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.
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.
