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Ohtsuki Tomi

  (大槻 東巳)

Profile Information

Affiliation
Professor, Faculty of Science and Technology, Department of Engineering and Applied Sciences, Sophia University
Degree
Doctor of Philosophy(The University of Tokyo)
理学修士(東京大学)
理学博士(東京大学)
Researcher number
50201976
J-GLOBAL ID
200901008827204586
researchmap Member ID
1000082891
External link

I took ph.D on the quantum Hall effect at Univ. Tokyo.
I studied numerical scaling methods while working at PTB Germany as a post doctral fellow.
I developed scaling of the level statistics at Osaka and Toho universities.
After moving to Sophia University, I have been studing the localization and conductance scaling properties. The main focus of recent research is on the topological insulators and superconductors.

Tomi Ohtsuki, Doctor of Science (University of Tokyo, 1989), is Professor of physics at Sophia University, Tokyo, where he conducts theoretical and computational researches in condensed matter physics. His recent research focuses on quantum transport phenomena such as the Anderson transition, conductance fluctuations, Hall and spin Hall effects in nanoscale systems. He has taught physics for more than 15 years in several universities and graduate schools. His research has been published by Physical Review Letters, Physical Review B, Physics Reports, and others.
The main classes he has are mechanics, electromagnetics, linear algebra, statistical physics as well as solid state physics.

(Subject of research)
Numerical Study of Anderson transitions
spin related quantum transport phenomena

