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.
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
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
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
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
2019
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
6.
P. A. Gilev, I. Yu. Popov, “Quantum image transmission based on linear elements”, Nanosystems: Physics, Chemistry, Mathematics, 10:4 (2019), 410–414
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
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
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
2018
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
11.
I. F. Melikhov, I. Yu. Popov, “Asymptotic analysis of thin viscous plate model”, Nanosystems: Physics, Chemistry, Mathematics, 9:4 (2018), 447–456
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
13.
Igor Popov, Nikita Lisitsa, Yuri Baloshin, Mikhail Dudin, Stepan Bober, “Variational model of scoliosis”, Theor. Appl. Mech., 45:2 (2018), 167–175
2010
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; Theoret. and Math. Phys., 162:3 (2010), 332–340
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; Comput. Math. Math. Phys., 50:11 (2010), 1830–1836
2009
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; Theoret. and Math. Phys., 158:1 (2009), 40–47
2006
17.
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
2003
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; J. Math. Sci. (N. Y.), 128:2 (2005), 2807–2811
2002
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; Theoret. and Math. Phys., 131:3 (2002), 791–800
1999
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; Math. Notes, 65:5 (1999), 590–597
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; Theoret. and Math. Phys., 119:2 (1999), 629–639
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; Comput. Math. Math. Phys., 39:7 (1999), 1154–1162
1997
23.
I. Yu. Popov, “Ýâîëþöèÿ êâàçè÷àïëûãèíñêîé ñðåäû è âîçìóùåíèå îïåðàòîðà Ëàïëàñà íà ìíîæåñòâå íóëåâîé ìåðû”, Matem. Mod., 9:10 (1997), 21
1996
24.
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
1995
25.
I. Yu. Popov, “A model of creeping fluid motion in domains connected by a small opening”, Matem. Mod., 7:5 (1995), 81
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; Math. Notes, 58:6 (1995), 1276–1285
27.
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
1994
28.
I. Yu. Popov, “On operator treatment of a Stokeslet”, Sibirsk. Mat. Zh., 35:5 (1994), 1148–1153; Siberian Math. J., 35:5 (1994), 1022–1026
1992
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; Russian Acad. Sci. Sb. Math., 75:2 (1993), 285–315
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; Siberian Math. J., 33:5 (1992), 856–861
1991
31.
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
32.
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
1990
33.
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
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; 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; Math. USSR-Sb., 71:1 (1992), 209–234
1989
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; Siberian Math. J., 30:3 (1989), 428–432
1987
37.
I. Yu. Popov, “A slit of zero width and the Dirichlet condition”, Dokl. Akad. Nauk SSSR, 294:2 (1987), 330–334
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; U.S.S.R. Comput. Math. Math. Phys., 27:2 (1987), 99–102
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