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Quantum Markovian Evolutions in Adiabatic and Nonadiabatic Regimes

Kashef, Arman | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54429 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Memarzadeh, Laleh
  7. Abstract:
  8. In this thesis, our aim is to analyse the environment effects on adiabatic and non-adiabatic evolutions. In this regard, first we need to establish a suitable framework for describing the dynamics. While describing the evolution of a quantum system without interaction with its surrounding environment is easy, describing the time evolution of a quantum system in interaction with its surrounding environment is challenging. In this thesis, first we review the formalism for deriving the Markovian master equation for describing the evolution of a system in weak coupling limit. In the standard formalism, it is assumed that the system Hamiltonian is time-independent. But as our aim is to analyse environment effects on adiabatic/non-adiabatic evolutions, we continue with describing how the Markovian master equation is derived for a system with time-dependent Hamiltonian. Then for two-level and three-level Landau-Zener systems we derive the master equation analytically. By solving the master equations numerically, we study the transition probabilities between different energy levels and comparing these transition probabilities in presence and absence of the external environment, we discuss how interaction with the environment affects the adiabatic/non-adiabatic evolution
  9. Keywords:
  10. Open Quantum System ; Markovian Quantum Process ; Quantum Markovian Master Equation ; Adiabatic Evolution