FY2012 Annual Report

Mathematical and Theoretical Physics Unit

Professor Shinobu Hikami



Mathematical and theoretical physics unit studied a random matrix theory, which has wide applications. We obtained the compact formula of the intersection numbers in the moduli space of the p-spin curves, for arbitrary values of p. The large p limit was evaluated and the density of state of the black hole was obtained from this expression.

This unit studied the scanning near field optical microscope (SNOM) images of the yeast by the tunable wave lengths lasers, particularly for the infrared (IR) wave length (five and ten micrometer- finger print area). Resolution of measurements improved by the higher harmonics.

The detector for the optical infrared wave was made by the lithography equipment in OIST.

1. Staff

  • Dr. Shinobu Hikami, Professor
  • Dr. Reuven Pnini, Researcher
  • Dr. Ayumi Kikkawa, Researcher
  • Dr. Momoka Higa, Technician
  • Dr. Susumu Komiyama, Researcher
  • Dr. Hirofumi Nema, Researcher
  • Kaori Yamashiro, Research Administrator

2. Collaborations

  • Theme: Random matrix theory project
    • Type of collaboration: Joint research
    • Researchers:
      Professor Edouard Brezin (Ecole Normale Superieure)
  • Theme: Equipment of infrared microscope
    • Type of collaboration: Joint research
    • Researchers:
      • Professor Satoshi Sawai (University of Tokyo)
      • Researcher Susumu Komiyama (University of Tokyo)

3. Activities and Findings

3.1 Random matrix theory

We find the compact formula of the intersection numbers in the moduli space of the p-spin curves, for arbitrary values of p, from the calculation of the correlation functions of RMT with external source. The theory is shown to be equivalent to gauged supersymmetric minimal conformal field theory, and Wess-Zumino-Witten theory, with the relation of p=k+2, where k is a level of SU(2). The large p limit was evaluated and the density of state of the black hole was obtained from this expression.

3.2 Measurement of yeast cell by SNOM

By the scanning near field optical microscope, with the use of infrared CW laser of 9.5um, we measure the yeast cell and mitochondria. We confirm the sensitivity of order 10nm from the measurement of fourth higher harmonics (1MHz) and observe the proteins and enzymes. Changing the wave length of tunable laser, we measure the absorption of the materials inside the cell.


Figure 1: Images of SNOM by infrared laser for the mitochondria of yeast cell. The forth harmonics has better precision.

3.3 Device by the lithography for Infrared detector

Lithography for the infrared detector by electron bean lithograpy (EBL) in the clean room at OIST is made on the GaAs wafer. This device will be used for the detection of infrared wave around 10-15um, and will be mounted in scanning tunneling microscope of OIST.


Figure 2:  The central part of the infrared detecting device made by EBL in OIST.

4. Publications

4.1 Journals

  1. Brezin E. and Hikami S.  The intersection numbers of the p-spin curves from random matrix theory, JHEP 02,035 (2013).
  2. Kajihara Y, Nakajima T, Wang Z, and Komiyama S. Terahertz single-photon detectors based on quantum wells, J. Appl. Physics.,113, 136506 (2013).

4.2 Books and other one-time publications

  1. Hikami S., “Logic and method of modern physical science”, School of Graduate Studies, the Open University of Japan, Chapter 9,10,11. (2013).

4.3 Oral and Poster Presentations

  1. Hikami S., Random matrix theory and its development, Maskawa Institute Seminar, Kyoto University of Industry, Nov. 16. 2012

5. Intellectual Property Rights and Other Specific Achievements

Nothing to report

6. Meetings and Events

6.1 RMT2012

  • Date: April 15-21, 2012
  • Organizer: Hikami S.
  • Venue: OIST Seaside House
  • Lecturers and Speakers:
    • Dr. E. Brezin (lpt. Ecole Normale Superieure)
    • Dr. R.Monnason (lpt. Ecole Normale Superieure)
    • Dr.A.Morozov, (ITEP, Moscow)
    • Dr. S. Ganguli ( Stanford)
    • Dr. P.Wiegmann (Chicago Univ.)
    • Dr. J.Zinn-Justin (Saclay)
    • Dr.H.Sompolinsky (Hebrew Univ.)
    • Dr. S. Cocco (lpt. Ecole Normale Superieure)
    • Dr. M.Vergassola (Pasteur Inst.)

