Title: Computational studies on high temperature superconductivityLecturer: Kazuhiko Kuroki, Professor, University of Electro-Communication, (UEC), Tokyo
Superconductivity is a phenomenon in which the resistivity disappears at a certain transition temperature Tc. In conventional superconductors, Tc is as low as (O(10K), but in the past quarter of a century, two families of high Tc superconductors, cuprates (max Tc～150K) and the iron pnictides (max Tc～55K), have been discovered. It is widely believed that theoretical understanding of these materials can lead to finding new, even higher Tc materials. In the present lecture, we start with some basic learning on solid state physics and superconductivity in the first half. In the second half, some of the essential experimental observations of the actual high Tc materials are presented, and the lecture will focus on how these experiments can be understood through computational approaches based on model Hamiltonians. Finally, a possible way of reaching even higher Tc is discussed.
Title: Journey to the Wonderful World of Quantum ElectrodynamicsLecturer: Alexander TITOV, Dubna, Russia
The aim of our lecture is to make a journey to the impressive world of Quantum Electrodynamics (QED). QED, being the relativistic quantum field theory, describes how light and matter interact and it is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electrodynamics giving a complete account of matter and light interaction. In technical terms, QED can be described as a perturbation theory of the electromagnetic quantum processes. We plan to show how to derive the equations of QED from the Lagrange formalism, the appearance of the spin/magnetic moment of electrons, the prediction of anti-particles. Then we will formulate the Feynman rules for the evaluation of the amplitudes of physical processes and illustrate how to apply them to calculations of probabilities of elastic photon-electron scattering (Compton scattering) and electron-positron creation in photon-photon interaction (Breit-Wheeler process) in a second order of perturbation theory. We will also discuss di-muon production in interaction of photons and electrons with atomic nuclei. Then we will move to the non-perturbative solution of QED. We will derive solution of Dirac equation in a (strong) electromagnetic (EM) field of a plane wave (Volkov solution). Such a strong EM field may be interpreted as a field of laser radiation. We will show that in such a field the properties of the electron are changed drastically. The electron mass increases and its three-momentum transforms to the quasi-momentum. The quantum mechanical processes are also modified significantly. As examples, we will show how such modifications apply to photon and neutrino emissions by electron in a strong EM field, to electron-positron production in interaction of photon with strong laser fields, and to particle-decay properties. All these effects are relatively new, but they are widely discussed now, and, hopefully, they will shed light on the non-trivial, non-perturbative effects of QED.
Title: Physics of Core-Collapse SupernovaeLecturer: Kohsuke SUMIYOSHI, Numazu College of Technology and Theory Group at KEK
Core collapse supernovae are one of the most energetic phenomena in astronomy and physics. Supernovae occur as a consequence of the gravitational collapse of massive stars of about 20 solar masses at the end of stellar evolution. The supernova explosion mechanism is still unknown after more than four decades of investigations. In this lecture, I introduce the broad and interesting features of core-collapse supernovae and describe the physics at extreme conditions inside supernova cores. I will try to explain the role of hot and dense matter in the dynamics and to demonstrate that the neutrino emission is one of the essential aspects for the explosion as well as the observation. I would also like to talk about the numerical challenge of supernova simulations on high-performance supercomputers.
Title: The Physics of ComplexityLecturer: Zhensho YOSHIDA, University of Tokyo
In the history going back to Galilei and Newton, physics gained triumphs in describing the "cosmos"---the periodic movements of planets and similar regular motions in various systems. However, we have yet to write the theory of the other form of motion ---a more general actuality of events in nature and society that is the so-called "chaos". We must speak of what the theories of sciences have understood; we must speak of the limits of their legitimacy; we shall have to speak of what these theories are leaving in abeyance. Then, and only then, we can determine the realm in which the cosmos and chaos are not disjunct: the complexity is not eliminated from the scope of studies. Beneath the complexity of actual phenomena, there is a mathematical structure that is called nonlinearity---this is the main theme of this lecture. The term nonlinear is worded by a negation form ---it is not a descriptive (deistic) word characterizing a particular property, but it is a distinctive word indicating opposition to linear. The meaning of nonlinear is infinitely wide as a vague area, and is not bound to a concrete frame. Therefore, when we say "mathematical structure that is nonlinear", we do not mean that there is a prescribed structure giving a framework of the theory, but we are paying attention to the unboundedly developing differences from linearity. We will critically analyze the structure of linear theory and reveal its limitations. By this process, the meaning of nonlinear (and, simultaneously, linear) will become more clear and precise. It is hoped that partly through these arguments, the complexity that linear theory has abandoned might be revived on the horizon of science.
[from Z. YOSHIDA, Nonlinear Science-the challenge of complex systems (Springer, 2010)]