Mesoscopic Electronics and Optics

0084501石头这个补助金支持相关的理论研究课题的电子和光子的行为在受限的几何形状的空间限制规模是大相比，波长，但足够小（在许多情况下），量子或波效应是重要的。 这项研究的一个统一主题是，限制势要么是无序的，要么是复杂的，足以产生混沌的经典运动，因此必须采用量子输运理论和/或半经典方法来研究经典混沌系统（“量子混沌理论”）。 目前提出的具体方案主要涉及两大类系统：介质微腔谐振器和微激光器以及半导体量子点;对于光学谐振器，非对称谐振腔（ACR's）理论将得到进一步发展。 ACR是从旋转对称平滑变形的圆柱形或球形介电谐振器。 这样的系统的共振是非微扰相关的对称系统。 在这种情况下，半经典方法是非常强大的，因为光子是非相互作用的（在线性制度），这些方法将进一步发展。 在这个理论中，我们将试图描述混沌辅助隧穿和光子的动力学局域化等效应。 此外，我们期望在ARC的基本谐振腔理论方面取得实质性进展，发展各种不同参数范围内输出方向性和Q值的完整定量理论，并了解单模和多模激光的条件。 最后，我们将首次讨论这些谐振器和微激光器的非线性和量子光学特性。 对于半导体量子点的情况下，这个问题是更困难的，因为处理强电子-电子相互作用是必不可少的。 这里的重点将是无序和/或混乱的作用，造成相互作用的波动，这是不捕获的平均场理论。 具体来说，我们打算探索我们最近的发现，即在无序量子点模型中，相互作用波动在抑制自发磁化方面起着重要作用，即，相互作用涨落一般与巡游电子系统的Stoner不稳定性相反。 这些效应似乎随着电导的降低而增加，因此它们也可能在金属-绝缘体或超导体-绝缘体转变附近起重要作用。 在平均场理论适用的区域，我们将用半经典方法研究自洽势的自洽谱的演化。该补助金支持电子（电荷）和光子（光）的纳米科学的理论研究。 这些主题与电子和光子在受限几何中的行为有关，其中空间限制尺度与波长相比很大，但足够小（在许多情况下），量子或波效应很重要。 这项研究的一个统一主题是，限制势要么是无序的，要么是复杂的，足以产生混沌的经典运动，因此必须采用量子输运理论和/或半经典方法来研究经典混沌系统（“量子混沌理论”）。 大多数具体的提议涉及两类系统：介质微腔谐振器和微激光器，以及半导体量子点。 这些主题既有深刻的学术兴趣，又有巨大的应用潜力。

0084501StoneThis grant supports theoretical research topics related to the behavior of electrons and photons in confined geometries for which the spatial confinement scale is large compared to the wavelength but small enough (in many cases) that quantum or wave effects are important. A unifying theme of this research is that the confining potential is either disordered or complex enough to generate chaotic classical motion, so that one must employ techniques from quantum transport theory and/or semiclassical methods for classically chaotic systems ("quantum chaos theory"). Most of the specific proposals relate to two categories of systems: dielectric micro-cavity resonators and micro-lasers, and semiconductor quantum dots.For optical resonators, the theory of asymmetric resonant cavities (ACR's) will be further developed. ACR's are cylindrical or spherical dielectric resonators smoothly deformed from rotational symmetry. The resonances of such systems are non-perturbatively related to those of the symmetric system. In such a case semiclassical methods are very powerful since photons are non-interacting (in the linear regime) and these methods will be developed further. Within this theory, we will attempt to describe such effects as chaos-assisted tunneling and dynamical localization of photons. In addition, we expect to make substantial progress on the basic resonator theory of ARC's, developing a full quantitative theory of the output directionality and Q-value in various different parameter regimes, and understanding the conditions of single and multi-mode lasing. Finally, we will for the first time address the non-linear and quantum-optical properties of these resonators and micro-lasers. For the case of semiconductor quantum dots the problem is more difficult because treatment of the strong electron-electron interactions is essential. Here the focus will be on the role of disorder and/or chaos in causing interaction fluctuations which are not captured by mean-field theory. Specifically we intend to explore our recent discovery that interaction fluctuations play a major role in suppressing spontaneous magnetization in a model for a disordered quantum dot, i.e., the interaction fluctuations generically oppose the Stoner instability of itinerant electron systems. These effects appear to increase as the conductance decreases, so that they may also play an important role near the metal-insulator or superconductor-insulator transitions. In the regime where mean-field theory does work, we will study the evolution of the self-consistent spectrum using semiclassical methods applied to the self-consistent potential.%%%This grant supports theoretical research on the nanoscience of electrons (electrical charge) and photons (light). The topics are related to the behavior of electrons and photons in confined geometries for which the spatial confinement scale is large compared to the wavelength but small enough (in many cases) that quantum or wave effects are important. A unifying theme of this research is that the confining potential is either disordered or complex enough to generate chaotic classical motion, so that one must employ techniques from quantum transport theory and/or semiclassical methods for classically chaotic systems ("quantum chaos theory"). Most of the specific proposals relate to two categories of systems: dielectric micro-cavity resonators and micro-lasers, and semiconductor quantum dots. The topics are both of deep intellectual interest and of great potential application.***