Theory of Quantum Many-Bodied Systems Under Restricted Geometry

受限几何下的量子多体系统理论

基本信息

批准号：
63540273
负责人：
TAKANO Ken'ichi
金额：
$ 1.02万
依托单位：
Nagoya University
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1990
项目状态：
已结题

项目摘要

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.

为了阐明几何约束对量子多体系的影响，我们研究了以下三个问题并获得了各种重要结果。1。 ^4he的超流体过渡吸附在多孔材料上。结果发现，在超流体过渡中，一维或二维和三维之间出现了交叉。尤其是在后一种情况下，发现在 ^4he膜上激发的涡流之间的相互作用在短距离内具有二维的性质，并且在长距离之间具有一维。2。在介观系统中的电子状态和传输现象。在小于I妈妈的介质系统中，在低于1 MK的温度下，通过整个系统保持电子状态的连贯性，这会强烈影响电子传输现象。 Aharonov-bohm效应的尺寸依赖性主要通过计算机模拟研究，该系统在多个连接系统的磁性抗性中以及由于强大的随机性而导致的定位状态附近系统的电导依赖性。3。在低维度上的相关电子密切相关。一或二维晶格上的电子受到大量量子波动的影响。在强烈的相关性和波动下，它们可能处于异常状态。我们通过数值对角线化检查了下一个最近的邻居跳和/或相互作用的情况。发现在某些特定的参数区域中，实现了共鸣 - 价键状态，孤子状态和二聚体状态。