This book first introduces a single polaron and describes recent achievements in analytical and numerical studies of polaron properties in different e-ph models. It then describes multi-polaron physics as well as many key physical properties of high-temperature superconductors, colossal magnetoresistance oxides, conducting polymers and molecular nanowires, which were understood with polarons and bipolarons.

This book reviews recent developments in the field of polarons, starting with the basics and covering a number of active directions of research. It integrates theory and experimental results.

This book presents recent research results on the illustrious verge of polaron science, which is broadly applied in condensed matter physics, solid state physics, and chemistry fields. It covers the modern progress of the polaron effect in various classes of materials. This book provides a thorough overview of the recent advancements in the polarons arena, and presents several active forms of guidance of scrutiny developed by well-known researchers. It describes interesting topics related to the new physical phenomena, experimental results, and applications of polarons. The scope includes both theoretical models and experimental works on different aspects of polarons, manifesting in conducting polymers, functionalized nanowires, glasses and their nanocomposites, organic semiconductors, semiconducting nanostructures, manganites, ferrites, transition metal oxides, high-temperature superconductors, colossal magnetoresistance oxides, and magnetic semiconductors. A collective of authoritative research articles provide recent achievements of theoretical models and experimental realizations of polaron properties in solid state physics and chemistry. They involve substantial research varying from single polaron phenomena to multi-polarons problems in advanced materials. This book will be beneficial as a reference to support an inclusive perspective of the polaron phenomena in advanced materials and will be of prodigious significance to a broad range of researchers in condensed matter physics and material sciences.

Written for researchers and academics, this monograph provides a detailed introduction to the strong-coupling theory of high-temperature superconductivity.

An enormous theoretical effort has been made to treat electron-phonon coupled systems, with particular emphasis on Many Body aspects for dense electron systems, taking into account continuum as well as lattice polaron effects. Treating such aspects of polaron theory has been made possible because of powerful Many Body techniques which include: Exact Diagonalization techniques, Quantum Monte Carlo approaches, Density Matrix renormalization group and Dynamical Mean Field Theory. All these advances in polaron theory needed to be accompanied by: (i) an equally important advance in material research which produced many new materials such as the high Tc cuprates, the manganites and nickelates and the fullerines; (ii) as well as significant advances in the refinement of experimental analysis and, in particular, the spectroscopic means such as Angel Resolved Photoemission Spectroscopy, X Ray Absorption Spectroscopy (EXAFS, XANES), Pulsed Neutron Diffraction measurements allowing to study the local dynamical lattice de-formations and optical spectroscopy including time resolved measurements. The scope and purpose of this publication is to review both these theoretical and experimental advances which occurred over the last few decades and to introduce the study of such systems, where both strong electron-electron correlations and large electron-phonon coupling strengths play important roles.

The 1982 Antwerp Advanced Study Institute on "Physics of Polarons and Excitons in Polar Semiconductors and Ionic Crystals" took place from July 26 till August 5 at the Conference Center Priorij Corsen donk, a restored monastery, close to the city of Antwerp. It was the seventh Institute in our series which started in 1971. This Advanced Study Institute, which was held fifty years after Landau introduced the polaron concept, can be considered as the third major international symposium devoted to the physics of pola rons. The first such symposium took place in St. Andrews in 1962 under the title "Polarons and Excitons" [I]. The early theoretical developments related to polarons were reviewed in depth at this meeting; the derivation of the polaron hamiltonian by Frohlich, the Frohlich weak coupling theory (and the equivalent weak coupling canonical transformations), the Landau-Pekar and Bogolubov strong coupling theory and the Feynman polaron model formulated with his path integrals. The main emphasis was on the polaron self-energy, effective mass and mobility. From the experimental side the first evidence for polaron effects was provided by the pioneering cyclotron and mobility measurements o~ the silver halides by F. e. Brown and his group. Also the significance of polaron effects for the under standing of excitons in ionic crystals was a central topic in St. Andrews. The second Advanced Study Institute concerning polaron physics was organized at the University of Antwerp (R. U. C. A.

We review the Dynamical Mean Field Theory of the Holstein Polaron Problem in order to compute the small polaron Green's functions. The Renormalized Perturbation Expansion (RPE) play a central role and allows to compute all the local and non local Green's functions for the electron and the small polaron, for finite or infinite size systems, with periodic or non periodic boundary conditions. We introduce a restricted basis for the phonons to study the decoupling scheme of the Green's functions in a Local Approximation via exact diagonalizations. As a bonus, we furnish all the C/C++ programs built step by step, from a pedagogical point of view.