najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМОnajo-1302Research ArticleYOUNG RESEARCHES SIMPOSIUMYOUNG RESEARCHES SIMPOSIUMHartree-Fock approximation for the problem of particle storage in deformed nanolayerMelikhovI. F.

49 Kronverkskiy, St. Petersburg 197101

ivan.melikhov@gmail.comPopovI. Yu.

49 Kronverkskiy, St. Petersburg 197101

popov1955@gmail.comSt. Petersburg National Research University of Information Technologies, Mechanics and OpticsRussian Federation20132008202544Special Issue. INTERNATIONAL CONFERENCE "MATHEMATICAL CHALLENGE OF QUANTUM TRANSPORT IN NANOSYSTEMS - 2013. PIERRE DUCLOS WORKSHOP"559563Copyright © Melikhov I.F., Popov I.Y., 20252025Melikhov I.F., Popov I.Y.Melikhov I.F., Popov I.Y.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/1302

The paper deals with the problem of quantum particle storage in a nanolayered structures. The system of a few electrons interacting via a δ-potential is considered. The particles are placed into a two-dimensional deformed waveguide. From a mathematical point of view, the bound state of the system means that the corresponding Hamiltonian will have eigenvalues. To treat a multi-particle problem, the Hartree-Fock approach and the finite element method are used. Three different types of the perturbation are considered: deformation of the layer boundary, a small window in a wall between two layers and a bent layer. The systems of 2–10 particles with various total spins are studied. The dependence of the minimal deformation parameter, which keeps bound state on the number of particles, is given. Comparison of the storage efficiencies in those cases is made.

discrete spectrummulti-particle problemwaveguideSupported by Federal Targeted Program “Scientific and Educational Human Resources for Innovation-Driven Russia” (contracts P689 NK-526P, 14.740.11.0879, and 16.740.11.0030), grant 11-08-00267 of Russian Foundation for Basic Researches and by Federal Targeted Program “Researches and Development in the Priority Directions Developments of a Scientific and Technological Complex of Russia 2007-2013” (state contract 07.514.11.4146) and grants of the President of Russia.ReferencesP. Duclos, P. Exner, P. Stovichek. Curvature induced resonances in a two-dimensional Dirichlet tube. Annales de l’I.H.P. Section A. 62 (1), p. 81–101 (1995).P. Duclos, P. Exner, P. Stovichek. Curvature induced resonances in a two-dimensional Dirichlet tube. Annales de l’I.H.P. Section A. 62 (1), p. 81–101 (1995).P. Duclos, P. Exner, D. Krejcirik. Locally curved quantum layers Ukrainian J. Phys., 45, P. 595–601 (2000).P. Duclos, P. Exner, D. Krejcirik. Locally curved quantum layers Ukrainian J. Phys., 45, P. 595–601 (2000).P. Exner, S.A. Vugalter. Bounds states in a locally deformed waveguide: the critical case. Lett. Math. Phys., 39, P. 59–68 (1997).P. Exner, S.A. Vugalter. Bounds states in a locally deformed waveguide: the critical case. Lett. Math. Phys., 39, P. 59–68 (1997).P. Exner, S.A. Vugalter. Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window. Ann. Inst. H. Poincare, 65, P. 109–123 (1996).P. Exner, S.A. Vugalter. Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window. Ann. Inst. H. Poincare, 65, P. 109–123 (1996).P. Exner, P. Seba, M.Tater, D. Vanek. Bound states and scattering in quantum waveguides coupled laterally through a boundary window. J. Math. Phys., 37, P. 4867–4887 (1996).P. Exner, P. Seba, M.Tater, D. Vanek. Bound states and scattering in quantum waveguides coupled laterally through a boundary window. J. Math. Phys., 37, P. 4867–4887 (1996).I.Yu. Popov. Asymptotics of bound state for laterally coupled waveguides. Rep. on Math. Phys., 43 (3), P. 427–437 (1999).I.Yu. Popov. Asymptotics of bound state for laterally coupled waveguides. Rep. on Math. Phys., 43 (3), P. 427–437 (1999).I.Yu. Popov. Asymptotics of resonances and bound states for laterally coupled curved quantum waveg-uides. Phys. Lett. A, 269, P. 148–153 (2000).I.Yu. Popov. Asymptotics of resonances and bound states for laterally coupled curved quantum waveg-uides. Phys. Lett. A, 269, P. 148–153 (2000).H. Linde. Geometrically induced two-particle binding in a waveguide. J. Phys. A: Math. Gen., 39, P. 5105 (2006).H. Linde. Geometrically induced two-particle binding in a waveguide. J. Phys. A: Math. Gen., 39, P. 5105 (2006).P. Exner, S.A. Vugalter. On the number of particles that a curved quantum waveguide can bind. J. Math. Phys., 40, P. 4630–4638 (1999).P. Exner, S.A. Vugalter. On the number of particles that a curved quantum waveguide can bind. J. Math. Phys., 40, P. 4630–4638 (1999).S.I. Popov, M.I. Gavrilov, I.Yu. Popov. Two interacting particles in deformed nanolayer: discrete spectrum and particle storage. Phys. Scr., 3 (6), P. 17–23 (2012).S.I. Popov, M.I. Gavrilov, I.Yu. Popov. Two interacting particles in deformed nanolayer: discrete spectrum and particle storage. Phys. Scr., 3 (6), P. 17–23 (2012).A. Messiah. Quantum mechanics. V. 2. Moscow.: Nauka, 1979, 583 pA. Messiah. Quantum mechanics. V. 2. Moscow.: Nauka, 1979, 583 p

The authors declare that there are no conflicts of interest present.