Day 2 :
University of Houston, USA
Keynote: Generalizing the harmonic oscillator and Fourier analysis: An infinite family of mutually unbiased bases
Time : 09:00-09:40
Donald J Kouri has completed his PhD from University of Wisconsin in the year 1965. He carries research in the fundamental implications of the Heisenberg uncertainty principle and the resulting applications and also generalized coherent states, quantum theory of atomic and molecular collisions.
We consider canonical transformations from the standard coordinate, x, to new coordinates that either stretch or compress the real line. The guide to our choice of transformation comes from consideration of supersymmetric quantum mechanics and the fact that it shows that any 1-D ground state minimizes the Heisenberg uncertainty product of the new coordinate and conjugate momentum. Using the fact that the transformation is a point transformation, it is easy to obtain the conjugate classical momentum. These are quantized, resulting in Heisenberg-Weyl Lie algebra. In parallel to the connection of the harmonic oscillator eigenstates and the Fourier transform, we obtain a generalization of the Fourier transform kernel which is ideally suited to the harmonic analysis of chirps. In addition, the (improper) eigenstates of the new position and momentum operators, as well as their sum are shown to constitute a mutually unbiased set of basis states. The appearance of the Heisenberg-Weyl Lie algebra also leads to a generalized harmonic oscillator (GHO), whose eigenstates are also eigenstates of the generalized Fourier transform kernel. The ground states of these GHOs are simply generalizations of the Gaussian and share many important properties of the Gaussian. In particular, they are attractor solutions of a Fokker-Planck equation who’s laplacian is simply the kinetic energy operator of the GHO. The simplest form of these ground states is , where N is the normalization factor and the integer, n, ranges from zero on up. The generalized laplacian for the GHO is , . The potential of the GHO is . However, we show that one may also have polynomials (of a specific structure) as the argument of the exponential ground state. We will discuss various possible applications of our results.
Kobe Tokiwa University, Japan
Time : 09:40-10:20
Masayoshi Tanaka did his PhD Physics and currently, is Professor of Clinical Technology and Physics and Collaborative Physicist at RCNP, Osaka University. He got the Prefectural Award of Hyogo for research and education in 2013. He organized the Int. Workshop, HELION97 on polarized 3He beams and gas targets and their application in 1997. He was a guest Researcher at University of Michigan in 2001, CEN (Centre d'études nucléaires de Grenoble in 1990, and at MPI (Max Planck Institut für Kern Physik), Heidelberg in 1982.
The last century was no doubt, an epoch-making century for physics. Guided by the new concept such as the quantum mechanics, and the special and general relativities, the territory of physics was broadened diversely from the elementary particles to the cosmos in size, from 10-6 to 10+8 K in temperature, and from inanimate to animate objects. In particular, the discovery of the atomic nucleus by E. Rutherford in 1911 and the quantum mechanical interpretation of hydrogen atom by N. Bohr in 1913 greatly contributed in opening a new window of physics. Even now, atomic and nuclear physics keep on evolving as heart and soul of the modern physics. Today, I am going to emphasize how deeply nuclear physics research I have committed for long time has been luckily helped by atomic physics in my talk. My first job as a nuclear physicist is to determine the magnetic sub-state populations of the product nucleus implanted in a metallic foil following the nuclear reaction. However, experimental results could not uniquely predict the magnetic sub-state populations. For breaking this difficulty, we must decide the sign of eqQ (electric quadrupolar interaction) of the product nucleus in the metal. This was done by combining the particle-γ angular correlation measurement of this nuclear reaction. Thus, new information on the nuclear wave function of the product nucleus was extracted successfully. We started, after that, developing the polarized 3He ion source for nuclear physics at an intermediate energy region. The device used an ECR (Electron Cyclotron Resonance) ionizer, and laser optical pumping. My experience at MPI, Heidelberg and CEN, Grenoble decisively helped in promoting our project. People from
either domestic (Osaka, Konan, and Niigata) or foreign institutes (Dubna, Madison, and Vancouver) joined us from time to time to contribute to atomic physics as well as nuclear physics. Meanwhile, we succeeded in experimentally proving the principle of electron pumping, which an extended concept of the optical is pumping, i.e., electrons can play a role of photons in the optical pumping. The latest 10 years have been spent on the development of the Hyperpolarized MRI (Magnetic Resonance Imaging) for medical diagnosis as presented in this conference.
University of Lorraine, France
Keynote: Non-particle vlasov codes: Key issues and impact on plasma turbulence modeling for thermonuclear fusion
Time : 10:20-11:00
Alain Ghizzo has received his PhD degree in Plasma Physics in 1987. He is currently a Professor at the University of Lorraine at the Institue Jean Lamour (UMR 7198). He has been performing research in the field of computer experiments in plasma physics. His recent research includes laser-plasma interaction and gyrokinetic models for plasma core physics in tokamaks and astrophysics.
Often referred to as “the fourth state of matter”, plasmas comprise over 99% of the visible universe and are rich in complex nonlinear and collective phenomena. The quest for harnessing fusion energy is a major component of research in the field of plasma physics. Thus the development of fusion as a secure and reliable energy system that is environmentally and economically sustainable is a formidable scientific but also technological challenge today. Although the fundamental laws that determine the behaviour of plasmas, such as Maxwell's equations and those of classical statistical mechanics are well known, obtaining their solution under realistic conditions is a scientific problem of extraordinary complexity. The use of fundamental equations often retains the full nonlinear effects, and space charge and other collective effects can be included self-consistently by coupling charged particles to the field equations via the source terms. For collisionless plasmas, the kinetic model is based on the vlasov equation (supplemented by the Poisson or Maxwell equations). Its numerical integration is one of the key challenges of computational plasma physics. This keynote summarizes the concepts and the latest developments in collisionless semi- Lagrangian vlasov plasma simulations and their impact on phase space topology and on turbulence modeling. Recent advances in simulations of hot fusion plasmas are reviewed, with illustrative examples, chosen from associated research areas as relativistic laser-plasma interaction or micro turbulence in tokamak plasmas. These examples illustrate the challenges in modeling wave- particle interactions in fusion plasmas. High accuracy and resolution are required to correctly model such Landau-type resonances. The challenging nature of plasma physics in general and fusion research in particular leads to establish an inter-disciplinarily research that targets the development of capabilities that “bridge” various areas of plasma physics together with computer science and applied mathematics.