Theory of the Fractional Quantum Hall Effect

9615005 Jain目前的拨款是为了支持PI对分数量子霍尔效应的复合费米子描述的早期工作的扩展。 更具体地说，PI设计了一种形式主义，使用蒙特卡罗技术计算大系统的基态和激发态的波函数。 热力学极限计算的可能性保证了对各种悬而未决的实验问题的定量理解。 特别是补助金计划计算一般分数下的能隙和集体模式色散，包括塞曼能量的偏振度，分数量子霍尔态和维格纳晶体之间的跃迁，以及介观量子点对施加的高磁场的响应。 分数量子霍尔效应的主题近年来一直是一个活跃的领域，在很大程度上是由于这个PI发现的复合费米子描述。 一个严重的局限性是，迄今为止，理论计算仅限于较小尺寸的系统，而实验通常是为较大的尺寸。 PI最近的一项重大进展表明可能会消除这一限制。 这项资助是为了支持在大系统极限下的各种实验观测的计算。 ***

9615005 Jain The present grant is to support the extension of earlier work by the PI on composite fermion description of the fractional quantum Hall effect. More specifically, the PI has devised a formalism to calculate the wave functions of the ground as well as the excited states for large systems using Monte Carlo techniques. The possibility of calculations in thermodynamic limit promises a quantitative understanding of various outstanding experimental issues. In particular the grant plans to calculate the energy gaps and collective mode dispersions at general fractions, degree of polarization including the Zeeman energy, transitions between the fractional quantum Hall states and a Wigner crystal and finally the response of a mesoscopic quantum dot to applied high magnetic fields. %%% The subject of fractional quantum Hall effect has been an active area in recent years, in significant part due to this PI's discovery of the composite fermion description. A serious limitation so far has been that the theoretical calculations are limited to system of smaller sizes, as opposed to the experiments which are generally for larger sizes. A significant development recently by the PI suggests possible removal of this limitation. This grant is to support calculations of various experimental observable in the large system limit. ***