Research Interests

 7

Research Areas

 1

Awards

 8
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Papers

 205
  • T Ohtsuki, K Slevin, T Kawarabayashi
    ANNALEN DER PHYSIK, 8(7-9) 655-664, 1999  
    A review of recent progress in numerical studies of the Anderson transition in three dimensional systems is presented. From high precision calculations the critical exponent nu for the divergence of the localization length is estimated to be nu = 1.57 +/- 0.02 for the orthogonal universality class, which is clearly distinguished from nu = 1.43 +/- 0.03 for the unitary universality class. The boundary condition dependences of some quantities at the Anderson transition are also discussed.
  • T Ohtsuki, K Slevin, T Kawarabayashi
    JOURNAL OF PHYSICS-CONDENSED MATTER, 10(49) 11337-11343, Dec, 1998  Peer-reviewed
    The nature of the critical point of the Anderson transition in high magnetic fields is discussed with an emphasis on scale invariance and universality of the critical exponent. Special attention is paid to the distribution function of the conductance which becomes size and model independent at the critical point. The fractal properties of the wave function which are related to scale invariance are also discussed.
  • T Kawarabayashi, B Kramer, T Ohtsuki
    JOURNAL OF PHYSICS-CONDENSED MATTER, 10(49) 11547-11550, Dec, 1998  Peer-reviewed
    The Anderson transitions in a random magnetic field in three dimensions are investigated in detail by means of the transfer-matrix method with high accuracy. Both systems with and systems without an additional random scalar potential are considered. We find the critical exponent nu for the localization length to be 1.45 +/- 0.09 with a strong random scalar potential. Without it, the exponent is smaller but increases with the system size and extrapolates to the above value within the error bars. These results support the conventional classification of universality classes according to symmetry. The mobility edge trajectory in the random magnetic field is also obtained.
  • J Yoshida, T Ohtsuki, Y Ono
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 67(11) 3886-3890, Nov, 1998  
    Ballistic transport properties in a two dimensional electron gas are studied numerically, where magnetic fields are perpendicular to the plane of two dimensional electron systems and periodically modulated both in x and y directions. We show that there are three types of trajectories of classical electron motions in this system; chaotic, pinned and runaway trajectories. Tt is found that the runaway trajectories can explain the peaks of magnetoresistance as a function of external magnetic fields, which is believed to he related to the commensurability effect between the classical cyclotron diameter and the period of magnetic modulation. The similarity with and difference from the results in the antidot lattice are discussed.
  • Akita Yasuyuki, Ohtsuki Tomi
    J Phys Soc Jpn, 67(8) 2954-2955, Aug 15, 1998  
  • Takeshi Nakanishi, Tomi Ohtsuki
    Physica B: Condensed Matter, 249-251 801-804, Jun, 1998  
  • T Kawarabayashi, B Kramer, T Ohtsuki
    PHYSICAL REVIEW B, 57(19) 11842-11845, May, 1998  Peer-reviewed
    The Anderson transition in three dimensions in a randomly varying magnetic flux is investigated in detail by means of the transfer-matrix method with high accuracy. Systems both with and without an additional random scalar potential are considered. We find a critical exponent of nu=1.45+/-0.09 with random scalar potential. Without it, nu is smaller bur increases with the system size and extrapolates within the error bars to a value close to the above. The present results support the conventional classification of universality classes due to symmetry. [S0163-1829(98)09219-4].
  • Nakanishi, T., Ohtsuki, T.
    Physica B: Condensed Matter, 249-251, 1998  
  • Varga, I, Y Ono, T Ohtsuki, J Pipek
    PHYSICA STATUS SOLIDI B-BASIC RESEARCH, 205(1) 373-376, Jan, 1998  Peer-reviewed
    The shape analysis of the energy spacing distribution P(s) obtained from numerical simulation of two-dimensional disordered electron systems subject to strong magnetic fields is performed. In the present work we reanalyze the data obtained in a previous publication. Special moments of the P(s) function related to Renyi entropy differences show a novel scale invariant relation that is attributed to the presence of one-parameter scaling. This relation seems to show both deviations and universality depending on which Landau band is considered and whether the disorder is correlated or uncorrelated. Furthermore, our analysis shows the existence of an huge, however, irrelevant length scale in the case of the second lowest Landau band and no disorder correlations that completely disappear with the introduction of disorder correlations in the range of one magnetic length.
  • Tohru Kawarabayashi, Bernhard Kramer, OHTSUKI TOMI
    Physical review. B, Condensed matter, 57(19) 11842, 1998  
  • K Slevin, T Ohtsuki
    PHYSICAL REVIEW LETTERS, 78(21) 4083-4086, May, 1997  
    We report a finite size scaling study of the Anderson transition. Different scaling functions and different values for the critical exponent have been found, consistent with the existence of the orthogonal and unitary universality classes which occur in the field theory description of the transition. The critical conductance distribution at the Anderson transition has also been investigated and different distributions for the orthogonal and unitary classes obtained.
  • T Ohtsuki, T Kawarabayashi
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 66(2) 314-317, Feb, 1997  
