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20 - Open Many-Fermion Systems

Published online by Cambridge University Press:  11 May 2023

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

We introduce a kinetic theory of electron transport on the nanoscale, formulated in terms of the Fock space of an open many-electron system, and the “second quantization” Hamiltonian. To model a thermal electron reservoir (e.g., a metal electrode), the Fermi–Dirac distribution is derived from the corresponding density operator. A nanoscale system, weakly coupled to the reservoir, is modeled as an impurity. When the Born–Markov and secular approximations are valid, quantum master equations are derived, showing that the impurity equilibrates with the reservoir. To account for charge transport through the impurity, as in atomic point contacts or single molecule junctions, the master equations are generalized for cases of an impurity coupled to different reservoirs at different chemical potentials/temperatures. In these cases, we show that the system reaches a nonequilibrium steady state, where current flows through the impurity. Analytic expressions are derived for this steady state in simple models.

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  • Open Many-Fermion 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/10.1017/9781108877787.021
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  • Open Many-Fermion 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/10.1017/9781108877787.021
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 Many-Fermion 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/10.1017/9781108877787.021
Available formats
×