Abstract
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.
Similar content being viewed by others
References
F.-M. Dittes, “The Decay of Quantum Systems with a Small Number of Open Channels,” Physics Rep., No. 339, 215–336 (2000).
V. Jakšić, E. Krichevski, and C.-A. Pillet, Mathematical theory of the Wigner-Weisskopf Atom. http://ma.utexas.edu/mp-arc/05-333.
J. Derezinski and V. Jakšić, “Spectral Theory of Pauli-Fierz Operators,” J. Functional Anal. 180, 243–327 (2001).
J. S. Howland, “The Livsic Matrix in Perturbation Theory,” J. Math. Anal. Appl. 50, 415–435 (1975).
S. Agmon, “A Perturbation Theory of Resonances,” Commun. Pure Appl. Math. 51, 1255–1309 (1998).
S. Albevero and R. Hoeg-Krohn, “Perturbation of Resonances in Quantum Mechanics,” J. Math. Anal. Appl. 101, 491–513 (1984).
K. Sasando, N. Hatano, and G. Ordonez, “Resonant Spectrum Analysis of the Conductance of Open Quantum System and Three Types of the Fano Parameter,” arXiv:0905.3953v1.
A. A. Arsen’ev, “Mathematical Model of Resonance Scattering,” Mat. Zametki 70, 491–502 (2001).
A. A. Arsen’ev, “Resonance Scattering in Quantum Wave Guides,” Mat. Sb. 199(1), 3–22 (2003).
A. A. Arsen’ev, “Mathematical Model of Resonances and Tunneling in a System with a Bound State,” Teor. Mat. Fiz. 136, 507–516 (2003).
L. Hörmander, The Analysis of Linear Partial Differential Operators Vol. 2: Differential Operators with Constant Coefficients (Springer-Verlag, Berlin, 1983; Mir, Moscow, 1986).
O. A. Ladyzhenskaya and N. N. Ural’tseva, Linear and Quasilinear Elliptic Equations (Nauka, Moscow, 1973; Academic, New York, 1987).
O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type (Nauka, Moscow, 1967; Am. Math. Soc., Providence, R.I., 1968).
C. Cacelier, A. Martinez, and T. Ramond, “Quantum Resonance without Analyticity” http://ma.utexas.edu/mp-arc/04-251.
D. R. Yafaev, Mathematical Theory of Scattering (S.-Peterb. Univ., St. Petersburg, 1994) [in Russian].
A. Friedman, Partial Differential Equations of Parabolic Type (Prentice Hall, Englewood Cliffs, N.J., 1964; Mir, Moscow, 1968).
T. Kato, Perturbation Theory for Linear Operators (Springer-Verlag, Berlin, 1966; Mir, Moscow, 1972).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.A. Arsen’ev, 2010, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2010, Vol. 50, No. 7, pp. 1222–1232.
Rights and permissions
About this article
Cite this article
Arsen’ev, A.A. Tunneling through a quantum dot in a quantum waveguide. Comput. Math. and Math. Phys. 50, 1162–1171 (2010). https://doi.org/10.1134/S0965542510070055
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542510070055