- 1) Establishment of the concept of fractons, "quantized vibrations in fractal structures". Pioneering works by Nakayama and his colleagues in terms of large-scale computer simulations have revealed for the first time the characteristics of fractons. A series of their works have conducted the research direction on the dynamics of fractal structures both experimentally and theoretically. The review article with his colleagues K. Yakubo and R. Orbach was published in a highly prestigious journal in physics " Reviews of Modern Physics, vol.66, No.2(1994) pp. 381-443" under the title "Dynamical properties of fractal structures: scaling, numerical simulations and physical realizations".
- 2) The 2nd achievement is the elucidation of the heat-exchange mechanism at millikelvin (mK) temperatures; the so-called the Kapitza resistance. The elucidation had been demanded by cryo-engineers and low-temperature physicists from its first experimental confirmation in 1975. Nakayama predicted in early 1980's the relevance of the magnetic interaction between He
^{3}nuclear spin and chemisorped oxygen (with spin) on nano-metal-particles to the anomalous Kapitza resistance. Nakayama contributed a review in "Progress in Low Temperature Physics, vol. XII (1989) pp.117-194", whose series are well accepted as a prestigious one in the community of low temperature physics. - 3) The 3rd important contribution is the development of the efficient computer-algorithm for large-scale physical systems. Nakayama and his colleagues developed the dynamic method for treating the equations of motion proposed by H. J. Maris for calculating response functions given by huge matrices such as 10
^{6}x10^{6}or more. The simplicity and the efficiency of this algorithm have attracted much attention among chemists, physicists and engineers so far. The performance of this algorithm, which Nakayama termed the forced oscillator method (FOM), was demonstrated in the article " The forced oscillator method: Eigenvalue analysis and computing linear response function, Reports in Physics, vol. 349, No.3(2001), pp.239-299". - 4) The 4th is concerned with the "boson peak" observed in glasses; an unexpectedly large/broad spectra around at THz frequency range. Since its first observation by Raman scattering in 1953 by Krishnan, numerous researchers have paid much attention to the origin of boson peak, but not successful. Nakayama predicted theoretically in 1998 that the boson peak is a manifestation of the flat band consisting of "coupled" acoustic/optic modes emerged from high/low density parts in glasses. The prediction was confirmed experimentally in terms of high-resolution inelastic neutron scattering measurements (INS) by M. Arai (now at J-PARC at Tokai) in 1999. The main achievements are summarized by Nakayama in "Boson peak and terahertz frequency dynamics in vitreous silica, Reports in Progress in Physics, vol.65, (2002), pp.1195-1242".

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- Personal history, honors and awards, chairs
- Research areas and achievements of research activities
- Selected review papers and books
- List of publications(Complex disordered systems/Glasses, Dynamics of fractal structures, Localization Problems/High-Tc superconductors, Computaional Physics/Numerical simulations, Low temperature physics, Soft matters, Phonon physics)