Print Email Facebook Twitter The Kernel Polynomial Method applied to tight binding systems with time-dependence Title The Kernel Polynomial Method applied to tight binding systems with time-dependence Author ter Hoeven, R.S. Contributor Akhmerov, A.R. (mentor) Budko, N.V. (mentor) Sticlet, D.C. (mentor) Faculty Applied Sciences Department QN/Quantum Nanoscience Date 2016-09-27 Abstract The Kernel Polynomial Method (KPM) is a method to approximate any function as a polynomial of finite order. In this research the KPM will be used to approximate the density of states and expectation values of physical observables in a tight binding system. To be able to use the KPM a tight binding Hamiltonian is obtained by using the python package Kwant. A python implementation of KPM combined with a time propagator then results in time-dependent expectation values of any operator. This approach benefits from large system sizes, since KPM uses a statistical approximation that increases in accuracy with larger size. The statistical approximation always converges, but there is limited guarantee as to how fast it converges. In further research the KPM could be compared to other available approaches. Another possibility is to use the KPM to get a general overview of the system and combine it with more exact approaches to find specific results. Subject Kernel Polynomial MethodTight binding systemGrapheneExpectation valuesDensity of statesTime-dependence To reference this document use: http://resolver.tudelft.nl/uuid:c7c70ef2-6f19-4b70-b7ef-deaa6f1b1d45 Part of collection Student theses Document type bachelor thesis Rights (c) 2016 ter Hoeven, R.S. Files PDF Kernel polynomial method.pdf 635.74 KB Close viewer /islandora/object/uuid:c7c70ef2-6f19-4b70-b7ef-deaa6f1b1d45/datastream/OBJ/view