Theory of Quantum Many-Bodied Systems Under Restricted Geometry

为了阐明几何约束对量子多体系统的影响，我们研究了以下三个问题，得到了一些重要结果.吸附在多孔材料上的^4 He的超流转变吸附在多孔材料如沸石、玻璃和填充微粒中的^4 He系统具有局部的一维或二维结构，而整体的结构是拜特三维的。结果发现，在超流转变中，出现了一维或二维与三维之间的交叉。特别是在后一种情况下，发现在^4He膜上激发的涡旋之间的相互作用在短距离内具有二维性质，在长距离内具有一维性质.介观系统中的电子态和输运现象。在尺寸小于1 μ m且温度低于1 ℃的介观系统中，电子态的相干性贯穿整个系统，这强烈影响电子输运现象。主要通过计算机模拟的方法研究了多连通系统磁阻中Aharonov-Bohm效应的尺寸依赖性，以及系统在局域区附近由于强随机性而导致的电导的能量依赖性.低维强关联电子。一维或二维晶格上的电子受到大的量子涨落的影响。在强相关性和波动下，它们可能会处于一种不寻常的状态。我们研究，通过数值对角化，在下一个最近的邻居跳跃和/或相互作用存在的情况下。发现在某些特定的参数范围内，可以实现共振价键态、孤子态和二聚体态。

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.