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Implementation and Application of the Time Dependent Variational Monte Carlo method in real and imaginary time / submitted by Mathias Gartner
AutorInnenGartner, Mathias
Beurteiler / BeurteilerinZillich, Robert
ErschienenLinz, 2018
Umfang74 Seiten : Illustrationen
HochschulschriftUniversität Linz, Masterarbeit, 2018
Schlagwörter (GND)Vielteilchensystem / Quantenmechanik / Monte-Carlo-Simulation / Zeitabhängigkeit / Flüssiges Helium
URNurn:nbn:at:at-ubl:1-21337 Persistent Identifier (URN)
 Das Werk ist gemäß den "Hinweisen für BenützerInnen" verfügbar
Implementation and Application of the Time Dependent Variational Monte Carlo method in real and imaginary time [3.1 mb]
Zusammenfassung (Englisch)

The behaviour of many-body systems has always been attracting a lot of research interest at the experimental as well as the theoretical level. Understanding the role and effects of correlations between particles is a key requirement to provide a profound description of manybody quantum systems. The use of Quantum Monte Carlo simulation methods allow for very precise calculations, nevertheless, the possibility to simulate time dynamics constitutes still a challenging task, where substantial progress has been made over the last few years. In this thesis I will focus on the description and applicability of the new time dependent variational Monte Carlo method, and in particular its imaginary time variant, in which the variational wavefunction is propagated to the optimal approximation of the real ground state of the underlying system. A detailed derivation of the method based on the principles of stationary action will be given. I will show that the method is suited to describe few-particle systems as well as bulk systems where up to 1000 particles in a periodic box are studied. These simulations will demonstrate the possibility to efficiently optimize very generic trial wavefunctions, parametrized with up to a hundred parameters. The well studied liquid 4He will serve as a test system in all the calculations, for which a Jastrow-Feenberg-like trial wavefunction will be used. In particular I will present the optimized ground state energies as well as the two-body correlation function used in the variational ansatz. Furthermore, the particle density and the pair distribution function are presented for the cluster and bulk simulations respectively.

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