Geodesic
Splitting of lower energy levels in a~quantum double well in a~magnetic field and tunneling of wave packets in nanowires
Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 206-225

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We consider the problem of the splitting of lower eigenvalues of the two-dimensional Schrödinger operator with a double-well-type potential in the presence of a homogeneous magnetic field. The main result is the observation that the partial Fourier transformation takes the operator under study to a Schrödinger-type operator with a (new) double-well-type potential but already without any magnetic field. We use this observation to investigate the influence of the magnetic field on the tunneling effects. We discuss two methods for calculating the splitting of lower eigenvalues: based on the instanton and based on the so-called libration. We use the obtained result to study the tunneling of wave packets in parallel quantum nanowires in a constant magnetic field.
Keywords: Schrödinger operator, double-well-type potential, homogeneous magnetic field, tunneling, double quantum wire, wave packet. 
@article{TMF_2013_175_2_a5,
     author = {J. Br\"uning and S. Yu. Dobrokhotov and R. V. Nekrasov},
     title = {Splitting of lower energy levels in a~quantum double well in a~magnetic field and tunneling of wave packets in nanowires},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {206--225},
     publisher = {mathdoc},
     volume = {175},
     number = {2},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a5/}
}
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J. Brüning; S. Yu. Dobrokhotov; R. V. Nekrasov. Splitting of lower energy levels in a~quantum double well in a~magnetic field and tunneling of wave packets in nanowires. Teoretičeskaâ i matematičeskaâ fizika, Tome 175 (2013) no. 2, pp. 206-225. http://geodesic.mathdoc.fr/item/TMF_2013_175_2_a5/