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Priodically Driven Floquet Systems and Time Crystals

Einollahzadeh Samadi, Moien | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 51258 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdolla
  7. Abstract:
  8. Recent experimental progress in approximating closed quantum many-body systems such as ultra-cold atomic gases, has leads to surge of interest in the dynamics of closed quantum systems. In addition, driving a closed quantum system out of its equilibrium can create an appropriate conditions in order to archive novel phases of matter such as discrete Time-Crystals.In the present work, following a brief introduction, we start with basic principles of the Floquet theory. According to the matrix representation of the Floquet theory, we examine solutions of a quantum system which is driven by external periodic perturbation.We then turn to study of thermalization in closed quantum system and introduce eigenstate thermalization hypothesis (ETH). We also review the localized phase of the Heisenberg spin model as a candidate of ergodicity breaking in closed quantum systems. Afterward, We extend the idea of localization into the periodically driven systems and by studying phase structure of Floquet systems, we show that they can display nontrivial phases, some of which show a novel form of correlations in spatial and temporal dimensions.The next part of the thesis addresses the idea of Time-Crystals. It was shown that time translation symmetry breaking can only be realized in out-of-equilibrium systems. Hence, the interplay of periodically driven Floquet systems and localization can be a good candidate for observing time crystalline behavior which leads to a Floquet or discrete Time-Crystals
  9. Keywords:
  10. Localization ; Floquet Eigenfunctions ; Many Body System ; Spontaneous Gauge Symmetry Breaking ; Time Crystals ; Ergodicity Breaking

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