Polaron and bipolaron dispersion curves in one dimension for intermediate coupling

Bipolaron energies are calculated as a function of wave vector by a variational method of Gurari appropriate for weak or intermediate coupling strengths, for a model with electron-phonon interactions independent of phonon wave vectors and a short-ranged Coulomb repulsion. It is assumed that the bare electrons have a constant effective mass. A two-parameter trial function is taken for the relative motion of the two electrons in the bipolaron. Energies of bipolarons are compared with those of two single polarons as a function of wave vector for various parameter values. Results for effective masses at the zone center are also obtained. Comparison is made with data of other authors for bipolarons in the Hubbard-Holstein model, which differs mainly from the present model in that it has a tight-binding band structure for the bare electrons.Comment: 11 pages including six figures. Physical Review B, to be publishe

Optical conductivity of polaronic charge carriers

The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.Comment: 23 pages, 11 figure

Signatures of Superfluidity in Dilute Fermi Gases near a Feshbach Resonance

We present a brief account of the most salient properties of vortices in dilute atomic Fermi superfluids near a Feshbach resonance.Comment: 6 pages, 1 figure, and jltp.cls. Several typos and a couple of inaccuracies have been correcte

Mobile small polaron

Extending the Froehlich polaron problem to a discrete ionic lattice we study a polaronic state with a small radius of the wave function but a large size of the lattice distortion. We calculate the energy dispersion and the effective mass of the polaron with the 1/\lambda perturbation theory and with the exact Monte Carlo method in the nonadiabatic and adiabatic regimes, respectively. The ``small'' Froehlich polaron is found to be lighter than the small Holstein polaron by one or more orders of magnitude.Comment: 4 pages, 4 figures, published versio

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. \ Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM)--usually neglected in BCS theory--and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent {\it linear} term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory {\it per se,} is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality $d\leq 2$ for quadratic dispersion, but is {\it nonzero} for all $d\geq 1$ for linear dispersion.Comment: 11 pages plus 3 figures, revised version accepted in Physical Review