    Diffusion of electrons in three-dimensional disordered systems is investigated numerically for all three universality classes, namely, orthogonal, unitary and symplectic ensembles. The second moment of the wave packet (r(2)(t)) at the Anderson transition is shown to behave as similar to t(a)(a approximate to 2/3). From the temporal autocorrelation function C(t), the fractal dimension D-2 is deduced, which is almost half the value of the space dimension for all of the universality classes.
  • Takeshi Nakanishi, Tomi Ohtsuki, Tohru Kawarabayashi
    Journal of the Physical Society of Japan, 66(4) 949-952, 1997  Peer-reviewed
    Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. The correction to the conductivity due to inelastic scatterings by oscillating potentials is shown to be a universal function of the frequency ω. which is consistent with the weak localization prediction[formula omitted] log ω. © 1997, THE PHYSICAL SOCIETY OF JAPAN. All rights reserved.
  • OHTSUKI TOMI, Kawarabayashi Tohru
    Butsuri, 51(11) 821-828, Nov, 1996  
  • T Kawarabayashi, T Ohtsuki, K Slevin, Y Ono
    PHYSICAL REVIEW LETTERS, 77(17) 3593-3596, Oct, 1996  
    The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent nu of the localization length is extracted and estimated to be nu 1.3 +/- 0.2. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution P(s) at the critical point is found to be different from that for the orthogonal ensemble, suggesting that the breaking of spin rotation symmetry is relevant at the critical point.
  • Y Ono, T Ohtsuki, B Kramer
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 65(6) 1734-1743, Jun, 1996  
    The scaling property of level statistics in the quantum Hall regime, i.e. 2D disordered electron systems subject to strong magnetic fields. is analyzed numerically in the light of the random matrix theory. The energy dependences of the effective level repulsion parameter, the two level correlation, the GUE-GOE crossover parameter, and the rigidity (or Delta(3)-statistics) of the level distributions are investigated for different system sizes by unfolding the original data and by dividing the unfolded spectrum into small regions. It is shown that the critical exponent of the localization length as a function of energy can be determined through the energy dependence of the level statistics. The analyses are carried out not only for the lowest Landau band (LB) but also for the second lowest LB. Furthermore the effect of finite range of disordered potential is studied. The short-ranged potential case in the second lowest LB is found to be pathological as in other studies of critical behavior, and it is confirmed that this pathological behavior is improved in the case of disordered potential with finite ranges.
  • T Kawarabayashi, T Ohtsuki
    PHYSICAL REVIEW B, 53(11) 6975-6978, Mar, 1996  Peer-reviewed
    Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal autocorrelation function are examined. At the critical point, the autocorrelation function exhibits the power-law decay with a nonconventional exponent alpha, which is related to the fractal structure in the energy spectrum and in the wave functions. In the metallic regime, the present results imply that transport properties can be described by the diffusion equation for normal metals.
  • Tohru Kawarabayashi, OHTSUKI TOMI
    Physical review. B, Condensed matter, 53(11) 6975-6978, Mar, 1996  
  • Tohru Kawarabayashi, Tomi Ohtsuki
    Physical Review B - Condensed Matter and Materials Physics, 53(11) 6975-6978, 1996  Peer-reviewed
    Diffusion of electrons in two-dimensional disordered systems with spin-orbit interactions is investigated numerically. Asymptotic behaviors of the second moment of the wave packet and of the temporal autocorrelation function are examined. At the critical point, the autocorrelation function exhibits the power-law decay with a nonconventional exponent α, which is related to the fractal structure in the energy spectrum and in the wave functions. In the metallic regime, the present results imply that transport properties can be described by the diffusion equation for normal metals. © 1996 The American Physical Society.
  • T OHTSUKI, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 64(11) 4088-4091, Nov, 1995  
    The level statistics in two dimensional disordered electron systems in magnetic fields (unitary ensemble) or in the presence of strong spin-orbit scattering (symplectic ensemble) are investigated at the Anderson transition points. The level spacing distribution functions P(s) are found to be independent of the system size or of the type of the potential distribution, suggesting universality. They behave as s(2) in the small s region in the former case, while increase proportional to s4 is seen in the latter.
  • Nakanishi Takeshi, Ohtsuki Tomi, Saitoh Motohiko
    J Phys Soc Jpn, 64(6) 2092-2099, Jun 15, 1995  
    Electronic states of a two-dimensional tight-binding lattice with finite size in the presence of both uniform electric and magnetic fields are studied. Numerical solutions for eigenenergies are presented. The magnetic subbands at zero electric field known as the Hofstadter butterfly are modified by the electric field and the eigenenergies for high electric fields are represented by the Stark ladder states associated with each of the magnetic subbands. When the electric potential drop across the system becomes comparable to the bandwidth of zero field, the density of states becomes the pyramid shape with steps, the steps being induced by the finiteness of the lattice. The influence on the density of states by the change of the direction of the electric field is also discussed.
