Energy level statistics for ballistic and mesoscopic quantum systems
Abstract
Systems modelling nanoscale structures have been studied in the context of the theory of energy level statistics in the ballistic and mesoscopic as well as the insulating regimes. Statistics were obtained using a new unfolding scheme based on the existence of a local stationary property for fluctuations of the energy spectra. Two different models were used in the study with particular emphasis on the relevance to the physics of nanoscale devices. Thus, a quantum billiard model composed of a quasi-two-dimensional tight-binding atomic lattice was introduced. The results of the statistical analysis of the spectra of the models were compared throughout the thesis with Random Matrix Theory (RMT). The applicability of RMT and the universality predicted by RMT were verified. The statistical behavior of energy levels for systems in the crossover region between regular and chaotic behavior was studied in all three regimes. Gradual transitions were observed for both ballistic and mesoscopic systems, and found to be similar in the cases. For systems in the insulating regime, the statistical behavior of levels was found to be of Poisson type. The transition from GOE to Poisson behavior when the system is changed from the mesoscopic to the insulating regime was also studied, a spectral dependence of the local fluctuations of energy levels was found, indicating the break-down of translation invariance of the local fluctuations. The transition due to time reversal invariant symmetry…
Read the paper
Related studies
- Chaos and quantum thermalization
- The Dalton quantum chemistry program system
- Cord Blood Leptin and Adiponectin as Predictors of Adiposity in Children at 3 Years of Age: A Prospective Cohort Study
- Quantitative metabolomics by H-NMR and LC-MS/MS confirms altered metabolic pathways in diabetes
- Stable adiabatic quantum batteries
- A novel self-lipid antigen targets human T cells against CD1c(+) leukemias
Go deeper in Evidence Hub
Evidence Hub adds a study data sheet (design, sample size, evidence level, key numbers), an AI summary and a chat grounded in the paper's text.