*High-frequency electromagnetic and acoustic phenomena in metals*

This direction was led by E.A. Kaner (1955 – 1986), N.M. Makarov (1986 – 1998), V.A. Yampolsky (2000 – present).

- Â Prediction and construction of the theory of cyclotron resonance in metals (Azbel M.Ya. and Kaner E.A., 1956)
- Construction of the theory of acoustic cyclotron resonance in metals (Kaner E.A., 1962)
- Construction of the theory of anomalous penetration of an electromagnetic field into metals (Azbel M.Ya. and Kaner E.A., 1963)
- Prediction of various weakly damped electromagnetic waves in metals, in particular, cyclotron waves (Kaner E.A. and Skobov V.G., 1963)
- Construction of the theory of surface scattering of electrons and the study of its role in the electromagnetic properties of metals (Kaner E.A., Krokhin A.A., Makarov N.M., Moroz A. and Yampolsky V.A., 1980-1995)
- Construction of the theory of the Casimir effect in thin metal plates (Dubrava V.N., Lyubimov O.I. and Yampolsky V.A., 1999 – 2009)
- Prediction of anomalous non-monotonic temperature dependence of the Casimir attraction force of thin metal films (Yampolsky V.A., Maizelis Z.A., Apostolov S.S., Saveliev S. and Nori F., 2007)
- Constructing a theory of the Casimir effect for bad conductors and predicting sharp temperature changes in the Casimir force in materials demonstrating a metal-dielectric transition (Ivanov B.A., Galkina E.G., Yampolsky V.A., Saveliev S. and Nori F., 2009)

- Â Azbel M. Ya., Kaner EA The theory of cyclotron resonance in metals // ZhETF. – 1965 .– T. 29, no. 6. – P. 876-878.
- Kaner E.A. Theory of acoustic cyclotron resonance in metals // ZhETF. – 1962 .– T. 43, no. 1. – P. 216-226.
- Kaner EA, Gantmakher V.F. Anomalous penetration of the electromagnetic field in metals and radiofrequency dimensional effects // UPhS. – 1968. – T. 94, no. 2. – P. 193-241.
- Kaner E.A., Skobov V.G. Electromagnetic waves in metals in a magnetic field // UPhS. – 1966 .– T. 89, no. 3. – P. 367-408.
- Yampol’skii V. A., Savel’ev S., Mayselis Z. A., Apostolov S. S., and Franco Nori. Anomalous temperature dependence of the Casimir force for thin metal films // Phys. Lett. – 2008. – V. 101, 096803.

- Â Diploma for discovery â 45. Cyclotron resonance in metals / Azbel M.Ya., Kaner EA .. – OT – 4272 // Discovery. Inventions 1966. – No. 19. – P. 5.
- Diploma for opening No. 80. Electromagnetic bursts in a conducting medium / Azbel M.Ya., Gantmakher V.F., Kaner E.A. – OT – 7163 // Discovery. Inventions 1970. – No. 18. – P. 5-6.
- State Prize of the Ukrainian SSR (E.A. Kaner, 1980)

*Theory of transport electromagnetic phenomena in semiconductors*

This direction was led by F.G. Bass (1961 – 1980), F.G. Bass and Yu.G. Gurevich (1980 – 1985), Yu.G. Gurevich (1985 – 2001), I.N. Volovichev (2001 – up to the present).

- Study of the transport of hot carriers in gas-discharge plasma and solids (Bass F.G. and Gurevich Yu.G., 1975)
- Construction of the theory of electrodynamic phenomena in magnetic semiconductors (Bass F.G. and Oleinik I.N., 1982)
- Construction of the theory of thermoelectric and thermomagnetic effects in limited semiconductors (Bass F.G., Bochkov V.S. and Gurevich Yu.G., 1984)
- Study of electron-phonon interaction, the effect of electron drag in semiconductors (Gurevich Yu.G. and Mashkevich Yu.G., 1989)
- Theory of thermoelectricity in bipolar semiconductors (Gurevich Yu.G., 1994)
- Study of transport processes in heterostructures of radiation-resistant intrinsic semiconductors (Gurevich Yu.G. and Volovichev I.N., 1995)
- Study of the recombination of charge carriers in bipolar semiconductors in highly nonequilibrium conditions (Volovichev IN, 2002)
- Theory of transport processes in bipolar semiconductors and semiconductor heterostructures with nonequilibrium charge carriers (Volovichev IN, 2008)
- Study of charge and energy transport in multicomponent systems in nonstationary conditions (Volovichev I.N., 2016)

