Multi particle states calculations and particles storage in perturbed nanolayers
Abstract
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.
Supporting agencies: The work was supported by Federal Targeted Program “Scientific and Educational Human Resources for Innovation-Driven Russia” (contracts P689 NK-526P, 14.740.11.0879, 16.740.11.0030), grant 11-08-00267 of Russian Foundation for Basic Researches.
About the Author
S. I. Popov
Saint Petersburg National Research University of Information Technologies, Mechanics and Optics
Russian Federation
Russian Federation
49 Kronverkskiy, Saint Petersburg, 197101
References
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)
Review
For citations:
Popov S.I. Multi particle states calculations and particles storage in perturbed nanolayers. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(2):173-181.
Views:
5
Email this article 