  • T KAWARABAYASHI, T OHTSUKI
    PHYSICAL REVIEW B, 51(16) 10897-10904, Apr, 1995  Peer-reviewed
  • Katsumi Kishino, Akihiko Kikuchi, Hiroto Sekiguchi, Masaru Sakai, Yuta Inose, Kazuhiro Ema, Tomi Ohtsuki, Tomi Ohtsuki, Katsumi Kishino, Akihiko Kikuchi, Hiroto Sekiguchi, Tomi Ohtsuki, Kazuhiro Ema, Masaru Sakai
    Journal of Lightwave Technology, 13(7) 1490-1499, 1995  Peer-reviewed
  • B Kramer, T Ohtsuki, M Henneke
    QUANTUM DYNAMICS OF SUBMICRON STRUCTURES, 291 21-29, 1995  Peer-reviewed
  • M Henneke, B Kramer, T Ohtsuki
    Europhysics Letters (EPL), 27(5) 389-394, Aug 10, 1994  
  • T OHTSUKI, Y ONO, B KRAMER
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 63(2) 685-694, Feb, 1994  
    The localization problem in a three dimensional tight binding system in the presence of a spatially random vector potential is investigated. The density of states exhibits tails of localized states that are induced by large regions in space where the vector potential is accidentally constant. In the center of the band the states are shown to be extended by investigating the system size dependence of the inverse participation number. The existence of a metal-insulator transition at a critical energy with non-vanishing density of states is demonstrated. The system size and energy dependent exponential decay length of the modulus of the Green's function satisfies a one-parameter scaling law. The value of the critical exponent is estimated, v almost-equal-to 1, which is different from those found previously for the disordered tight binding (Anderson) model with and without homogeneous magnetic field.
  • Henneke, M., Kramer, B., Ohtsuki, T.
    EPL, 27(5), 1994  
  • T OHTSUKI, K SLEVIN, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 62(11) 3979-3987, Nov, 1993  
    The conductance of a two-dimensional system subject to a random magnetic field is calculated within the Landauer-Buttiker formalism. Although there is no potential disorder the random fluctuating magnetic field introduces a random vector potential. Electrons in bulk states are found to be strongly scattered by the fluctuating field. In contrast, edge states are found to be quite stable even if the fluctuation of the field is of the order of a uniform background field. In a fully random field, the U(1) model, clear universal conductance fluctuations (UCF) are observed. The magnitude of the fluctuations is compared with that in the time reversal symmetric Z2 model.
  • Y ONO, T OHTSUKI
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 62(11) 3813-3817, Nov, 1993  
    The spacing distributions of unfolded energy levels in the lowest Landau band formed in disordered two-dimensional electron systems are numerically studied for different energy regions. By fitting the distribution function to an appropriate interpolation formula, the level repulsion parameter beta is obtained as a function of the unfolded energy x. The functional forms of beta(x) for different system sizes are found to exhibit a certain scaling behavior. From this scaling property, it is possible to estimate the exponent of the localization length as a function of energy, which is found to be 2.4 +/- 0.2, consistent with previously reported values. Possible applications to other Anderson transitions are also discussed.
  • Y ONO, H KUWANO, K SLEVIN, T OHTSUKI, B KRAMER
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 62(8) 2762-2772, Aug, 1993  
    The statistical properties of the energy levels of the lowest Landau band are analyzed. The eigenvalues are obtained numerically for a random matrix model that describes a 2D disordered electron system in a strong magnetic field. In order to avoid the problems related to an energy region dependent average level spacing, the original data are unfolded using the ensemble averaged integrated density of states. For the unfolded data, the level spacing distribution and the DELTA3-statistics are investigated in order to clarify the level correlations. The statistical properties depend on the energy and the magnitude of the level separation. A continuous change from Poissonian to Gaussian unitary statistics is observed between the edge and the center of the band. For the statistics within a given energy region, a highly non-trivial crossover of symmetries takes place between small and large level separations. Even if the localization length is much larger than the system size the deviations from the Gaussian unitary statistics are not negligible.
  • T NAKANISHI, T OHTSUKI, M SAITOH
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 62(8) 2773-2782, Aug, 1993  
    Electronic states of a two-dimensional tight-binding model in a uniform electric field are studied. Numerical solutions for eigenenergies and eigenfunctions are presented as functions of the angle between the electric field and the symmetry axis of the lattice. When the direction of the electric field is [M, N], where M and N are mutually prime each other and MN not-equal 0, the eigenenergies are shown to be quantized with an interval equal to the potential drop between the nearest neighbor net lines. Though the level separation varies discontinuously with the change of the direction, the density of states is shown to be independent of the direction of the electric field, except for the direction [1 0] where the motions parallel and perpendicular to the electric field directions are separable. Unexpected gaps open near the band edges for appropriate electric fields, the magnitudes and the positions of which are smooth functions of the angle for a fixed electric field. The effects of the system edges are also discussed.
