the spin gap behavior is also severely influenced by the contraction of the a–b plane due to the pressure.

A Davies model of an imperfect boson gas is considered. The model includes not only a convex, but also a concave type of an interaction function which depends on a dencity operator. A sufficient condition of the Bose–Einstein condensation is proved. An exact value of the critical temperature is obtained.

The conductance G in a narrow constriction and its dependence on the Fermi energy and on the transverse position of an impenetrable magnetic flux tube is studied. G exhibits oscillatory-like behavior as the transverse position of the tube changes. When there are n propagating subbands, there are n-1 minimums of G first (except for n=1) and n minimums later when the Fermi energy grows. Both just below and just above the critical energy exhibiting n propagating subbands, minimums occur at tube positions mW/n, where W is the transverse width of the constriction and 1≤m≤n-1.

We derive the modified Young's equation for the contact angle of a fluid droplet on a rigid substrate using an interface displacement model and identify the line tension with the excess free energy per unit length calculated previously for a straight three-phase contact line.

A statistical mechanical based theory is developed for incorporating the long range correlations in the frame work of the first order perturbation theory to study the liquid–vapour equilibrium. The transition temperature and the liquid–vapour coexistence curves are found to depend considerably on the long range correlations and on the realistic radial distribution function. The calculated liquid–vapour equilibrium curves are in good agreement with the computer simulation results.