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We propose a new disorder-induced insulator-metal transition of one-electron states, which may be called the "inverse Anderson transition." We first make a highly degenerated localized states by constructing a three-dimensional periodic system possessing only flat dispersion relations. When we introduce a disorder into it, a finite-size scaling of the level statistics shows two clear (localization-delocalization and delocalization-localization) transitions for a wide range of the energy, with increasing the degree of disorder. These transitions are confirmed also by finding the system-size-independent characteristic of the wave function.

Elementary excitations associated with atomic motion in non-crystalline solids and liquids are studied with particular attention paid to the dependence of their dispersion on local order. In doing this, an attempt is made to obtain an exact formal expression for an effective dynamical matrix giving the eigenfrequencies of phonons in a non-crystalline solid in terms of "effective pair-correlation functions". A brief remark is also given on the moment method and sum rules for the dynamic structure factor to study high-frequency collective motion in liquids. It is suggested that under certain restrictions the phonon-rotan-like behavior of excitations as observed in liquid helium is likely to exist in almost all types of structure or topological disorder systems (amorphous and glassy solids, liquids, etc.). To substantiate this, a model one-dimensional system is chosen to show how a phonon dispersion curve in a crystal lattice is modified, as the partial disorder characterizing a structure disorder system is introduced. Such a local disorder is shown to give rise to a frequency gap which decreases with increasing local order and eventually vanishes in the case of complete order. This result is also in qualitative agreement with the pressure-and the temperature-dependence of the rotan minimum energy in liquid helium. Simple numerical calculations are made to compare the obtained results with experiments for collective motion in liquid argon and also in liquid helium. Fairly good agreement is obtained.Historically, elementary excitations in disordered systems have been studied most extensively for quantum liquids or liquid helium. 8 l' 9 l On the other hand, several works, both experimentaP 0~12 l and theoretical, 2 ),B),lB)"' 18 ) have implied that dispersion curves of collective motion in simple liquids bear some resemblance to those of phonon-roton-like excitations as observed in liquid helium. It is worthy of note in this connection that the general behavior of phonon dispersion curves in solid helium, which is a typical quantum crystal, is little different from those in ordinary

A constructive method to find flat bands is demonstrated for a model describing tight-binding electrons on the hexagonal lattice in which each atomic site has three orbitals. The system may representelectrons of an sp 2 -hybridized material but we assume transfer integrals between orbitals to be free parameters for general discussion. Finding highly degenerate eigenfunctions of each flat band is identified as finding a localized eigenfunction, which is determined as a basis function of an irreducible representation of, for example, a point group C 6v . This approach yields not only flat bands on all over the k-space but also some partial flat bands only on a partial k-space. In the former case, if the flat band locates at the bottom (or the top) of a band structure, it is shown that Mielke's condition holds, allowing occurrence of the flat band ferromagnetism.

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