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- All Subjects: Quantum Dots
- Creators: Akis, Richard
- Creators: Bennet, Peter
Description
he accurate simulation of many-body quantum systems is a challenge for computational physics. Quantum Monte Carlo methods are a class of algorithms that can be used to solve the many-body problem. I study many-body quantum systems with Path Integral Monte Carlo techniques in three related areas of semiconductor physics: (1) the role of correlation in exchange coupling of spins in double quantum dots, (2) the degree of correlation and hyperpolarizability in Stark shifts in InGaAs/GaAs dots, and (3) van der Waals interactions between 1-D metallic quantum wires at finite temperature. The two-site model is one of the simplest quantum problems, yet the quantitative mapping from a three-dimensional model of a quantum double dot to an effective two-site model has many subtleties requiring careful treatment of exchange and correlation. I calculate exchange coupling of a pair of spins in a double dot from the permutations in a bosonic path integral, using Monte Carlo method. I also map this problem to a Hubbard model and find that exchange and correlation renormalizes the model parameters, dramatically decreasing the effective on-site repulsion at larger separations. Next, I investigated the energy, dipole moment, polarizability and hyperpolarizability of excitonic system in InGaAs/GaAs quantum dots of different shapes and successfully give the photoluminescence spectra for different dots with electric fields in both the growth and transverse direction. I also showed that my method can deal with the higher-order hyperpolarizability, which is most relevant for fields directed in the lateral direction of large dots. Finally, I show how van der Waals interactions between two metallic quantum wires change with respect to the distance between them. Comparing the results from quantum Monte Carlo and the random phase approximation, I find similar power law dependance. My results for the calculation in quasi-1D and exact 1D wires include the effect of temperature, which has not previously been studied.
ContributorsZhang, Lei (Author) / Shumway, John (Thesis advisor) / Schmidt, Kevin (Committee member) / Bennet, Peter (Committee member) / Menéndez, Jose (Committee member) / Drucker, Jeff (Committee member) / Arizona State University (Publisher)
Created2011
Description
Complex dynamical systems consisting interacting dynamical units are ubiquitous in nature and society. Predicting and reconstructing nonlinear dynamics of units and the complex interacting networks among them serves the base for the understanding of a variety of collective dynamical phenomena. I present a general method to address the two outstanding problems as a whole based solely on time-series measurements. The method is implemented by incorporating compressive sensing approach that enables an accurate reconstruction of complex dynamical systems in terms of both nodal equations that determines the self-dynamics of units and detailed coupling patterns among units. The representative advantages of the approach are (i) the sparse data requirement which allows for a successful reconstruction from limited measurements, and (ii) general applicability to identical and nonidentical nodal dynamics, and to networks with arbitrary interacting structure, strength and sizes. Another two challenging problem of significant interest in nonlinear dynamics: (i) predicting catastrophes in nonlinear dynamical systems in advance of their occurrences and (ii) predicting the future state for time-varying nonlinear dynamical systems, can be formulated and solved in the framework of compressive sensing using only limited measurements. Once the network structure can be inferred, the dynamics behavior on them can be investigated, for example optimize information spreading dynamics, suppress cascading dynamics and traffic congestion, enhance synchronization, game dynamics, etc. The results can yield insights to control strategies design in the real-world social and natural systems. Since 2004, there has been a tremendous amount of interest in graphene. The most amazing feature of graphene is that there exists linear energy-momentum relationship when energy is low. The quasi-particles inside the system can be treated as chiral, massless Dirac fermions obeying relativistic quantum mechanics. Therefore, the graphene provides one perfect test bed to investigate relativistic quantum phenomena, such as relativistic quantum chaotic scattering and abnormal electron paths induced by klein tunneling. This phenomenon has profound implications to the development of graphene based devices that require stable electronic properties.
ContributorsYang, Rui (Author) / Lai, Ying-Cheng (Thesis advisor) / Duman, Tolga M. (Committee member) / Akis, Richard (Committee member) / Huang, Liang (Committee member) / Arizona State University (Publisher)
Created2012