A non-perturbative treatment of the generalized Su-Schreiffer-Heeger Hamiltonian on a dimer

Starting from the Hamiltonian for a dimer which includes all the electronic and electron-phonon terms consistent with a non-degenerate orbital, by a sequence of displacement and squeezing transformation we obtain an effective polaronic Hamiltonian. The renormalized electronic interactions differ from the results of semiclassical or perturbative treatments. The properties of the variationally determined ground state of two particles in the orbital are discussed for variable dimer length in the adiabatic limit.Comment: 6 pages, 3 figures, to be published in Int. Journal of Modern Physics

Effective inter-band coupling in MgB2 due to anharmonic phonons

We investigate the origin of the inter-band coupling in MgB2 by focusing on its unusual phononic features, namely, the strong anharmonicity of the phonons and the presence of both linear and quadratic electron-phonon interactions of the Su-Schrieffer-Heeger (SSH) type. The bare electronic Hamiltonian has two bands with intra- and inter-band hopping, which lead to two decoupled hybridized bands. The phonon Hamiltonian including the anharmonic terms is diagonalized approximately by a squeezing transformation, which causes the softening of the phonon frequency. The linear SSH coupling amplitude is reduced, consistently with the estimates from first-principle calculations. Additionally, the quadratic coupling generates an effective phonon-induced interaction between the hybridized bands, which is non-vanishing even in the limit of vanishing inter-bare-band hopping amplitude.Comment: 11 page

A model Hamiltonian for MgB2 which takes into account its unusual phononic features

Taking as a starting point the results of LDA calculations, which show that in MgB2 the phonons have a strong quartic anharmonicity and that the bond-stretching electron-phonon interaction (EPI) has both a linear and a large quadratic component, we propose a model Hamiltonian which succesfully matches a number of experimental evidences. We relate the single critical temperature for both superconducting gaps to a phonon-induced inter-band coupling whose amplitude increases with temperature. We also obtain phonon frequencies and linewidths depending on the band filling, as well as band energies and hybridization amplitudes depending on the phonon number.Comment: 19 pages, no figures, accepted on The European Physical Journal

Distance-depending electron-phonon interactions from one- and two-body electronic terms in a dimer

For a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape we evaluate all the electron-phonon couplings derived from the one-body and two-body electronic interactions, considering both the adiabatic and extreme non-adiabatic limit. Not only the values of the coupling parameters in the two limits, but also the expressions of the corresponding terms in the Hamiltonian differ. Depending on the distance between the dimer ions, some of the two-body couplings are comparable, or even larger than the one-body ones.Comment: 8 pages, 3 figures, to be published in Int. Journal of Modern Physics

Model Calculation of Electron-Phonon Couplings in a Dimer with a Non-Degenerate Orbital

We evaluate all the electron-phonon couplings derived from the one-body electronic interactions, in both the adiabatic and extreme non-adiabatic limit, for a dimer with a non-degenerate orbital built from atomic wave functions of Gaussian shape. We find largely different values of the coupling parameters in the two cases, as well as different expressions of the corresponding terms in the Hamiltonian.Comment: 5 postscript figure

Summer and Fall Movements of Narwhals (Monodon monoceros) from Northeastern Baffin Island towards Northern Davis Strait

