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Title page for ETD etd-03282018-165208


Type of Document Dissertation
Author Kidd, Daniel Wayne
Author's Email Address daniel.w.kidd@vanderbilt.edu
URN etd-03282018-165208
Title Accelerated Time Propagation in Time-Dependent Density Functional Theory
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Kalman Varga Committee Chair
Andreas Berlind Committee Member
Neepa Maitra Committee Member
Robert Scherrer Committee Member
Sait Umar Committee Member
Keywords
  • Density Functional Theory
  • simulation
  • basis functions
  • Time-Dependent Density Functional Theory
  • exponential integrator
  • pseudospectral
Date of Defense 2018-03-27
Availability unrestricted
Abstract
Time-dependent density functional theory (TDDFT) is a widely used, formally exact approach for describing quantum many-body electron dynamics. This approach makes possible the theoretical investigation of laser-driven phenomenon occurring at the attosecond time scale and angstrom length scale, of interest in a wide range of fields including many subdisciplines of physics, optics, biology, material engineering, chemistry, and computer engineering. The increased sophistication in speed and accuracy of this computational method allows for the enhanced reliability, applicability, and accessibility of quantum dynamics simulation programs. In order to further advance these aspects of the computational implementation of TDDFT, various means of accelerating such programs have been investigated. First, a class of basis set representations which is growing in popularity for such applications due to enhanced accuracy, the pseudospectral bases, was tested. It was shown that by modifying an exemplary sinc basis with sum-acceleration weights, the pseudospectral accuracy is maintained while allowing the computational efficiency to match that of other conventional methods. Next, various time propagation techniques were applied to the description of electron dynamics in a one-dimensional Helium atom which had either been initialized in an excited state or subject to driving laser fields. It was learned that a class of time propagation techniques new to TDDFT, exponential integrator methods, outperform popular approaches due to their ability to well-represent the nonlinear terms in the relevant differential equations. Lastly, a new time-dependent basis set comprised of Volkov states was introduced to the TDDFT description of periodic systems subject to intense laser pulses. It was demonstrated that this basis is capable of allowing time step sizes of up to an order of magnitude larger than those available in conventional techniques, thus allowing a similar speed up in simulation runtimes. This new basis was employed in investigative simulations of a periodic jellium model meant to describe the electronic rectification effect of recently suggested nano-scale diode devices.
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