Mesoscopic Electronics and Optics

该基金支持与受限几何中电子和光子行为相关的理论研究课题，其中空间约束尺度与波长相比较大，但足够小（在许多情况下），量子或波效应很重要。本研究的一个统一主题是，限制势要么是无序的，要么是复杂到足以产生混沌的经典运动，因此必须采用量子输运理论和/或经典混沌系统的半经典方法（“量子混沌理论”）的技术。大多数具体的建议涉及两类系统：介电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，非对称谐振腔理论将得到进一步发展。ACR是圆柱或球形介质谐振器，从旋转对称平滑变形。这种系统的共振与对称系统的共振无摄动关系。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（在线性状态下），这些方法将进一步发展。在这个理论中，我们将尝试描述诸如混沌辅助隧穿和光子的动态局域化等效应。此外，我们期望在ARC的基本谐振腔理论上取得实质性进展，建立一个完整的定量理论，在不同的参数范围内输出方向性和q值，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性质。对于半导体量子点来说，这个问题更加困难，因为处理强电子-电子相互作用是必不可少的。这里的重点将放在无序和/或混沌在引起平均场理论没有捕捉到的相互作用波动中的作用。具体来说，我们打算探索我们最近的发现，即相互作用波动在抑制无序量子点模型中的自发磁化中起主要作用，即相互作用波动通常与巡回电子系统的斯通纳不稳定性相反。这些效应似乎随着电导的减小而增加，因此它们也可能在金属-绝缘体或超导体-绝缘体过渡附近发挥重要作用。在平均场理论起作用的情况下，我们将使用应用于自洽势的半经典方法研究自洽谱的演化。该基金支持电子（电荷）和光子（光）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较大，但足够小（在许多情况下），量子或波效应很重要。本研究的一个统一主题是，限制势要么是无序的，要么是复杂到足以产生混沌的经典运动，因此必须采用量子输运理论和/或经典混沌系统的半经典方法（“量子混沌理论”）的技术。大多数具体的建议涉及两类系统：介电微腔谐振器和微激光器，以及半导体量子点。这些课题既具有深厚的学术兴趣，又具有巨大的应用潜力

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.***