Ten narwhals (Monodon monoceros) were instrumented with satellite-linked radio transmitters in Tremblay Sound in August 1997 (N = 5) and August 1998 (N = 5). All whales stayed in the waters around Bylot Island until the end of September. On the basis of these animals and others tagged previously (total N = 24), it is believed that the Bylot Island summering population has limited or no contact with other summering populations in Canada or Greenland. Four whales were monitored during their southward movement along the east coast of Baffin Island. Three of them travelled close to the shore, visiting several fjords and bays, during September and October. The fourth whale started the southward migration at the same time as the other three, but it returned to the area east of Pond Inlet and made two trips northeast of Bylot Island. It headed south on 21 October 1998. South of Royal Society Fiord, it travelled offshore along the continental slope (1000 to 1500 m), probably because of ice formation in inshore areas. This narwhal and another male tagged in 1997 moved east toward the northern parts of the Davis Strait, reaching an area midway between Canada and Greenland in early November. Their winter movements were monitored until 30 January. The same wintering area in northern Davis Strait was previously documented for two male narwhals tracked from Melville Bay, NW Greenland, in 1993 and 1994. The whales showed a preference for deep areas, including deep fjords and the continental slope, where depths ranged between 500 and 1500 m. Even deeper areas, where maximum daily dives exceeded 1000 m, were also visited occasionally.On a équipé 10 narvals (Monodon monoceros) d'émetteurs radioélectriques en liaison avec un satellite dans le détroit de Tremblay en août 1997 (N = 5) et en août 1998 (N = 5). Toutes les baleines sont restées dans les eaux entourant l'île Bylot jusqu'à fin septembre. En considérant ces animaux et d'autres équipés précédemment (N total = 24), on pense que la population estivale de l'île Bylot n'a que peu, sinon pas de contact avec d'autres populations estivales du Canada ou du Groenland. Quatre baleines ont fait l'objet d'un suivi au cours de leur déplacement vers le sud le long de la côte est de l'île de Baffin. Durant les mois de septembre et d'octobre, trois d'entre elles longeaient la côte de près, effectuant des pauses dans divers fjords et baies. La quatrième a commencé sa migration vers le sud en même temps que les trois autres, mais elle est retournée dans la zone à l'est de Pond Inlet et s'est rendue par deux fois au nord-est de l'île Bylot. Elle a mis le cap vers le sud le 21 octobre 1998. Au sud du fjord Royal Society, elle s'est dirigée vers le large et a longé la pente continentale (à environ 1000 à 1500 m du rivage), probablement en raison de la formation de glace dans la zone côtière. Ce narval ainsi qu'un autre mâle équipé en 1997 se déplaçaient en direction de l'est vers la partie nord du détroit de Davis, atteignant début novembre une zone située à mi-chemin entre le Canada et le Groenland. En hiver, leurs déplacements ont été suivis jusqu'au 30 janvier. La même zone d'hivernage dans le nord du détroit de Davis a déjà été rapportée pour deux narvals mâles suivis en 1993 et 1994 depuis la baie Melville, au N.-O. du Groenland. Les baleines affichaient une préférence pour des zones profondes, y compris des fjords encaissés et la pente continentale, où la profondeur allait de 500 à 1500 m. De temps à autre, les baleines se rendaient aussi dans des zones encore plus profondes, où les plongées maximales quotidiennes dépassaient les 1000 m

H2H_2 and (H2)2(H_2)_2 molecules with an ab initio optimization of wave functions in correlated state: Electron-proton couplings and intermolecular microscopic parameters

The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic correlations taken into account between the $1s$ electrons exactly. The optimal single-particle Slater orbitals are evaluated in the correlated state of $H_2$ by combining their variational determination with the diagonalization of the full Hamiltonian in the second-quantization language. All electron--ion coupling constants are determined explicitly and their relative importance is discussed. Sizable zero-point motion amplitude and the corresponding energy are then evaluated by taking into account the anharmonic contributions up to the ninth order in the relative displacement of the ions from their static equilibrium value. The applicability of the model to the solid molecular hydrogen is briefly analyzed by calculating intermolecular microscopic parameters for $2 \times H_2$ rectangular configurations.Comment: 14 pages, 14 figures, 6 table

Electronic and phononic states of the Holstein-Hubbard dimer of variable length

We consider a model Hamiltonian for a dimer including all the electronic one- and two-body terms consistent with a single orbital per site, a free Einstein phonon term, and an electron-phonon coupling of the Holstein type. The bare electronic interaction parameters were evaluated in terms of Wannier functions built from Gaussian atomic orbitals. An effective polaronic Hamiltonian was obtained by an unrestricted displaced-oscillator transformation, followed by evaluation of the phononic terms over a squeezed-phonon variational wave function. For the cases of quarter-filled and half-filled orbital, and over a range of dimer length values, the ground state was identified by simultaneously and independently optimizing the orbital shape, the phonon displacement and the squeezing effect strength. As the dimer length varies, we generally find discontinuous changes of both electronic and phononic states, accompanied by an appreciable renormalization of the effective electronic interactions across the transitions, due to the equilibrium shape of the wave functions strongly depending on the phononic regime and on the type of ground state.Comment: 11 pages, RevTeX, 10 PostScript figures; to appear in Phys. Rev.