- Bass F.G., Gurevich Yu.G. Hot electrons and strong electromagnetic waves in the plasma of semiconductors and gas discharge.- Moscow: Nauka, 1975.- 399p.
- Bass F.G., Bochkov V.S., Gurevich Yu.G. Electrons and phonons in limited semiconductors.-M .: Nauka, 1984.-288p.
- Gurevich Yu.G., Mashkevich O.L.Â The Electron-Phonon Drag and Transport Phenomena in Semiconductors. // Physics Reports.-1989. v.181, p.327-394.
- Gurevich Yu.G., Titov O.Yu., Logvinov G.N., Lyubimov O.I.Â Nature of the Thermopower in Bipolar Semiconductor. // Phys. Rev. B.-1995.- v.51, p.6999–7004.
- Volovichev I.N., Logvinov G.N., Titov O.Yu., Gurevich Yu.G. Recombination and lifetimes of charge carriers in semiconductors // J. Appl. Phys.-2004.-v.95, No.8.-p.4494-4496.

*The theory of propagation of electromagnetic waves in solid state plasma*

This direction was led by V.M. Yakovenko (1964 – 1982)

- The theory of overheating instabilities in isotropic and magnetoactive semiconductor plasma has been developed (Bass F.G., Khankina S.I. and Yakovenko V.M., 1965 – 1968)
- The theory of instability of helicons and acoustic waves, which is caused by the drift of charged carriers in constant electric and magnetic fields, has been developed (N.N.Beletsky, Bulgakov A.A., Hankina S.I. and Yakovenko V.M., 1967 – 1976 .)
- The existence was predicted and the properties of surface helicon and AlfvĂ©n waves in a magnetoactive plasma were analyzed (Beletsky N.N., Khankina S.I. and Yakovenko V.M., 1967 – 1985)
- Investigation of the excitation of surface electromagnetic and sound waves by flows of charged particles crossing the interface (AA Bulgakov, SI Khankina and VM Yakovenko, 1966 – 1982)
- A method of analysis has been developed and a theory of weakly nonlinear processes in layered-periodic semiconductor structures has been developed (AA Bulgakov, Khankina SI and Yakovenko VM, 1980 – 1986)
- Studied turbulent phenomena and stabilization of instabilities in plasma-like media (Beletsky N.N., Bulgakov A.A., Khankina S.I. and Yakovenko V.M., 1969 – 1976)

- Bass F.G., Yakovenko V.M. Theory of radiation of a charge passing through an electrically inhomogeneous medium. // UFN .â1965.âT. 86, issue 2 – pp. 189â230.
- Bulgakov A.A., Khankina S.I., Yakovenko V.M. On the theory of weak turbulence of coupled waves in a magnetoactive plasma of a solid // ZhETF. – 1970.â T.59, issue 10.â S. 1327-1335.
- Bulgakov A.A., Kaner E.A., Khankina S.I., Yakovenko V.M. On the theory of overheating instability in semiconductors. // ZhETF. – 1973. â T.64, issue 1.â P. 331-340.
- Bulgakov A.A., Khankina S.I., Yakovenko V.M. Excitation of surface vibrations by electron beams crossing the interface between the media. // FTT.â 1976.â Vol. 18, no. 6.â P. 1568-1572.
- Beletsky N.N., Bulgakov A.A., Khankina S.I., Yakovenko V.M. Plasma instabilities and nonlinear phenomena in semiconductors. // Kiev: Naukova Dumka. â 1984. â 192 p.

