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2 results

  • 20 - Open Many-Fermion Systems

  • Uri Peskin, Technion - Israel Institute of Technology, Haifa
  • Book:
    Quantum Mechanics in Nanoscience and Engineering
    Published online:
    11 May 2023
    Print publication:
    01 June 2023, pp 431-472

  • 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.

  • Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport

  • Sihong Shao, Tiao Lu, Wei Cai
  • Journal:
    Communications in Computational Physics / Volume 9 / Issue 3 / March 2011
    Published online by Cambridge University Press:
    20 August 2015, pp. 711-739
    Print publication:
    March 2011

  • A new adaptive cell average spectral element method (SEM) is proposed to solve the time-dependent Wigner equation for transport in quantum devices. The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for the numerical solutions. The key feature of the proposed method is an analytical relation between the cell averages of the Wigner function in the k-space (local electron density for finite range velocity) and the point values of the distribution, resulting in fast transforms between the local electron density and local fluxes of the discretized Wigner equation via the fast sine and cosine transforms. Numerical results with the proposed method are provided to demonstrate its high accuracy, conservation, convergence and a reduction of the cost using adaptive meshes.