Recently there have been profound developments in the understanding and interpretation of liquids and soft matter centered on constituents with sho- range interactions. Ionic soft matter is a class of conventional condensed soft matter with prevailing contribution from electrostatics and, therefore, can be subject to possible long-range correlations among the components of the - terial and in many cases crucially affecting its physical properties. Among the most popular representatives of such a class of materials are natural and synthetic saline environments, like aqueous and non-aqueous electrolyte - lutions and molten salts as well as variety of polyelectrolytes and colloidal suspensions. Equally well known are biological systems of proteins. All these systems are examples of soft matter strongly in?uenced, if not dominated, by long-range forces. For more than half of century the classical theories by Debye and Hückel as well as by Derjaguin, Landau, Verwey and Owerbeek (DLVO) have been at the basis of theoretical physical chemistry and chemical engineering. The substantial progress in material science during last few decades as well as the advent of new instrumentation and computational techniques made it apparent that in many cases the classical theories break down. New types of interactions (e.g. hydrodynamic, entropic) have been discovered and a number of questions have arisen from theoretical and experimental studies. Many of these questions still do not have de?nite answers.

This book collects selected papers written by invited and plenary speakers of the 15th International Congress on Mathematical Physics (ICMP) in the aftermath of the conference. In extensive review articles and expository texts as well as advanced research articles the world leading experts present the state of the art in modern mathematical physics. New mathematical concepts and ideas are introduced by prominent mathematicalphysicists and mathematicians, covering among others the fields of Dynamical Systems, Operator Algebras, Partial Differential Equations, Probability Theory, Random Matrices, Condensed Matter Physics, Statistical Mechanics, General Relativity, Quantum Mechanics, Quantum Field Theory, Quantum Information and String Theory. All together the contributions in this book give a panoramic view of the latest developments in mathematical physics. They will help readers with a general interest in mathematical physics to get an update on the most recent developments in their field, and give a broad overview on actual and future research directions in this fascinating and rapidly expanding area.

A comprehensive collection of papers on theoretical aspects of electronic processes in simple and synthetic metals, superconductors, bulk and low-dimensional semiconductors under extreme conditions, such as high magnetic and electric fields, low and ultra-low temperatures. The main emphasis is on low-dimensional conductors and superconductors, where correlated electrons, interacting with magnetic or nonmagnetic impurities, phonons, photons, or nuclear spins, result in a variety of new physical phenomena, such as quantum oscillations in the superconducting state, Condon instability, Skyrmions and composite fermions in quantum Hall effect systems, and hyperfine field-induced mesoscopic and nanoscopic phenomena. Several new experimental achievements are reported that promise to delineate future trends in low temperature and high magnetic field physics, including the experimental observation of the interplay between superconductivity and nuclear spin ordering at ultra-low temperatures, new observations of Condon domains in normal metals, and an experimental proposal for the realisation of isotopically engineered, semiconductor-based spin-qubit elements for future quantum computation and communication technology.

This book concisely presents the latest trends in the physics of superconductivity and superfluidity and magnetism in novel systems, as well as the problem of BCS-BEC crossover in ultracold quantum gases and high-Tc superconductors. It further illuminates the intensive exchange of ideas between these closely related fields of condensed matter physics over the last 30 years of their dynamic development. The content is based on the author’s original findings obtained at the Kapitza Institute, as well as advanced lecture courses he held at the Moscow Engineering Physical Institute, Amsterdam University, Loughborough University and LPTMS Orsay between 1994 and 2011. In addition to the findings of his group, the author discusses the most recent concepts in these fields, obtained both in Russia and in the West. The book consists of 16 chapters which are divided into four parts. The first part describes recent developments in superfluid hydrodynamics of quantum fluids and solids, including the fashionable subject of possible supersolidity in quantum crystals of 4He, while the second describes BCS-BEC crossover in quantum Fermi-Bose gases and mixtures, as well as in the underdoped states of cuprates. The third part is devoted to non-phonon mechanisms of superconductivity in unconventional (anomalous) superconductors, including some important aspects of the theory of high-Tc superconductivity. |The last part considers the anomalous normal state of novel superconductive materials and materials with colossal magnetoresistance (CMR). The book offers a valuable guide for senior-level undergraduate students and graduate students, postdoctoral and other researchers specializing in solid-state and low-temperature physics.

This invaluable book contains pedagogical articles on the dominant nonstochastic methods of microscopic many-body theories — the methods of density functional theory, coupled cluster theory, and correlated basis functions — in their widest sense. Other articles introduce students to applications of these methods in front-line research, such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics that are of current relevance. The book addresses the striking lack of pedagogical reference literature in the field that allows researchers to acquire the requisite physical insight and technical skills. It should, therefore, provide useful reference material for a broad range of theoretical physicists in condensed-matter and nuclear theory.

Focusing on recent developments and current priorities in various areas of physics, this book presents advances in high temperature superconductivity and super fluidity, physics of low dimensional systems, Bose-Einstein condensation, quantum dots, collective modes in finite systems, coherent correlations of particles, coherence of atomic levels under extreme conditions, tensor correlations in nuclei, super-heavy nuclei, the effect of relativity in nuclear structure, molecular dynamics and phase transitions in solids, nuclei and quarks and QCD dynamics for hadrons and hadronic matter.