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.
Biography
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.
A. G. Belolipetskaia, I. Yu. Popov, “Influence of quantum graph parameters on the asymptotics of the number of resonances”, Chelyab. Fiz.-Mat. Zh., 9:4 (2024), 682–688
2.
I. Y. Popov, E. S. Trifanova, A. S. Bagmutov, I. V. Blinova, “Barrier composed of perforated resonators and boundary conditions”, Eurasian Math. J., 15:3 (2024), 68–76
3.
Igor Yu. Popov, Anton I. Popov, Pavel A. Gilev, Ashok Chatterjee, “Quantum graph as a benchmark for persistent current”, Nanosystems: Physics, Chemistry, Mathematics, 15:4 (2024), 469–472
4.
Alina S. Melikhova, Anton I. Popov, Irina V. Blinova, Igor Yu. Popov, “Mathematical model of weakly coupled spherical resonator chains under the influence of external magnetic field”, Nanosystems: Physics, Chemistry, Mathematics, 15:2 (2024), 155–159
2023
5.
E. S. Trifanova, A. S. Bagmutov, V. G. Katasonov, I. Yu. Popov, “Asymptotic expansions of resonances for waveguides coupled through converging windows”, Chelyab. Fiz.-Mat. Zh., 8:1 (2023), 72–82
6.
I. Yu. Popov, T. S. Yurova, “Resonances for a solvable model of ultrasound scattering by a cell membrane”, Pis'ma v Zh. Èksper. Teoret. Fiz., 118:2 (2023), 135–140; JETP Letters, 118:2 (2023), 146–151
7.
Igor Y. Popov, “A model of charged particle on the flat Möbius strip in a magnetic field”, Nanosystems: Physics, Chemistry, Mathematics, 14:4 (2023), 418–420
8.
Irina V. Blinova, Evgeny N. Grishanov, Anton I. Popov, Igor Y. Popov, Maria O. Smolkina, “On spin flip for electron scattering by several delta-potentials for 1D Hamiltonian with spin-orbit interaction”, Nanosystems: Physics, Chemistry, Mathematics, 14:4 (2023), 413–417
2022
9.
Timur N. Topaev, Anton I. Popov, Igor Yu. Popov, “On Keller–Rubinow model for Liesegang structure formation”, Nanosystems: Physics, Chemistry, Mathematics, 13:4 (2022), 365–371
10.
A. S. Bagmutov, H. Najar, I. F. Melikhov, I. Y. Popov, “On the discrete spectrum of a quantum waveguide with Neumann windows in presence of exterior field”, Nanosystems: Physics, Chemistry, Mathematics, 13:2 (2022), 156–163
I. A. Nesterenko, I. Yu. Popov, “Modeling the evolution of surface nanobubbles”, Nanosystems: Physics, Chemistry, Mathematics, 12:5 (2021), 603–611
12.
A. G. Belolipetskaia, I. Yu. Popov, “Dirac operator with different potentials on edges of quantum graph: resonance asymptotics”, Nanosystems: Physics, Chemistry, Mathematics, 12:4 (2021), 425–429
13.
A. S. Melikhova, M. P. Faleeva, I. Yu. Popov, “On the choice of parameters for a model of small window”, Nanosystems: Physics, Chemistry, Mathematics, 12:2 (2021), 151–155
I. S. Lobanov, A. I. Trifanov, E. S. Trifanova, I. Y. Popov, E. Fedorov, K. V. Pravdin, M. A. Moskalenko, “Photon generation in resonator with time dependent boundary conditions”, Nanosystems: Physics, Chemistry, Mathematics, 12:1 (2021), 73–80
15.
A. A. Lytaev, I. Yu. Popov, “Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory”, Zhurnal SVMO, 23:4 (2021), 433–443
16.
I. V. Blinova, A. S. Gnedash, I. Y. Popov, “A time-dependent metric graph with a fourth-order operator on the edges”, Theor. Appl. Mech., 48:2 (2021), 187–200
2020
17.
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
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
19.
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
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
2019
21.
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
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
24.
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
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
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
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
M. P. Faleeva, I. Yu. Popov, I. Žežula, “On quantitative determination of the degree of independence of qubit transformation by a quantum gate or channel”, Optics and Spectroscopy, 124:5 (2018), 686–690; Optics and Spectroscopy, 124:5 (2018), 720–725
D. A. Eremin, E. N. Grishanov, O. G. Kostrov, D. S. Nikiforov, I. Yu. Popov, “Time dependent quantum graph with loop”, Nanosystems: Physics, Chemistry, Mathematics, 8:4 (2017), 420–425
D. L. Meynster, I. Yu. Popov, A. I. Popov, “Model of tunnelling through double quantum layer in a magnetic field”, Nanosystems: Physics, Chemistry, Mathematics, 8:2 (2017), 194–201
2016
33.
