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Review of Thermalization in Closed Quantum Systems

Seif, Negar | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54558 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rezakhani, Ali
  7. Abstract:
  8. For a physical system, equilibrium is defined as a state in which the values of macroscopic quantities describing the system do not change in time. We observe systems around us reaching equilibrium every day. Describing such a seemingly simple phenomena has remained as one of the important challenges in theoretical physics. So far, various explanations for thermalization (approach to equilibrium) have been offered within classical and quantum thermodynamics. In classical statistical mechanics, the microcanonical ensemble provides a suitable prediction of the thermal behavior of a closed system. In this ensemble, using ergodic hypothesis and chaos theory one can assume that all microstates with equal energies are equiprobable. According to ergodic hypothesis and Liouville's theorem, in a sufficiently large physical system, for every neighborhood in phase space, there will be a moment in time at which the system passes from that neighborhood, and it basically spends equal times in equal phase space volumes. However, due to uncertainty principle and linearity of Schrodinger equation the situation is rather different. Consequently, different approaches have been considered for the problem of thermalization in quantum systems: Quantum Ergodic Theorem, Typicality of Thermal Equilibrium, Random Matrix Theory, Eigenstate Thermalization Hypothesis, etc. The aim of this thesis is to study and review the necessary conditions for thermalization in closed quantum systems. For this purpose, we first study the dynamics in closed quantum systems and then investigate, analytically and numerically, some of the theorems that imply existence of an asymptotic thermal state in closed quantum system, the most important of which: the Eigenstate Thermalization Hypothesis
  9. Keywords:
  10. Quantum Thermodynamics ; Random Matrix Theory ; Ergodic Hypothesis ; Microcanonical Ensemble ; Closed Quantum Systems ; Eigenstate Thermalization Hypothesis (ETH)

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