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Dynamical Behavior in Statistical Mechanics of Open Quantum Systems

Bakhshinezhad, Faraj | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45792 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Rezakhani, Ali
  7. Abstract:
  8. A fundamental question in investigating decoherence and equilibrium of a system in contact with a bath is how its entropy changes in time. Normally, von Neumann’s entropy is used in such studies to quantize degree of decoherence. Recently, certain researches have been conducted addressing entropy rate and various bounds have been achieved for this quantity, utilizing which one can discuss decoherence rate and equilibrium state of open systems.In this thesis, we introduce these bounds and try to improve them. Using improved bound we will show that for almost all conceivable initial states of the system and the bath, average of entropy rate will be negligible. This result is obtained under rather general circumstances for systems interacting with a sufficiently larger bath.This bound outmatches previous results in certain senses: (i) the bound depends one initial state of the system and the bath, based on which we can discern initial states with less decoherence rate, (ii) it depends on the interval over which an average has been calculated which in turn provides us with a quantitative measure of approach to equilibrium, and (iii) it depends on the Hamiltonian of the entire system and the bath. Previous bounds lack the aforementioned characteristics. Furthermore, certain bounds had been achieved on entropy rate of systems with non-degenerate energy gap (non-resonant Hamiltonian) which we managed to improve and extend to resonant Hamiltonians as well. A simulation has also been carried out studying our bound we actual entropy rate of a configuration of spins
  9. Keywords:
  10. Quantum Thermodynamics ; Open Quantum System ; Equilibrium ; Entropy

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