6.2 Japan-Israel bi-national conference “Quantum Phenomena”

  • Date: March 10-13, 2013
  • Venue: OIST Seaside House
  • Organizer: Hikami S.
  • Co-organizers:  Avishai Y., Entin-Wohlman O., Tarucha S., Otsuki T., Katsumoto S. Orgad D.
  • Speakers:
    • Dr. Seigo Tarucha, "Manipulation of Quantum Coherence and Entanglement with Quantum Dots"
    • Dr. Yasuhiro Utsumi, "Full-counting statistics for molecular junctions: the fluctuation theorem and singularities "
    • Dr. Ora Entin-Wohlman, "Thermoelectric transport in three-terminal junctions"
    • Dr. Oded Agam, "Manifestations of electron interactions in photogalvanic effect in chiral nanotubes"
    • Dr. Yoshiro Hirayama, "Nuclear spin -environmental interactions in semiconductor systems"
    • Dr. Michihisa Yamamoto, "Measurement of Kondo phase with a two-path interferometer"
    • Dr. Yigal Meir, "Emergence of localized states and alternating Kondo effects in quantum point contacts"
    • Dr. Mikio Eto, " Kondo screening cloud in an Aharonov-Bohm ring with an embedded quantum dot"
    • Dr. Efrat Shimshoni, "Nernst Effect as a Signature of Quantum Fluctuations in Quasi-1D Superconductors"
    • Dr. Hiraku Toida, "Circuit quantum electrodynamics using a semiconductor quantum dot coupled to a superconducting resonator"
    • Dr. Russell Deacon, "Cooper pair splitting in parallel quantum dot Josephson junctions"
    • Dr. Ophir Auslender, "Disorder induced power-law behavior of individual superconducting vortices on a twin boundary: using magnetic force microscopy to study directed polymers in random media"
    • Dr. Nobuhiko Nishida, "Superconductivity seen from STS Studies of Vortex Core states in Bi2Sr2CaCu2Ox and YNi2B2C "
    • Dr. Hideaki Obuse, "Boundary critical phenomena at the Anderson transition of topological insulators"
    • Dr. Ken-ichiro Imura, "Why does the gapless state appear only on the surface?"
    • Dr. Eran Sela, "Topological phases and Majorana fermions in strongly interacting quantum wires with spin-orbit coupling"
    • Dr. Tetsuo Hanaguri, "Landau-level spectroscopies on topological insulators "
    • Dr. Kensuke Kobayashi, "Shot Noise in Spin-dependent Transport through Mesoscopic Systems"
    • Dr. Amnon Aharony, “Spin Filtering”
    • Dr. Yuji Matsuda, "Quantum spin liquid: novel quantum phase in a Mott insulator with triangular lattice"
    • Dr. Eldad Bettelheim, "Conformal invariance in two dimensional quantum liquids"
    • Dr. Eyal Buks, "Cavity Optomechanics"
    • Dr. Dror Orgad, "Enhanced pairing in the plaquette Hubbard model"
    • Dr. Richard Berkovits, "Entanglement entropy of low-lying excitation in localized interacting system: Signature of Fock space delocalization"
    • Dr. Boris Shapiro, "Transport of cold atoms in the presence of disorder"
    • Dr. Akira Furusaki, "Anderson localization in two-dimensional electron gas with strong spin-orbit coupling"
    • Dr. Zvi Ovadyahu, "Testing for many-body localization in electronic system "
    • Dr. Yasuhiro Tokura, "Initialization of quantum spins under non-equilibrium bias condition"
    • Dr. Jeng-Chung Chen, "Spin-polarized currents in parallel coupled double quantum point contacts"
    • Dr. Yishay Manassen, "Electron spin resonance scanning tunneling microscopy on Si(111) containing C and O defects"
    • Dr. Toshimasa Fujisawa, "Electron-nuclear feedback in a double quantum dot"
    • Dr. Takashi Nakajima, "Gate-Controlled Spin Precession in Quantum Hall Edge Channels"
    • Dr. Keith Slevin, "Finite size scaling analysis of the Chalker-Coddington model"
    • Dr. Naokazu Shibata, "Fractional quantum Hall states and valley skyrmions in graphene"
    • Dr. Tohru Kawarabayashi, "Chiral symmetry and robust zero-mode Landau levels in disordered graphene and related materials"
    • Dr. Yshai Avishai, "Feshbach Resonance in a Tight-binding Model"

6.3 Seminar

  • Date: March 5, 2013
  • Venue: OIST Campus Lab1 C016
  • Speaker:
    • Dr. B. Shapiro (Technion-Israel Institute of Technology),
      “Fluctuating electromagnetic fields”

6.4 Seminar

  • Date: Jan. 24, 2013
  • Venue: OIST Campus Lab1 C209
  • Speaker:
    • Dr. Sergiu Amarie, (NeaSpec),
      “Biomedical nano-imagining and spectroscopy”

6.5 Seminar

  • Date: December 11,2012
  • Venue: OIST Campus Lab1 C015
  • Speaker:
    • Dr. Hiroshi Kubota (Kumamoto Univ.),
      “New Silicon-island Kyushu Toward the QTAT production site in Japan”

6.6 Seminar

  • Date: December 11,2012
  • Venue: OIST Campus Lab1 C015OIST Campus Lab1 C016
  • Speaker:
    • S. Komiyama (University of Tokyo),
      “Circuit QED in a Double Quantum Dot System”