Abstract:
The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated electrons coupled to low energy acoustic phonons in one dimension. The Wentzel--Bardeen singularity suppresses antiferromagnetic fluctuations and pushes the system toward the metallic phase via an intermediate, metallic phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions.

Abstract:
The Green function and the ordering correlation functions of a system of electrons coupled to acoustic phonons are calculated explicitly. The sensitivity of the correlation function exponents to the Wentzel-Bardeen singularity is discussed. A phase diagram is established for the Hubbard model coupled to phonons, using the integral equations of Lieb and Wu. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity can be reached for arbitrary phonon coupling. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.

Abstract:
We derive the effective low-energy theory for interacting electrons in metallic single-wall carbon nanotubes taking into account acoustic phonon exchange within a continuum elastic description. In many cases, the nanotube can be described as a standard Luttinger liquid with possibly attractive interactions. We predict surprisingly strong attractive interactions for thin nanotubes. Once the tube radius reaches a critical value $R_0 \approx 3.6\pm 1.4$ \AA, the Wentzel-Bardeen singularity is approached, accompanied by strong superconducting fluctuations. The surprisingly large $R_0$ indicates that this singularity could be reached experimentally. We also discuss the conditions for a Peierls transition due to acoustic phonons.

Abstract:
A macroscopic realization of the strange virtual particles is presented. The classical Helmholtz and the quantum mechanical Schr\"odinger equations are analogous differential equations. Their imaginary solutions are called evanescent modes in the case of elastic and electromagnetic fields. In the case of non-relativistic quantum mechanical fields they are called tunneling solutions. The imaginary solutions of this differential equation point to strange consequences: They are non local, they are not observable, and they described as virtual particles. During the last two decades QED calculations of the imaginary solutions have been experimentally confirmed for phonons, photons, and for electrons. The experimental proofs of the predictions of the non-relativistic quantum mechanics and of the Wigner phase time approach for the elastic, the electromagnetic and the Schr\"odinger fields will be presented in this article. The results are zero tunneling time and an interaction time (i.e. a phase shift) at the barrier interfaces. The measured barrier interaction time (i.e. the barrier transmission time) scales approximately inversely with the particle energy.

Abstract:
A Generalized Kinetic Theory was proposed in order to have the possibility to treat particles which obey a very general statistics. By adopting the same approach, we generalize here the Kinetic Theory of electrons and phonons. Equilibrium solutions and their stability are investigated.

Abstract:
The electronic structure and selected zone-center phonons in Yb graphite intercalation compound (YbC6) are investigated {theoretically} using density functional calculations and LDA+U approximation for Coulomb correlations in the f shell, and experimentally using angle-resolved photoemission. We find that both in LDA and LDA+U approach the Yb f states are fully occupied providing no evidence for mixed-valent behavior. The obtained theoretical results are in good agreement with photoemission experiments. The 4f states are considerably hybridized both with the Yb 5d and C 2p states resulting in a substantial admixture of Yb f at the Fermi level. Soft Yb phonons, given a noticeable presence of the Yb states at the Fermi level, are probably responsible for the superconductivity recently reported in YbC6.

Abstract:
The defect-induced anharmonic phonon-electron problem in high-temperature superconductors has been investigated with the help of double time thermodynamic electron and phonon Green’s function theory using a comprehensive Hamiltonian which includes the contribution due to unperturbed electrons and phonons, anharmonic phonons, impurities, and interactions of electrons and phonons. This formulation enables one to resolve the problem of electronic heat transport and equilibrium phenomenon in high-temperature superconductors in an amicable way. The problem of electronic heat capacity and electron-phonon problem has been taken up with special reference to the anharmonicity, defect concentration electron-phonon coupling, and temperature dependence. 1. Introduction With the remarkable discovery of high-temperature superconductivity (HTSC) in the Ba-La-Cu-O system with ？K by Bednorz and Mullers there begins a new exciting era in condensed matter physics because of their variety of applications in science and technology. The pairing mechanism in high temperature superconductors (HTS), however, being an unresolved problem, there are large number of experimental evidences that the electron-phonon (e-p) interaction together with strong electronic correlations plays a decisive role in understanding the phenomenon of superconductivity [1]. In the literature, it is reported that e-p coupling plays a crucial role in determining the electron density of states (EDOS) and electronic heat capacity (EHC). The specific heat which can be determined from temperature dependence and the spectrum of electrons and phonons has always been a central one in view of its importance in understanding the low-temperature phenomenon in solids. The total heat capacity of HTS is contributed by lattice heat capacity (LHC) and EHC [2]. The EHC (~ ) is only appreciable at low-temperatures and changes dramatically at the superconducting transition, whereas the phonon contribution dominates at room temperature and is generally undisturbed by the transition at . The Sommerfeld constant provides an important test for proposed theories [3–5], where is the EDOS evaluated at Fermi energy . In the present work, the expressions for EDOS and EHC have been obtained with the help of many body Green's function theory which uses an almost complete Hamiltonian via quantum dynamics of electrons and phonons. 2. The Hamiltonian and Green’s Functions In order to formulate the problem with special reference to HTS, we consider an almost complete (without BCS type) Hamiltonian [6, 7] in the form: where , , , , and

Abstract:
We investigate the interaction of correlated electrons with acoustical phonons using the extended Hubbard-Holstein model in which both, the electron-phonon interaction and the on-site Coulomb repulsion are considered to be strong. The Lang-Firsov canonical transformation allows to obtain mobile polarons for which a new diagram technique and generalized Wick's theorem is used. This allows to handle the Coulomb repulsion between the electrons emerged into a sea of phonon fields (\textit{phonon clouds}). The physics of emission and absorption of the collective phonon-field mode by the polarons is discussed in detail. Moreover, we have investigated the different behavior of optical and acoustical phonon clouds when propagating through the lattice. In the strong-coupling limit of the electron-phonon interaction, and in the normal as well as in the superconducting phase, chronological thermodynamical averages of products of acoustical phonon-cloud operators can be expressed by one-cloud operator averages. While the normal one-cloud propagator has the form of a Lorentzian, the anomalous one is of Gaussian form and considerably smaller. Therefore, the anomalous electron Green's functions can be considered to be more important than corresponding polarons functions, i.e., pairing of electrons without phonon-clouds is easier to achieve than pairing of polarons with such clouds.

Abstract:
Ultrafast laser excited hot electrons can transport energy supersonically far from the region where they are initially produced. We show that this ultrafast energy transport is responsible of the emission of coherent acoustic phonons deeply beneath the free surface of a copper metal sample. In particular we demonstrate that enough energy carried by these hot electrons over a distance as large as 220nm at room temperature in copper can be converted into coherent acoustic phonons. In order to demonstrate this effect, several configurations of time-resolved optical experiments of time of flight of coherent acoustic phonons and of hot electrons have been performed.