Phonons and d-wave pairing in the two-dimensional Hubbard model

We analyze the influence of phonons on the d-wave pairing instability in the Hubbard model on the two-dimensional square lattice at weak to moderate interaction U, using a functional renormalization group scheme with frequency-dependent interaction vertices. As measured by the pairing scale, the B1g buckling mode enhances the pairing, while other phonon modes decrease the pairing. When various phonon modes are included together, the net effect on the scale is small. However, in situations where d-wave superconductivity and other tendencies, e.g. antiferromagnetism, are closely competing, the combined effect of different phonons may be able to tip the balance towards pairing.Comment: 4 pages, 3 figure

Resonant Energy Exchange between Atoms in Dispersing and Absorbing Surroundings

Within the framework of quantization of the macroscopic electromagnetic field, a master equation describing both the resonant dipole-dipole interaction (RDDI) and the resonant atom-field interaction (RAFI) in the presence of dispersing and absorbing macroscopic bodies is derived, with the relevant couplings being expressed in terms of the surroundings-assisted Green tensor. It is shown that under certain conditions the RDDI can be regarded as being governed by an effective Hamiltonian. The theory, which applies to both weak and strong atom-field coupling, is used to study the resonant energy exchange between two (two-level) atoms sharing initially a single excitation. In particular, it is shown that in the regime of weak atom-field coupling there is a time window, where the energy transfer follows a transfer-rate law of the type obtained by ordinary second-order perturbation theory. Finally, the spectrum of the light emitted during the energy transfer is studied and the line splittings are discussed.Comment: 9 pages, 5 figs, Proceedings of ICQO'2002, Raubichi, to appear in Optics and Spectroscop