*Â Propagation of linear and non-linear sound waves*

This direction was led by V.M. Kontorovich (1957 – 1977)

- Solution of the problem of stability of shock waves (Kontorovich V.M., 1957)
- Construction of the theory of elasticity of metals and solution of the problem of dispersion of the speed of sound in metals at low temperatures (Kontorovich V.M., 1963)
- Theory of weak turbulence and sea wave spectra (Kontorovich V.M. and Katz A.V., 1971 – 1975)
- The theory of stimulated scattering of volumetric light and sound waves on surface (capillary-gravitational, elastic) waves was developed (Kats A.V., Gavrikov V.K., Kontorovich V.M and Maslov V.V., 1968 – 1975)
- The theory of surface self-focusing and lens effect has been developed (Kats A.V., Gavrikov V.K., Kontorovich V.M., 1968 – 1975)

- Kontorovich V.Đ. On the question of the stability of shock waves // ZhETF. – 1957 .– T. 33 .– P. 1525-1526.
- Kontorovich V.Đ. Equations of the theory of elasticity and dispersion of the speed of sound // ZhETF. – 1963 .– T. 45 .– P. 1638-1653.
- Gavrikov V.K., Kontorovich V.M., Katz A.V. Stimulated scattering of light by surface waves // ZhETF. – 1970 – T. 58, No. 4. – P. 1318-1331, 1970
- Kats A.V., Kontorovich V.M. Drift stationary solutions in the theory of weak turbulence // JETP Letters. – 1971. – T. 14, no. 6. – P. 392-395.
- Kats A.V., Kontorovich V.M., Moiseev S.S., Novikov V.E. Power-law solutions of the Boltzmann kinetic equation describing the propagation of particles with fluxes along the spectrum // JETP Letters. – 1975 .– T. 21, no. 1. – P. 13-16.

*Â Theory of waves propagation and diffraction in randomly inhomogeneous media and scattering of radio waves on statistically uneven interfaces*

This direction was led by F.G. Bass, I.M. Fuchs (1955 – 1985)

- A two-scale model of wave scattering on a statistically uneven surface was constructed, which made it possible to explain the main regularities of radar scattering of microwave radio waves on an agitated sea surface (Fuchs I.M., 1966 – 1975) and experimental data on multifrequency radar of the Moon (I.M. Fuchs, 1983 g)
- A statistical approach has been developed to take into account shading when scattering waves on a statistically uneven surface (Bass F.G. and Fuchs I.M., 1964; Fuchs I.M., 1969)
- The effect of amplification of backscattering of waves on a statistically uneven surface was predicted for grazing irradiation angles and the presence of strong shadows (Fuchs I.M., 1979)
- The theory of the coherence of fluctuations of the amplitude and phase of frequency-separated signals propagating in a turbulent medium has been developed (Fuchs I.M., 1974 – 1975)
- A theory of radio wave propagation in statistically inhomogeneous waveguides was developed, which was successfully applied to the interpretation of experimental data on the propagation of VLF radio waves in the Earth-ionosphere waveguide (Bezrodny V.G. and Fuchs I.M., 1971 – 1972), as well as to over-the-horizon propagation of microwave radio waves in the drive waveguides over the sea (Kukushkin A.V., Freilikher V.D. and Fuchs I.M., 1976 – 1983)
- The theory of wave phase fluctuations in the presence of a turning point in a randomly stratified medium was developed (Fuchs I.M., 1973 – 1974)
- The decisive role of metal surface roughness in the formation of the spectrum and damping of magnetic surface levels (Vilenkin A.V., Kaner E.A., Makarov N.M. and Fuchs I.M., 1969 – 1972), the viscosity of liquid He II in narrow capillaries and anomalous thermal resistance of the boundary of liquid He II with a metal (Adamenko I.N. and Fuchs I.M., 1970 – 1971)