  • T OHTSUKI, B KRAMER, Y ONO
    PHYSICA B, 184(1-4) 26-29, Feb, 1993  
    A stack of two-dimensional (2D) disordered layers in quantizing magnetic fields is considered, where the electrons are allowed to hop from one layer to another. By using numerical scaling analysis, the mobility edges as well as the critical exponent for the divergence of the localization length are obtained. It is shown that a small amount of hopping between the layers is sufficient to delocalize the states near the centre of the Landau band. The critical exponent is almost independent of the hopping energy and is equal to 1.3 +/- 0.2. The results are compared with those obtained for the 2D limit, the 3D Anderson model without a magnetic field and for a 3D system with a random magnetic field applied.
  • T NAKANISHI, T OHTSUKI, M SAITOH
    PHYSICA B, 184(1-4) 310-313, Feb, 1993  
    The energy spectra of a two-dimensional tight-binding model in the presence of both magnetic and electric fields are studied. When the electric potential through the system becomes comparable to the bandwidth of zero field, the step-like structure is seen in the density of states. The physical origin is discussed.
  • T OHTSUKI, B KRAMER, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 62(1) 224-238, Jan, 1993  
    The Anderson transition in three dimensional layered systems is investigated in the presence of a quantizing magnetic field perpendicular to the layers. The density of states is calculated. By computing numerically the modulus of the one-body Green's function, the system size dependence of the exponential decay length of the transmission probability is calculated. It satisfies a one-parameter scaling law. The existence of a metal insulator transition is demonstrated. The mobility edge trajectory, and the critical parameters are obtained. The value of the critical exponent, nu = 1.35 +/- 0.15, is found to be close to that reported previously for the Anderson model without magnetic field.
  • Takaaki Kawaguchi, Tomi Ohtsuki, Motohiko Saitoh
    Surface Science, 263(1-3) 671-673, Feb, 1992  
  • T OHTSUKI, Y ONO, B KRAMER
    SURFACE SCIENCE, 263(1-3) 134-136, Feb, 1992  Peer-reviewed
    Electronic states in the lowest Landau subband of a disordered double layered system in a quantizing magnetic field are investigated. The random potential is assumed to be short-ranged. When the transfer probability of electrons between the layers is small, the plateau of the filling factor nu = 1 seems to vanish, while it is clearly observed when the transfer is large. The energetic position of the extended states is also investigated using the finite size scaling method.
  • T OHTSUKI, B KRAMER, Y ONO
    SOLID STATE COMMUNICATIONS, 81(6) 477-480, Feb, 1992  
    The density of states, and the mobility edge are calculated numerically for a new model of a three-dimensional disordered system in the presence of a quantizing magnetic field. The critical exponent of the disorder induced metal-insulator transition is found to be nu = 1.3 +/- 0.2 close to the value reported previously for the Anderson model without magnetic field.
  • Kawaguchi, T., Ohtsuki, T., Saitoh, M.
    Surface Science, 263(1-3), 1992  
  • Y ONO, T OHTSUKI, B KRAMER
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 60(1) 270-279, Jan, 1991  
    Electronic states in a two dimensional random system with a perpendicular strong magnetic field are analyzed by using a model Hamiltonian matrix which has random elements reflecting the characteristics of the random potential such as the correlation length. The random matrix model is suitable for numerical calculations and has advantages compared to preparing the random potential by distributing impurities particularly when discussing correlated potential. As an example, the fractal dimensionality of extended states in the lowest Landau band is considered. It is found that the extended states have multifractal properties. The results are compared with those obtained through the random potential model.
  • T OHTSUKI, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 59(2) 637-648, Feb, 1990  
  • T OHTSUKI, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 58(10) 3863-3864, Oct, 1989  
  • T OHTSUKI, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 58(7) 2482-2494, Jul, 1989  
  • Y ONO, T OHTSUKI, B KRAMER
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 58(5) 1705-1716, May, 1989  
  • T OHTSUKI, Y ONO
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 58(3) 956-968, Mar, 1989  
  • T OHTSUKI, Y ONO
    SOLID STATE COMMUNICATIONS, 68(8) 787-790, Nov, 1988  
  • T OHTSUKI, Y ONO
    SOLID STATE COMMUNICATIONS, 65(5) 403-407, Feb, 1988  
  • B. Kramer, Y. Ono, T. Ohtsuki
    Surface Science, 196(1-3) 127-133, 1988  
    It is argued that the extended states in two-dimensional electronic systems subject to a strong perpendicular magnetic field must not be "area-filling". Their fractal dimensionality d* is calculated from the inverse participation number for the ideal Landau model, and the Teller model. For disordered systems the fractal dimensionality is obtained in the limit of strong magnetic field from percolation theory. The result is d*=1.75. The quantum mechanical Teller model with disorder is treated numerically. © 1987.
  • OHTSUKI TOMI, Y. Ono
    Springer Proceedings in Physics 28, "Anderson Localization"ed. Springer-Verlag, 260-263, 1988  
  • Y ONO, T OHTSUKI
    ZEITSCHRIFT FUR PHYSIK B-CONDENSED MATTER, 68(4) 445-450, 1987  Peer-reviewed
  • OHTSUKI TOMI
    "Proceeding of the 18th International Conference on Physics of Semiconductors"ed. World Scientific, 1213-1216, 1987  

