TY - JOUR

T1 - A semispectral approach for the efficient calculation of scattering matrices in quasi-1D quantum systems and transmission coefficients for the Landauer formula

AU - Goncharov, L.I.

AU - Yafyasov, A.M.

AU - Tsurikov, D.E.

PY - 2014

Y1 - 2014

N2 - Abstract This paper proposes the semispectral method for the calculation of the scattering matrices for the charge carriers in quasi-one-dimensional quantum systems described by the Schrodinger equation. An efficient and accurate calculation method is achieved by adding of reference solutions at selected energy points to the eigenfunction expansion of the Green’s function. A numerical simulation of the quantum wire with the square cross-section in transverse electric field was performed by different methods. The example problem of a quantum wire in a transverse electric field is used to compare the semispectral method with alternative approaches. We find that the semispectral method reliably converges and is significantly faster than the direct solution while the eigenfunction expansion approach has convergence issues. These results allow us to propose the semispectral method as a universal and efficient approach to calculation of the transmission coefficients for the Landauer formula as well as other scatter

AB - Abstract This paper proposes the semispectral method for the calculation of the scattering matrices for the charge carriers in quasi-one-dimensional quantum systems described by the Schrodinger equation. An efficient and accurate calculation method is achieved by adding of reference solutions at selected energy points to the eigenfunction expansion of the Green’s function. A numerical simulation of the quantum wire with the square cross-section in transverse electric field was performed by different methods. The example problem of a quantum wire in a transverse electric field is used to compare the semispectral method with alternative approaches. We find that the semispectral method reliably converges and is significantly faster than the direct solution while the eigenfunction expansion approach has convergence issues. These results allow us to propose the semispectral method as a universal and efficient approach to calculation of the transmission coefficients for the Landauer formula as well as other scatter

KW - Landauer formula · Dirichlet-to-Neumann map · Quantum scattering · Green’s function · 1D conductivity

U2 - 10.1007/s10825-014-0605-9

DO - 10.1007/s10825-014-0605-9

M3 - Article

VL - 13

SP - 885

EP - 893

JO - Journal of Computational Electronics

JF - Journal of Computational Electronics

SN - 1569-8025

IS - 4

ER -