Popov, Igor Yurievich

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Total publications: 37
Scientific articles: 37

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Abstract pages:6538
Full texts:2414
Popov, Igor Yurievich
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.03 (Mathematical physics)
Birth date: 24.01.1955
E-mail: ,
Keywords: scattering theory, spectral theory, quantum theory, mathematical modelling, fluid mechanics.


A new class of explicitly solvable model based on the operator extensions theory is constructed and investigated. It is applied to problems of acoustics, quantum physics, nanoelectronics, fluid mechanics and biophysics. Spectral and transport properties of some low-dimensional quantum systems (including the case of presense a magnetic field) was studied. Constructions of some nanoelectronic devices based on quantum interference were suggested. Asymptotics of bound states, bands and resonances close to the threshold for the Dirichlet Laplacian in waveguides and layers coupled through small windows was obtained.


Graduated from Physical Faculty of Leningrad State University (LSU) in 1978 (department of mathematical physics). Ph. D. thesis was defended in1984. D.;Sci. thesis was defended in;1996. A list of my works contains more than 250;titles. I am Editor-in-Chief of journal "Nanosystems: Physics, Chemistry, Mathematics".

Main publications:
  • Popov I. Yu. The resonator with narrow slit and the model based on the operator extensions theory // J. Math. Phys., 1992, 33(11), 3794–3801.
  • Geyler V. A., Pavlov B. S., Popov I. Yu. Spectral properties of a charged particle in antidot array: A limiting case of quantum billiard // J. Math. Phys., 1996, 37(10), 5171–5194.
  • Gugel Yu. V., Popov I. Yu., Popova S. L. Hydrotron: creep and slip // Fluid Dynam. Res., 1996, 18(4), 199–210.
  • Popov I. Yu. Asymptotics of bound states and bands for laterally coupled waveguides and layers // J. Math. Phys., 2002, 43(1), 215–234.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. M. P. Faleeva, I. Y. Popov, “On quantum bit coding by Gaussian beam modes for the quantum key distribution”, Nanosystems: Physics, Chemistry, Mathematics, 11:6 (2020),  651–658  mathnet
2. A. S. Bagmutov, I. Y. Popov, “Window-coupled nanolayers: window shape influence on one-particle and two-particle eigenstates”, Nanosystems: Physics, Chemistry, Mathematics, 11:6 (2020),  636–641  mathnet
3. A. M. Vorobiev, E. S. Trifanova, I. Y. Popov, “Resonance asymptotics for a pair quantum waveguides with common semitransparent perforated wall”, Nanosystems: Physics, Chemistry, Mathematics, 11:6 (2020),  619–627  mathnet
4. A. E. Baranov, A. I. Popov, I. Yu. Popov, “Modelling of surface water waves concentrated near moving points”, Zap. Nauchn. Sem. POMI, 493 (2020),  29–39  mathnet
5. E. G. Fedorov, A. I. Popov, I. Y. Popov, “Metric graph version of the FitzHugh–Nagumo model”, Nanosystems: Physics, Chemistry, Mathematics, 10:6 (2019),  623–626  mathnet  isi  elib
6. P. A. Gilev, I. Yu. Popov, “Quantum image transmission based on linear elements”, Nanosystems: Physics, Chemistry, Mathematics, 10:4 (2019),  410–414  mathnet  isi  elib
7. A. A. Boitsev, I. Yu. Popov, “A model of an electron in a quantum graph interacting with a two-level system”, Nanosystems: Physics, Chemistry, Mathematics, 10:2 (2019),  131–140  mathnet  isi  elib
8. A. Chatterjee, M. O. Smolkina, I. Y. Popov, “Persistent current in a chain of two Holstein-Hubbard rings in the presence of Rashba spin-orbit interaction”, Nanosystems: Physics, Chemistry, Mathematics, 10:1 (2019),  50–62  mathnet  isi  elib
9. M. O. Smolkina, I. Yu. Popov, I. V. Blinova, E. Milakis, “On the metric graph model for flows in tubular nanostructures”, Nanosystems: Physics, Chemistry, Mathematics, 10:1 (2019),  6–11  mathnet  isi  elib
10. D. A. Eremin, E. N. Grishanov, D. S. Nikiforov, I. Y. Popov, “Wave dynamics on time-depending graph with Aharonov–Bohm ring”, Nanosystems: Physics, Chemistry, Mathematics, 9:4 (2018),  457–463  mathnet  isi  elib
11. I. F. Melikhov, I. Yu. Popov, “Asymptotic analysis of thin viscous plate model”, Nanosystems: Physics, Chemistry, Mathematics, 9:4 (2018),  447–456  mathnet  isi  elib
12. A. A. Boitsev, J. Brasche, H. Neidhardt, I. Y. Popov, “A model of electron transport through a boson cavity”, Nanosystems: Physics, Chemistry, Mathematics, 9:2 (2018),  171–178  mathnet  isi  elib
13. Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, Stepan Bober, “Variational model of scoliosis”, Theor. Appl. Mech., 45:2 (2018),  167–175  mathnet  isi  scopus
14. I. S. Lobanov, V. Yu. Lotoreichik, I. Yu. Popov, “Lower bound on the spectrum of the two-dimensional Schrödinger operator with a $\delta$-perturbation on a curve”, TMF, 162:3 (2010),  397–407  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 162:3 (2010), 332–340  isi  scopus
