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19 - Open Quantum Systems

Published online by Cambridge University Press:  11 May 2023

Uri Peskin
Affiliation:
Technion - Israel Institute of Technology, Haifa
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Summary

Typically, we are interested in a small system (a few particles, or some region in space), entangled with its surroundings. Exact equations (Dyson or Nakajima–Zwanzig) for the reduced system dynamics are readily derived using suitable projection operators. They are rarely solvable, however, since full account is taken for mutual influences between the system and its environment. Nevertheless, for weak mutual coupling, environment-induced dynamics in the (small) system can be much slower than system-induced dynamics in the (large) environment. This justifies the Born–Markov approximation, leading to closed equations for the system. In Hilbert space, we demonstrate the emergence of irreversible dynamics and exponential decay for pure sates. In Liouville space, we derive the Redfield equation. Invoking the secular (or, rotating-wave) approximation, we derive Pauli’s master equations, which properly account for relaxation to equilibrium. Rates of spontaneous emission, coherence transfer (Bloch equations), and pure dephasing are derived and analyzed for a dissipative qubit.

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Publisher: Cambridge University Press
Print publication year: 2023

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References

Meier, C. and Tannor, D. J., “Non-Markovian evolution of the density operator in the presence of strong laser fields,” The Journal of Chemical Physics 111, 3365 (1999).CrossRefGoogle Scholar
Breuer, H.-P. and Petruccione, F., “The Theory of Open Quantum Systems” (Oxford, 2002).Google Scholar
Redfield, A. G., “The theory of relaxation processes,” Advances in Magnetic and Optical Resonance 1, 1 (1965).CrossRefGoogle Scholar
Egorova, D., Thoss, M., Domcke, W., and Wang, H., “Modeling of ultrafast electron-transfer processes: Validity of multilevel Redfield theory,” The Journal of Chemical Physics, 119, 2761 (2003).CrossRefGoogle Scholar

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  • Open Quantum Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.020
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  • Open Quantum Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.020
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Open Quantum Systems
  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book: Quantum Mechanics in Nanoscience and Engineering
  • Online publication: 11 May 2023
  • Chapter DOI: https://doi.org/10.1017/9781108877787.020
Available formats
×