special lecture and seminar announcement @ Hongo campus, Univ. of Tokyo
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Dear Colleagues,
The following is the special lecture and seminar announcement.
Please feel free to join us.
Best regards,
Takashi
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Special lecture
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Lecturer: Ryoji Okamoto (Professor Emeritus, Kyushu Institute of Technology)
Title: "Nucleon-nucleon interaction and effective interaction"
Place: Room 201a, Faculty of Science Build.1, Hongo, University of Tokyo
Date:
7/4(Wed): 13:00 - 14:30, 14:50 - 16:20
7/5(Thu): 10:30 - 12:00, 13:00 - 14:30, 14:50 - 16:20 (seminar)
7/6(Fri): 10:30 -12:00, 13:00 - 14:30, 14:50 - 16:20
The details can be found at the following web site:
http://www.phys.s.u-tokyo.ac.jp/curriculum/H24shuchu-list.htm
http://www.s.u-tokyo.ac.jp/ja/current/lecture.html?department=grad-phys
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Seminar
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Lecturer: Dr. Ryoji Okamoto (Professor Emeritus, Kyushu Institute of
Technology)
Date: July 5th (Thursday) 14:50 - 16:20
Place: Room 201a, Faculty of Science Build.1, Hongo, University of Tokyo
Title: Recursion method for deriving effective interaction and its
application to eigenvalue problem
Abstract:
It is often useful to recast the full many-body problem of a quantum
system described by a Hamiltonian $H$ in the form of the effective
interaction acting within a chosen model space.
The central problem of the effective-interaction theory is how to
calculate the so-called $\widehat Q$ box introduced by Kuo et al. We
first show that the Hamiltonian $H$ is transformed to a block
tri-diagonal form in terms of submatrices of small dimensions.
With this transformed Hamiltonian, we next show that, making use of
recursion methods, the $\widehat Q$ box can be expressed as a
continued fraction form and/or a simple perturbative form with the
renormalized vertices and propagators. This procedure for the
$\widehat Q$ box ensures the exact calculation of the $\widehat Q$ box
if the dimension of the relevant Hilbert space is finite.
We apply this approach to solving the eigenvalue problem for a given
Hamiltonian $H$. We introduce a function $g(E)$ of an energy variable
$E$. This function is determined by the $\widehat Q$ box and has a
characteristic that the eigenvalues are represented as "resonance"
positions of $g(E)$.
We discuss a possibility of applying this method to solving an
eigenvalue problem with a huge dimension.
Contact person: Takaharu Otsuka and Takashi Abe
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