15. I. Yu. Popov, A. I. Trifanov, E. S. Trifanova, “Coupled dielectric waveguides with photonic crystal properties”, Zh. Vychisl. Mat. Mat. Fiz., 50:11 (2010),  1931–1937  mathnet; Comput. Math. Math. Phys., 50:11 (2010), 1830–1836  isi  scopus
16. V. A. Geiler, D. A. Ivanov, I. Yu. Popov, “Approximation of a point perturbation on a Riemannian manifold”, TMF, 158:1 (2009),  49–57  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 158:1 (2009), 40–47  isi  scopus
17. I. Yu. Popov, E. S. Tesovskaya, “Electron in a multilayered magnetic structure: resonance asymptotics”, TMF, 146:3 (2006),  429–442  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 146:3 (2006), 361–372  isi  elib  scopus
18. I. Yu. Popov, S. V. Frolov, “Violation of symmetry in the system of three laterally coupled quantum waveguides and resonance asymptotics”, Zap. Nauchn. Sem. POMI, 300 (2003),  221–227  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 128:2 (2005), 2807–2811
19. I. Yu. Popov, “Asymptotic Series for the Spectrum of the Schrödinger Operator for Layers Coupled Through Small Windows”, TMF, 131:3 (2002),  407–418  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 131:3 (2002), 791–800  isi
20. I. Yu. Popov, “Short-range potential and a model of the theory of extensions of operators for a resonator with a semitransparent boundary”, Mat. Zametki, 65:5 (1999),  703–711  mathnet  mathscinet  zmath; Math. Notes, 65:5 (1999), 590–597  isi
21. I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, TMF, 119:2 (1999),  295–307  mathnet  mathscinet  zmath  elib; Theoret. and Math. Phys., 119:2 (1999), 629–639  isi
22. I. Yu. Popov, S. L. Popova, “Parallel Stokes flow in a ring-like structure”, Zh. Vychisl. Mat. Mat. Fiz., 39:7 (1999),  1196–1204  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 39:7 (1999), 1154–1162
23. I. Yu. Popov, “Ёволюци€ квазичаплыгинской среды и возмущение оператора Ћапласа на множестве нулевой меры”, Matem. Mod., 9:10 (1997),  21  mathnet
24. V. A. Geiler, I. Yu. Popov, “Ballistic transport in nanostructures: explicitly solvable models”, TMF, 107:1 (1996),  12–20  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 107:1 (1996), 427–434  isi
25. I. Yu. Popov, “A model of creeping fluid motion in domains connected by a small opening”, Matem. Mod., 7:5 (1995),  81  mathnet  zmath
26. A. A. Kiselev, I. Yu. Popov, “Indefinite metric and scattering by a domain with a small hole”, Mat. Zametki, 58:6 (1995),  837–850  mathnet  mathscinet  zmath; Math. Notes, 58:6 (1995), 1276–1285  isi
27. I. Yu. Popov, “Stratified flow in electric field, Schrödinger equation and operator extension theory model”, TMF, 103:2 (1995),  246–255  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 103:2 (1995), 535–542  isi
28. I. Yu. Popov, “On operator treatment of a Stokeslet”, Sibirsk. Mat. Zh., 35:5 (1994),  1148–1153  mathnet  mathscinet  zmath; Siberian Math. J., 35:5 (1994), 1022–1026  isi
29. I. Yu. Popov, “The Helmholtz resonator and the theory of operator extensions in a space with indefinite metric”, Mat. Sb., 183:3 (1992),  3–37  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315  isi
30. I. Yu. Popov, “A model of zero width slits for an orifice in a semitransparent boundary”, Sibirsk. Mat. Zh., 33:5 (1992),  121–126  mathnet  mathscinet  zmath; Siberian Math. J., 33:5 (1992), 856–861  isi
31. A. A. Kiselev, I. Yu. Popov, “Higher moments in a model of zero-width slits”, TMF, 89:1 (1991),  11–17  mathnet  mathscinet; Theoret. and Math. Phys., 89:1 (1991), 1019–1024  isi
32. B. S. Pavlov, I. Yu. Popov, “Acoustic model of zero-width slits and hydrodynamic boundary layer stability”, TMF, 86:3 (1991),  391–401  mathnet  mathscinet  zmath; Theoret. and Math. Phys., 86:3 (1991), 269–276  isi
33. I. Yu. Popov, “Integral equations in a model of apertures of zero width”, Algebra i Analiz, 2:5 (1990),  189–196  mathnet  mathscinet  zmath; Leningrad Math. J., 2:5 (1991), 1111–1119
34. I. Yu. Popov, “Justification of a model of zero-width slits for the Neumann problem”, Dokl. Akad. Nauk SSSR, 313:4 (1990),  806–811  mathnet  mathscinet  zmath; Dokl. Math., 42:1 (1991), 91–96
35. I. Yu. Popov, “Extension theory and localization of resonances for domains of trap type”, Mat. Sb., 181:10 (1990),  1366–1390  mathnet  mathscinet  zmath; Math. USSR-Sb., 71:1 (1992), 209–234  isi
36. I.Yu.Popov, “Justification of the model of cracks of zero width for the Dirichlet problem”, Sibirsk. Mat. Zh., 30:3 (1989),  103–108  mathnet  mathscinet  zmath; Siberian Math. J., 30:3 (1989), 428–432  isi
37. I. Yu. Popov, “A slit of zero width and the Dirichlet condition”, Dokl. Akad. Nauk SSSR, 294:2 (1987),  330–334  mathnet  mathscinet
38. M. M. Zimnev, I. Yu. Popov, “Selection of parameters for a model of cracks of zero width”, Zh. Vychisl. Mat. Mat. Fiz., 27:3 (1987),  466–470  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 27:2 (1987), 99–102

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