Misc.

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Books and Other Publications

 11
  • 大槻 東巳 (Role: Joint author, p. 13-30 (第1章))
    朝倉書店, Oct 10, 2019 (ISBN: 9784254131291)
    機械学習を使って物理学で何ができるのかを解説した著書。大槻・真野の分担は機械学習，深層学習が物理に何を起こそうとしているかを波動関数の解析を例に解説した，第1章である。
  • Ohtsuki Tomi (Role: Joint author, 109-157)
    Wiley-Scrivener, Apr 9, 2019 (ISBN: 9781119407294)
    Topological properties are sometimes emergent or enforced by the breaking of translational invariance. Here, in this chapter we discuss dimensional crossover of topological properties in thin films of topological insulators (TI) and Weyl semi- metals, electronic properties on the surface of TI nanoparticles and TI nanowires as a constrained electronic system. To discuss the effects of disorder is another highlight of this chapter. We cast on the unusual robustness of Dirac and Weyl semimetal phases against disorder, then the discussion is turned to a novel type of quantum criticality emergent from this unusual robustness, leading us to formu- late the scaling theory of semimetal-metal transition. The concept of topological matter dose not fade under circumstances of absent translational invariance; it is on the contrary, emergent or enforced under such circumstances.
  • Ohtsuki Tomi
    Wiley online library, Mar 12, 2019 (ISBN: 9781119407317)
  • Ohtsuki Tomi (Role: Joint author)
    Oxford University Press, Jul 18, 2012 (ISBN: 9780199592593)
  • 大槻 東巳 (Role: Joint author, 295-305)
    朝倉書店, May 10, 2012 (ISBN: 9784254131031)
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Professional Memberships

 2

Research Projects

 27
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Other

 6
  • Oct, 2005 - Mar, 2008
    As the head of the curriculum committee for English for science and engineering program, I have organized more than 30 classes, and prepared electronic lecture materials. I also taught physics classes myself using DVD and other electronic lecture materials.
  • Apr, 1998 - Sep, 2007
    ナノスケールの物理学に関する講義ノートを電子化し，学生に配付した。これにより学生は予習，復習を容易に行えるようになった。さらに細かい記法と複雑な式を正確に学べるようになった。
  • Apr, 1995 - Sep, 2006
    線形代数学を物理学科向けに講義した。講義ノートを工夫して作成し，全員が簡単にダウンロードできるようにした。
  • Oct, 2003 - Mar, 2006
    電磁気学の講義ノートを電子化した。これにより学生は講義に集中できるようになった。また，予習，復習が容易になった。
  • Apr, 1999 - Sep, 2001
    物理学を学ぶ上で必要な数学と，それをふまえた体系的な力学を講義ノートを電子化して教授した。学生は詳しい講義ノートをダウンロード，印刷することで内容に集中できるようになった。
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