Window-coupled nanolayers: window shape influence on one-particle and two-particle eigenstates
https://doi.org/10.17586/2220-8054-2020-11-6-636-641
Abstract
In this work, we present a number of numerical results for the bound state energies of one and two-particle systems in two adjacent 3D layers, connected through a window. We investigate the relation between the shape of a window and energy levels, as well as number of eigenfunction’s nodal domains.
Supporting agencies: This work was partially financially supported by grant 20-31-90050 of Russian Foundation for Basic Research.
About the Authors
A. S. Bagmutov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, Saint Petersburg, 197101
I. Y. Popov
ITMO University
Russian Federation
Russian Federation
Kronverkskiy, 49, Saint Petersburg, 197101
References
1. Borisov D., Exner P., Gadylshin R., Krejcirik D. Bound states in weakly deformed strips and layers, Annales Henri Poincare, 2001, 2(3), P. 553–572.
2. Bulla W. and Renger W. Existence of bound states in quantum waveguides under weak conditions. Lett. Math. Phys., 1995, 35(1), P. 1–12.
3. Duclos P. and Exner P. Curvature-induced bound state in quantum waveguides in two and three dimensions. Rev. Math. Phys., 1995, 7(1), P. 73–102.
4. Duclos P., Exner P., Stovicek P. Curvature-induced resonances in a two-dimensional Dirichlet tube. Annales Henri Poincare, 1995, 62(1), P. 81–101.
5. Chenaud B., Duclos P., Freitas P. and Krejcirik D. Geometrically induced discrete spectrum in curved tubes. Diff. Geom. Appl., 2005, 23(2), P. 95–105.
6. Exner P. and Vugalter S.A. Bound States in a Locally Deformed Waveguide: The Critical Case. Lett. Math. Phys., 1997, 39(1), P. 59–68.
7. Briet Ph., Kovarik H., Raikov G. and Soccorsi E. Eigenvalue asymptotics in a twisted waveguide. Comm. PDE, 2009, 34(8), P. 818–836.
8. Ekholm T., Kovarik H. and Krejcirik D. A Hardy inequality in twisted waveguides. Arch. Rat. Mech. Anal., 2008, 188(2), P. 245–264.
9. Duclos P. and Exner P. Curvature-induced bound state in quantum waveguides in two and three dimensions. Rev. Math. Phys., 1995, 7(1), P. 73–102.
10. Borisov D., Ekholm T. and Kovarik H. Spectrum of the magnetic Schrodinger operator in a waveguide with combined boundary conditions. Annales Henri Poincare, 2005, 6(2), P. 327-342.
11. Ekholm T. and Kovarik H. Stability of the magnetic Schrodinger operator in a waveguide. Comm. PDE, 2005, 30(4), P. 539–565.
12. Grushin V.V. On the eigenvalues of finitely perturbed laplace operators in infinite cylindrical domains. Math. Notes, 2004, 75(3), P. 331–340.
13. Borisov D. Discrete spectrum of a pair of non-symmetric waveguides coupled by a window. Sbornik Mathematics, 2006, 197(4), P. 475–504.
14. Borisov D. and Exner P. Distant perturbation asymptotics in window-coupled waveguides. I. The non-threshold case. J. Math. Phys., 2006, 47(11), P. 113502-(1–24).
15. Borisov D., Exner P. and Gadylshin R. Geometric coupling thresholds in a two-dimensional strip. Journal of Mathematical Physics, 2002, 43(12), P. 6265–6278.
16. Bulla W., Gesztesy F., Renger W., Simon B. Weakly coupled bound states in quantum waveguides. Proc. Amer. Math. Soc., 1997, 125(5), P. 1487–1495.
17. Exner P., Seba P., Tater M., and Van?ek D. Bound states and scattering in quantum waveguides coupled laterally through a boundary window. J. Math. Phys., 1996, 37(10), P. 4867–4887.
18. Exner P. and Vugalter S. Bound-state asymptotic estimate for windowcoupled Dirichlet strips and layers. J. Phys. A., 1997, 30(22), P. 7863– 7878.
19. Gadylshin R. On regular and singular perturbation of acoustic and quantum waveguides. Comptes Rendus Mechanique, 2004, 332(8), P. 647– 652.
20. Vorobiev A.M., Bagmutov A.S., Popov A.I. On formal asymptotic expansion of resonance for quantum waveguide with perforated semitransparent barrier. Nanosystems: Physics, Chemistry, Mathematics, 2019, 10(4), P. 415–419.
21. Popov I.Yu. Asymptotics of bound states and bands for laterally coupled waveguides and layers. J. Math. Phys., 2002, 43(1), P. 215–234.
22. Borisov D. On the spectrum of two quantum layers coupled by a window. J. Phys. A: Math. Theor., 2007, 40(19), P. 5045–5066.
23. Linde H. Geometrically induced two-particle binding in a waveguide. J. Phys. A: Math. Gen., 2006, 39(18), P. 5105–5114.
24. Popov S.I., Gavrilov M.I. and Popov I.Yu., Two interacting particles in deformed nanolayer: discrete spectrum and particle storage. Phys. Scripta, 2012, 86(3), P. 035003.
25. Melikhov I.F. and Popov I.Yu. Hartree–Fock approximation for the problem of particle storage in deformed nanolayer. Nanosystems: Physics, Chemistry, Mathematics, 2013, 4(4), P. 559–563.
26. Popov I.Y., Bagmutov A.S., Melikhov I.F., Najar H. Numerical analysis of multi-particle states in coupled nano-layers in electric field. AIP Conference Proceedings, 2020, 2293, P. 360006.
27. Popov I.Y., Melikhov I.F. Multi-particle bound states in window-coupled 2D quantum waveguides. Chinese J. of Physics – Taipei, 2015, 53(3), P. 0802/1–12.
28. Calogero F. and Degasperis A. Comparison between the exact and Hartree solutions of a one-dimensional many-body problem. Phys. Rev. A, 1975, 11(1), P. 265–269.
29. Band R., Berkolaiko G., Raz H. et al. The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions. Commun. Math. Phys., 2012, 311, P. 815–838.
30. Band R., Oren I., Smilansky U. Nodal domains on graphs – how to count them and why? In: Analysis on graphs and its applications. Proc. Sympos. Pure Math., 2008, 77, P. 5–27.
31. Helffer B., Sundqvist M.P. On nodal domains in Euclidean balls. Proc. Amer. Math. Soc., 2016, 144(11), P. 4777–4791.
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Bagmutov A.S., Popov I.Y. Window-coupled nanolayers: window shape influence on one-particle and two-particle eigenstates. Nanosystems: Physics, Chemistry, Mathematics. 2020;11(6):636–641. https://doi.org/10.17586/2220-8054-2020-11-6-636-641
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