Quantum Nonlinear Science

9625549 Prange这项基金支持这位资深的杰出理论家的工作，他过去的贡献涵盖了凝聚态物理的各个不同领域。最近，PI已经涉足量子非线性科学的一般领域。本课题研究的是量子无序问题与混沌和分形等非线性性质之间的界面，预计将对纳米器件的新兴领域产生重大影响。PI在这一领域的重大概念进步中发挥了重要作用，即在准经典方法中消除了分歧。这项拨款将进一步发展准经典方法的应用。在另一个项目中，PI将探索随机矩阵理论和准经典方法在量子尺度上应用于无序特性的协同作用。小尺度（纳米级）器件具有一些特性，其描述有时会带来特殊的数学挑战。在这位杰出理论家的持续工作中，人们试图尝试各种现代数学技术，如随机矩阵理论和准经典近似，以寻求有效和高效的材料性质计算。这项工作将推动量子非线性科学的发展。＊＊＊

9625549 Prange This grant supports work of this senior, distinguished theorist whose past contributions have ranged over a variety of diverse areas in condensed matter physics. More recently the PI has been involved in the general area of quantum nonlinear science. This subject, on the interface between quantum disorder problems and such nonlinear properties as chaos and fractals is expected to have strong influence on the emerging fields of nanoscale devices. The PI has been instrumental in a major conceptual advance in this field, namely the removal of the divergence in a quasiclassical approach. This grant will further develop the applications of the quasiclassical approach. In another project the PI will explore the synergism of the random matrix theory and the quasiclassical methods in their application to the properties of disorder at quantum scale. %%% Small scale (nanoscale) devices have properties whose description sometimes poses a special mathematical challenge. In this continuing work of a distinguished theorist, attempts are being made to try a variety of modern mathematical techniques, such as random matrix theory and quasiclassical approximation in search of a effective and efficient computation of the material properties. This work will advance the state of quantum nonlinear science. ***