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Review of the Range of Validity of Markovian Master Equations for Harmonic Oscillators

Masoumian, Mohammad Reza | 2019

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53152 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rezakhani, Ali
  7. Abstract:
  8. Quantum mechanics, in the first place, investigates systems by introducing some principals about Hilbert space, Schrodinger equation etc. which are recognized as closed quantum systems. In principal, this is not possible to separate a system from its surrounding environment. Thus, the implications of the environment on the evolution of the system must be taken into consideration. As a matter of fact, all systems are considered open in a sense that, it is interacting with another system called the environment. In such circumstances, we tend to represent a description of open quantum systems in a way that following the evolution of the total system, i.e. system and the environment, is not needed. The evolution of an open system is delineated by a dynamical equation which stems from the approximate effect of the surrounding environment on the system. Employing different approximations, different differential equations have been suggested to identify the dynamical equation. The main purpose of this thesis is to investigate one of those differential equations called Markovian equation. In this dissertation, after introducing some principals such as dynamical maps, universal dynamical maps, Markovian evolution etc. we set sight on Markovian differential equation. Starting from the microscopic Hamiltonian of the total system we then calculate the most general equation which describes the evolution of the open system. Furthermore, by imposing conditions on the system, we transform this equation to a simple Markovian equation. Having done so, we find the conditions under which the evolution of the system can be described by a Markovian equation. At the end, using some examples, we will scrutinize the validity of the Markovian equation by putting it into comparison with the exact time evolution of the systems. This will lead us to understand if Markovian equation will be a good candidate to describe the evolution of the systems possessing the required conditions for the validity of the Markovian equation
  9. Keywords:
  10. Open Quantum System ; Harmonic Oscillator ; Damped Harmonic Oscillator ; Markov Differential Equation ; Quantum Mechanics

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