Green's and spectral functions of the small Frolich polaron

According to recent Quantum Monte Carlo simulations the small polaron theory is practically exact in a wide range of the long-range (Frohlich) electron-phonon coupling and adiabatic ratio. We apply the Lang-Firsov transformation to convert the strong-coupling term in the Hamiltonian into the form of an effective hopping integral and derive the single-particle Green's function describing propagation of the small Frohlich polaron. One and two dimensional spectral functions are studied by expanding the Green's function perturbatively. Numerical calculations of the spectral functions are produced. Remarkably, the coherent spectral weight (Z) and effective mass (Z') renormalisation exponents are found to be different with Z'>>Z, which can explain a small coherent spectral weight and a relatively moderate mass enhancement in oxides.Comment: RevTeX, 5 pages, 2 postscript figures, LaTeX processing problems correcte

Polaron and bipolaron transport in a charge segregated state of doped strongly correlated 2D semiconductor

The 2D lattice gas model with competing short and long range interactions is appliedused for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where with thetheir mobility is inversely proportional to the temperature. At the temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by the Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures

S-duality in Twistor Space

In type IIB string compactifications on a Calabi-Yau threefold, the hypermultiplet moduli space $M_H$ must carry an isometric action of the modular group SL(2,Z), inherited from the S-duality symmetry of type IIB string theory in ten dimensions. We investigate how this modular symmetry is realized at the level of the twistor space of $M_H$, and construct a general class of SL(2,Z)-invariant quaternion-Kahler metrics with two commuting isometries, parametrized by a suitably covariant family of holomorphic transition functions. This family should include $M_H$ corrected by D3-D1-D(-1)-instantons (with fivebrane corrections ignored) and, after taking a suitable rigid limit, the Coulomb branch of five-dimensional N=2 gauge theories compactified on a torus, including monopole string instantons. These results allow us to considerably simplify the derivation of the mirror map between type IIA and IIB fields in the sector where only D1-D(-1)-instantons are retained.Comment: 29 pages, 1 figur

Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

In view of some recent works on the role of vertex corrections in the electron-phonon system we readress an important question of the validity of the Migdal-Eliashberg theory. Based on the solution of the Holstein model and inverse coupling constant expansion, we argue that the standard Feynman-Dyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electron-phonon coupling constant $\lambda$ is larger than 1 for any ratio of the phonon and Fermi energies. In the extreme adiabatic limit of the Holstein model electrons collapse into self-trapped small polarons or bipolarons due to spontaneous translational-symmetry breaking when $\lambda$ is between 0.5 and 1.3 (depending on the lattice dimensionality). With the increasing phonon frequency the region of the applicability of the theory shrinks to lower values of the coupling constant.Comment: 4 pages, 1 figur

D3-instantons, Mock Theta Series and Twistors

The D-instanton corrected hypermultiplet moduli space of type II string theory compactified on a Calabi-Yau threefold is known in the type IIA picture to be determined in terms of the generalized Donaldson-Thomas invariants, through a twistorial construction. At the same time, in the mirror type IIB picture, and in the limit where only D3-D1-D(-1)-instanton corrections are retained, it should carry an isometric action of the S-duality group SL(2,Z). We prove that this is the case in the one-instanton approximation, by constructing a holomorphic action of SL(2,Z) on the linearized twistor space. Using the modular invariance of the D4-D2-D0 black hole partition function, we show that the standard Darboux coordinates in twistor space have modular anomalies controlled by period integrals of a Siegel-Narain theta series, which can be canceled by a contact transformation generated by a holomorphic mock theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich--Witten tau-function.Comment: 13 page

Pairing interactions and pairing mechanism in high temperature copper oxide superconductors

The polaron binding energy E_{p} in undoped parent cuprates has been determined to be about 1.0 eV from the unconventional oxygen-isotope effect on the antiferromagnetic ordering temperature. The deduced value of E_{p} is in quantitative agreement with that estimated from independent optical data and that estimated theoretically from the measured dielectric constants. The substantial oxygen-isotope effect on the in-plane supercarrier mass observed in optimally doped cuprates suggests that polarons are bound into the Cooper pairs. We also identify the phonon modes that are strongly coupled to conduction electrons from the angle-resolved photoemission spectroscopy, tunneling spectra, and optical data. We consistently show that there is a very strong electron-phonon coupling feature at a phonon energy of about 20 meV along the antinodal direction and that this coupling becomes weaker towards the diagonal direction. We further show that high-temperature superconductivity in cuprates is caused by strong electron-phonon coupling, polaronic effect, and significant coupling with 2 eV Cu-O charge transfer fluctuation.Comment: 11 pages, 7 figure