Theory of Quantum Many-Bodied Systems Under Restricted Geometry

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To clarify the effects of geometrical constraints on quantum many-bodied systems, we studied the following three problems and obtained various important results.1. The superfluid transition of ^4He adsorbed on porous materials.The ^4He system absorbed in porous materials such as zeolite, vycor glass and packed fine particles has the structure which is one- or two-dimensional locally byt three-dimensional as a whole system. It was found that, as a result, there appears a crossover between one- or two-dimensions and three-dimensions in the superfluid transition. Especially in the latter case, it was found that the interaction between vortices excited on the ^4He film has the property two-dimensional in the short distance and one-dimensional in the long distance.2. Electronic states and transport phenomena in mesoscopic systems.In mesoscopic systems of the size smaller than I mum and at temperatures below 1 mk, coherence of electronic states is maintained through the whole system, which strongly affects electronic transport phenomena. The size dependence of the Aharonov-Bohm effect which appears in the magneto-resistance of multiple connected systems, and the energy dependence of conductance of the systems near the localization regime due to strong randomness were studied mainly by means of computer simulation.3. Strongly correlated electrons in low dimensions.Electrons on a one-or two-dimensional lattice are affected by large quantum fluctuations. Under strong correlations as well as the fluctuations, they can fall in an unusual state. We examined, by numerical diagonalization, the cases in which the next nearest neighbor hopping and/or interaction exist. It is found that a resonating-valence-bond state, a soliton state and a dimer state are realized in some specific regions of parameters.