Geodesic
Tunneling through a quantum dot in a quantum waveguide
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1222-1232 
A. A. Arsen'ev. Tunneling through a quantum dot in a quantum waveguide. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 7, pp. 1222-1232. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_7_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The problem is considered of scattering in a system consisting of a quantum waveguide and a quantum dot weakly coupled to the waveguide. It is assumed that the quantum waveguide is described by the Pauli equations, and the Rashba spin-orbit interaction is taken into account. The possibility of tunneling through the quantum dot is proved.

[1] Dittes F.-M., “The decay of quantum systems with a small number of open channels”, Phys. Repts., 2000, no. 339, 215–336 | DOI | MR

[2] Jakšić V., Krichevski E., Pillet C.-A., Mathematical theory of the Wigner-Weisskopf atom, http://ma.utexas.edu/mp_arc/05-333

[3] Derezinski J., Jakšić V., “Spectral theory of Pauli-Fierz operators”, J. Functional Analys., 180 (2001), 243–327 | DOI | MR | Zbl

[4] Howland J. S., “The livsic matrix of perturbation theory”, J. Math. Analys. Appl., 50 (1975), 415–435 | DOI | MR

[5] Agmon S., “A perturbation theory of resonances”, Communs Pure and Appl. Math., 51 (1998), 1255–1309 | 3.0.CO;2-O class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[6] Albevero S., Hoeg-Krohn R., “Perturbation of resonances in quantum mechanics”, J. Math. Analys. Appl., 101 (1984), 491–513 | DOI | MR

[7] Sasando K., Hatano N., Ordonez G., Resonant spectrum analysis of the conductance of open quantum system and three types of the fano parameter, arXiv: 0905.3953v1

[8] Arsenev A. A., “Matematicheskaya model rezonansnogo rasseyaniya”, Matem. zametki, 70:4 (2001), 491–502 | MR

[9] Arsenev A. A., “Rezonansnoe rasseyanie v kvantovykh volnovodakh”, Matem. sb., 199:1 (2003), 3–22 | MR

[10] Arsenev A. A., “Matematicheskaya model rezonansov i tunnelirovaniya v sisteme so svyazannym sostoyaniem”, Teor. i matem. fiz., 136:3 (2003), 507–516 | MR

[11] Khermander L., Analiz lineinykh differentsialnykh operatorov s chastnymi proizvodnymi, v. 2, Mir, M., 1986

[12] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR

[13] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[14] Cancelier C., Martinez A., Ramond T., Quantum resonances without analyticity, http://ma.utexas.edu/mp_arc/04-251

[15] Yafaev D. R., Matematicheskaya teoriya rasseyaniya, Izd-vo SPbGU, SPb., 1994 | MR

[16] Fridman A., Uravneniya s chastnymi proizvodnymi parabolicheskogo tipa, Mir, M., 1968

[17] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl