Multi particle states calculations and particles storage in perturbed nanolayers
Аннотация
The problem of particle storage in nanolayered structures will be considered. Local perturbations of nanolayers can lead to the appearanceof eigenvalues of the corresponding one-particle Hamiltonian. To study particle storage it is necessary to deal with the multi-particle problem. This problem faces essential computational difficulties due to the great increase of the spatial dimension. Using a composite of natural physical models, analytical methods and computational approaches allows one to simplify the problem and to obtain useful results for application. Particularly, the Hartree method and Finite Elements Method (FEM) are used. The discrete spectrum of the Hamiltonian for two interacting particles is considered. Two different types of perturbation are considered: deformation of the layer boundary and a small window in a wall between two layers. The relation between the system parameters (interaction intensity- waveguide deformation) ensuring the existence of a non-empty discrete spectrum is studied. A comparison of particle storage efficiencies is made for these two cases.
Об авторе
S. Popov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Россия
Россия
Список литературы
1. Gavrilov M., Gortinskaya L., Pestov A., Popov I. and Tesovskaya E. Phys. Part. Nucl. Lett., 4(2), P. 137 (2007).
2. Pavlov B.S., Popov I.Yu., Geyler V.A. and Pershenko O.S. Europhys. Lett., 52(2), P. 196 (2000).
3. Roemer R.A. and Raikh M.E. Phys. Rev.B, 62(11), P. 7045 (2000).
4. Shepelyansky D.L. Phys. Rev. Lett., 73(19), P. 2607 (1994).
5. Sutherland B. Beautiful Models. 70 Years of Exactly Solved Quantum Many-body Problems (World Scientific, Singapore, 2004).
6. Shen J.-T. and Fan Sh. New J. Phys., 11, P. 113024 (2009).
7. Langmann G., Laptev A. and Paufler C. J. Phys. A: Math. Gen., 39, P. 1057 (2006).
8. Buslaev V.S., Levin S.B., Neittaanmaki P. and Ojala T. J. Phys. A: Math. Theor., 43, P. 285205 (2010).
9. Nogami Y., Toyama F.M. and Varshni Y.P. Phys. Lett. A, 207, P. 355 (1995).
10. Exner P. and Vugalter S.A. J. Math. Phys., 40(10), P. 4630 (1999).
11. Exner P. and Zagrebnov V.A. J. Phys. A: Math. Gen., 38, P. L463 (2005).
12. Linde H. J. Phys. A: Math. Gen., 39, P. 5105 (2006).
13. Newton R.G. J. Operator Theory, 10, P. 119 (1983).
14. Klaus M. Annals Phys., 108(2), P. 288 (1977).
15. Seto N. Publ. RIMS, 9, P. 429 (1974).
16. Popov I.Yu. J. Math. Phys., 33(5), P. 1685 (1992).
17. Popov I.Yu. Math. Proc. Cambridge Phil. Soc., 118(3), P. 555 (1995).
18. Lobanov I.S., Lotoreichik V.Yu. and Popov I.Yu. Theor. Math. Phys., 162(3), P. 397 (2010).
19. Exner P. and Vugalter S.A. Lett. Math. Phys., 39(1), P. 59 (1997).
20. Duclos P. and Exner P. Rev. Math. Phys., 7, P. 73 (1995).
21. Bulla W., Gesztesy F., Renger W. and Simon B. Proc. Am. Math. Soc., 125, P. 1487 (1997).
22. Okopinska A. J. Phys.: Conf. Series, 213(1), P. 012004 (2010).
23. Block I., Dalibard J. and Zwerger W. Rev. Mod. Phys., 80(3), P. 885 (2008).
24. Cornean H., Duclos P. and Ricaud B. Few-Body Systems, 38(2-4), P. 125 (2006).
25. Exner P. and Vugalter S., Ann. I.H.P. Phys. Theor., 65, P. 109–123 (1996).
26. Popov I.Yu. Appl. Math. Lett., 14, P. 109–113 (2001).
27. Popov I.Yu. J.Math.Phys., 43(1), P. 215–234 (2002)
Рецензия
Для цитирования:
. Наносистемы: физика, химия, математика. 2013;4(2):173-181.
For citation:
Popov S.I. Multi particle states calculations and particles storage in perturbed nanolayers. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(2):173-181.
Просмотров:
41
Послать статью по эл. почте 