This book is a collection of the papers presented at the workshop on "Symmetry and Heterogeneity in High Tc Superconductors" directed by Antonio Bianconi and Alexander F. Andreev in collaboration with K. Alex Müller and Giorgio Benedek. Philip B. Allen, Neil W. Ashcroft, Alan R. Bishop, J. C. Séamus Davis, Takeshi Egami, Francesco Iachello, David Pines, Shin-ichi Uchida, Subodh R. Shenoy, chaired hot sessione contributing to the success of the workshop. The object of the workshop was the quantum mechanism that allows the macroscopic quantum coherence of a superconducting condensate to resist to the attacks of high temperature. Solution to this problem of fundamental physics is needed for the design of room temperature superconductors, for controlling the decoherence effects in the quantum computers and for the understanding of a possible role of quantum coherence in living matter that is debated today in quantum biophysics. The discussions in the informal and friendly atmosphere of Erice was on new experimental data showing that high T in doped cuprate perovskites is c related with the nanoscale phase separation and the two component scenario, the two-band superconductivity in magnesium diboride and the lower symmetry in the superconducting elements at high pressure.

Key chapters by Neil Ashcroft and K. Alex Mueller

Electronic and Exchange-Like Pairing Scenarios.- Symmetry and Higher Superconductivity in the Lower Elements.- Feshbach Shape Resonances in Multiband High Tc Superconductors.- Modelling Cuprate Gaps in a Composite Two-Band Model.- Multi-Gap Superconductivity on MgB2.- Anomalous Electron-Phonon Interaction.- ELectron-Lattice Coupling in the Cuprates.- Symmetry Breaking, Non-Adiabatic Electron-Phonon Coupling and Nuclear Kinetic Effect on Superconductivity of MgB2.- Phase Separation and Two Components Cuprates.- Microscopic Phase Separation and Two Type of Quasiparticles in Lightly Doped La2?xSrxCuO4 Observed by Electron Paramagnetic Resonance.- Phase Separation in Cuprates Induced by Doping, Hydrostatic Pressure or Atomic Substitution.- Structural Symmetry, Elastic Compatibility, and the Intrinsic Heterogeneity of Complex Oxides.- A Case of Complex Matter: Coexistence of Multiple Phase Separations in Cuprates.- Anisotropy of the Critical Current Density in High Quality YBa2Cu3O7?? Thin Film.- Symmetry of the Condensate.- Symmetry of High-Tc Superconductors.- Evidence for d-Wave Order Parameter Symmetry in Bi-2212 from Experiments on Interlayer Tunneling.- Exotic Superconductivity.- Electronic State in Co-Oxide-Similar to Cuprates?.- Oxide Superconductivity.- Superconductivity Versus Antiferromagnetic SDW Order in the Cuprates and Related Systems.