E. N. Grishanov, I. Yu. Popov, “Computer simulation of periodic nanostructures”, Nanosystems: Physics, Chemistry, Mathematics, 7:5 (2016), 865–868
I. Yu. Popov, P. A. Kurasov, S. N. Naboko, A. A. Kiselev, A. E. Ryzhkov, A. M. Yafyasov, G. P. Miroshnichenko, Yu. E. Karpeshina, V. I. Kruglov, T. F. Pankratova, A. I. Popov, “A distinguished mathematical physicist Boris S. Pavlov”, Nanosystems: Physics, Chemistry, Mathematics, 7:5 (2016), 782–788
I. V. Makeev, I. Yu. Popov, “Steady Stokes flow between confocal semi-ellipses”, Nanosystems: Physics, Chemistry, Mathematics, 7:2 (2016), 324–331
2015
37.
I. V. Makeev, I. V. Blinova, I. Yu. Popov, “Analytical benchmark solutions for nanotube flows with variable viscosity”, Nanosystems: Physics, Chemistry, Mathematics, 6:5 (2015), 672–679
38.
E. N. Grishanov, D. A. Eremin, D. A. Ivanov, I. Yu. Popov, P. I. Smirnov, “Periodic chain of disks in a magnetic field: bulk states and edge states”, Nanosystems: Physics, Chemistry, Mathematics, 6:5 (2015), 637–643
39.
V. M. Adamyan, I. V. Blinova, A. I. Popov, I. Yu. Popov, “Waveguide bands for a system of macromolecules”, Nanosystems: Physics, Chemistry, Mathematics, 6:5 (2015), 611–617
A. I. Popov, I. S. Lobanov, I. Yu. Popov, T. V. Gerya, “On the Stokes flow computation algorithm based on woodbury formula”, Nanosystems: Physics, Chemistry, Mathematics, 6:1 (2015), 140–145
A. E. Ivanova, S. A. Chivilikhin, I. Yu. Popov, A. V. Gleim, “On the possibility of using optical Y-splitter in quantum random number generation systems based on fluctuations of vacuum”, Nanosystems: Physics, Chemistry, Mathematics, 6:1 (2015), 95–99
2014
42.
K. V. Pravdin, I. Yu. Popov, “Photonic crystal with negative index material layers”, Nanosystems: Physics, Chemistry, Mathematics, 5:5 (2014), 626–643
43.
O. A. Rodygina, S. A. Chivilikhin, I. Yu. Popov, V. V. Gusarov, “Crystallite model for flow in nanotube caused by wall soliton”, Nanosystems: Physics, Chemistry, Mathematics, 5:3 (2014), 400–404
44.
A. I. Popov, I. S. Lobanov, I. Yu. Popov, T. V. Gerya, “Benchmark solutions for nanoflows”, Nanosystems: Physics, Chemistry, Mathematics, 5:3 (2014), 391–399
2013
45.
I. Yu. Popov, “On the possibility of magnetoresistance governed by light”, Nanosystems: Physics, Chemistry, Mathematics, 4:6 (2013), 795–799
46.
A. A. Boitsev, H. Neidhardt, I. Yu. Popov, “Weyl function for sum of operators tensor products”, Nanosystems: Physics, Chemistry, Mathematics, 4:6 (2013), 747–759
47.
K. V. Pravdin, I. Yu. Popov, “Model of the interaction of point source electromagnetic fields with metamaterials”, Nanosystems: Physics, Chemistry, Mathematics, 4:4 (2013), 570–576
48.
I. F. Melikhov, I. Yu. Popov, “Hartree-fock approximation for the problem of particle storage in deformed nanolayer”, Nanosystems: Physics, Chemistry, Mathematics, 4:4 (2013), 559–563
2012
49.
A. A. Boitsev, I. Yu. Popov, O. V. Sokolov, “Hamiltonian with zero-range potentials having infinite number of eigenvalues”, Nanosystems: Physics, Chemistry, Mathematics, 3:4 (2012), 9–19
50.
D. G. Matveev, I. Yu. Popov, “Variational estimations of the eigenvalues for 3D quantum waveguides in a transverse electric field”, Nanosystems: Physics, Chemistry, Mathematics, 3:3 (2012), 6–22
51.
I. S. Lobanov, I. Yu. Popov, “Scattering by a junction of “zig-zag” and “armchair” nanoutubes”, Nanosystems: Physics, Chemistry, Mathematics, 3:2 (2012), 6–28
52.
S. A. Chivilikhin, V. V. Gusarov, I. Yu. Popov, “Flows in nanostructures: hybrid classical-quantum models”, Nanosystems: Physics, Chemistry, Mathematics, 3:1 (2012), 7–26
2011
53.
S. A. Chivilikhin, I. Yu. Popov, V. V. Gusarov, “Planar flows in nanoscale regions”, Nanosystems: Physics, Chemistry, Mathematics, 2:3 (2011), 49–52
54.
D. A. Eremin, I. Yu. Popov, “Quantum ring with wire: a model of two-particles problem”, Nanosystems: Physics, Chemistry, Mathematics, 2:2 (2011), 15–31
2010
55.
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; Theoret. and Math. Phys., 162:3 (2010), 332–340
V. A. Geiler, D. A. Ivanov, I. Yu. Popov, “Approximation of a point perturbation on a Riemannian manifold”, TMF, 158:1 (2009), 49–57; Theoret. and Math. Phys., 158:1 (2009), 40–47
I. Yu. Popov, E. S. Tesovskaya, “Electron in a multilayered magnetic structure: resonance asymptotics”, TMF, 146:3 (2006), 429–442; Theoret. and Math. Phys., 146:3 (2006), 361–372
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; J. Math. Sci. (N. Y.), 128:2 (2005), 2807–2811
2002
60.
I. Yu. Popov, “Asymptotic Series for the Spectrum of the Schrödinger Operator for Layers Coupled Through Small Windows”, TMF, 131:3 (2002), 407–418; Theoret. and Math. Phys., 131:3 (2002), 791–800
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; Math. Notes, 65:5 (1999), 590–597
I. Yu. Popov, D. A. Zubok, “Two physical applications of the Laplace operator perturbed on a null set”, TMF, 119:2 (1999), 295–307; Theoret. and Math. Phys., 119:2 (1999), 629–639
I. Yu. Popov, S. L. Popova, “Parallel Stokes flow in a ring-like structure”, Zh. Vychisl. Mat. Mat. Fiz., 39:7 (1999), 1196–1204; Comput. Math. Math. Phys., 39:7 (1999), 1154–1162
1997
64.
I. Yu. Popov, “Эволюция квазичаплыгинской среды и возмущение оператора Лапласа на множестве нулевой меры”, Matem. Mod., 9:10 (1997), 21
1996
65.
V. A. Geiler, I. Yu. Popov, “Ballistic transport in nanostructures: explicitly solvable models”, TMF, 107:1 (1996), 12–20; Theoret. and Math. Phys., 107:1 (1996), 427–434
I. Yu. Popov, “A model of creeping fluid motion in domains connected by a small opening”, Matem. Mod., 7:5 (1995), 81
67.
A. A. Kiselev, I. Yu. Popov, “Indefinite metric and scattering by a domain with a small hole”, Mat. Zametki, 58:6 (1995), 837–850; Math. Notes, 58:6 (1995), 1276–1285
I. Yu. Popov, “Stratified flow in electric field, Schrödinger equation and operator extension theory model”, TMF, 103:2 (1995), 246–255; Theoret. and Math. Phys., 103:2 (1995), 535–542
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; Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315
I. Yu. Popov, “A model of zero width slits for an orifice in a semitransparent boundary”, Sibirsk. Mat. Zh., 33:5 (1992), 121–126; Siberian Math. J., 33:5 (1992), 856–861
1991
72.
A. A. Kiselev, I. Yu. Popov, “Higher moments in a model of zero-width slits”, TMF, 89:1 (1991), 11–17; Theoret. and Math. Phys., 89:1 (1991), 1019–1024
B. S. Pavlov, I. Yu. Popov, “Acoustic model of zero-width slits and hydrodynamic boundary layer stability”, TMF, 86:3 (1991), 391–401; Theoret. and Math. Phys., 86:3 (1991), 269–276
I. Yu. Popov, “Integral equations in a model of apertures of zero width”, Algebra i Analiz, 2:5 (1990), 189–196; Leningrad Math. J., 2:5 (1991), 1111–1119
75.
I. Yu. Popov, “Justification of a model of zero-width slits for the Neumann
problem”, Dokl. Akad. Nauk SSSR, 313:4 (1990), 806–811; Dokl. Math., 42:1 (1991), 91–96
I. Yu. Popov, “Extension theory and localization of resonances for domains of trap type”, Mat. Sb., 181:10 (1990), 1366–1390; Math. USSR-Sb., 71:1 (1992), 209–234
I.Yu.Popov, “Justification of the model of cracks of zero width for the Dirichlet problem”, Sibirsk. Mat. Zh., 30:3 (1989), 103–108; Siberian Math. J., 30:3 (1989), 428–432
I. Yu. Popov, “A slit of zero width and the Dirichlet condition”, Dokl. Akad. Nauk SSSR, 294:2 (1987), 330–334
79.
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; U.S.S.R. Comput. Math. Math. Phys., 27:2 (1987), 99–102
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