- Bass F.G., Fuchs I.M. Scattering of waves on a statistically uneven surface. Moscow: Nauka, 1972, p. 461.
- Bass F.G., Fuchs I.M., Kalmykov A.I. et al. Very high frequency radiowave scattering by a disturbed sea surface, Pt 1, and Pt 2 // IEEE Trans. AP. – 1968. – V. 16, No 5. – PP. 554-568.
- Bass F.G., Freulicher V.D., and Fuchs I.M. Propagation in statistically irregular waveguides, Pt. 1 and Pt. 2 // IEEE Trans. – 1974. – V. 22, No. 2, PP. 278-295.
- Fuchs I.M. Amplification of backscattering from a statistically uneven surface in the presence of shading // Radiotekhn. Electronics. â 1979.â T. 21, No. 3.â PP. 633-636.
- Fuchs I.M. Structural function of the lunar relief from radar data // Izv. Universities, Radiophysics. – 1983. – T. 26, No. 10. – PP. 1194-1204.

*Nonlinear electromagnetic phenomena in metals*

This direction was led by N.M. Makarov and V.A. Yampolsky (1982-2000), V.A. Yampolsky (2000 – up to the present).

- Prediction and construction of the theory of nonlinear anomalous skin effect in metals (Lyubimov O.I., Makarov N.M. and Yampolsky V.A., 1983 – 1985)
- Theory of current states in metals (Makarov N.M. and Yampolsky V.A., 1983)
- Theory of the effects of magnetodynamic nonlinearity in the static conductivity of metals (Kaner E.A., Makarov N.M., Snapiro I.B. and Yampolsky V.A., 1984 – 1995)
- Theory of nonlinear interaction of electromagnetic waves in metals (E.A. Kaner, N.M. Makarov, I.V. Yurkevich, V.A. Yampolsky, G.B. Tkachev and S.A. Derevianko, 1985 – 2001. )
- Theory of nonlinear electromagnetic generation of sound in metals (Makarov N.M., Perez Rodriguez F. and Yampolsky V.A., 1988 – 1993)

- Lyubimov O.I., Makarov N.M., Yampolsky V.A. Nonlinear skin effect in metals // ZhETF. – 1983. – T. 85, no. 6 (12). – P. 2159-2170.
- Makarov N.M., Yampolsky V.A. Theory of “current states” in metals // ZhETF. – 1983. – T. 85, no. 2 (8). – P. 614-626.
- Kaner E.A., Makarov N.M., I.V. Yurkevich, Yampolsky V.A. Autowave structures and metastability of current states in metals // ZhETF. – 1987 .– T. 93, no. 1 (7). – P. 274-284.
- Makarov N.M., Yampolsky V.A. Nonlinear electrodynamics of metals at low temperatures // FNT. – 1991. – T. 17, No. 5. – P. 547-618.
- Derevianko S.A., Tkachev G.B., Yampolsky V.A. Abnormal penetration of an electromagnetic signal into a thin metal plate under conditions of strong magnetodynamic nonlinearity // ZhETF. – 2001. – T. 120, no. 3 (9). – P. 718-730.

- Grant 1050 E 9112 CONACyT (Mexico), 1992, N.Đ. Makarov.
- Grant 3004 E 9306 CONACyT (Mexico), 1994, N.M. Makarov.
- Soros grant for a long-term research program, project “Metal as active media”, 1993, N.Đ. Makarov.

*Theory of electromagnetic and acoustic waves in low-dimensional disordered metals*

This direction was led by E.A. Kaner (1982 – 1986), Yu.V. Tarasov (1986 – up to the present).

- Development of a method for calculating the response functions of one-dimensional disordered metals, calculating the spatial and temporal dispersion of the conductivity of such systems (Kaner E.A. and Chebotarev L.V., 1982 – 1984)
- Theory of propagation of acoustic waves in one-dimensional disordered conductors (Kaner E.A., Chebotarev L.V. and Tarasov Yu.V., 1987)
- Adiabatic theory of electron-phonon interaction and temperature dependence of the conductivity of one-dimensional disordered metals (Tarasov Yu.V., 1990 – 1992)

- Kaner E.A., Chebotarev L.V. Spatial dispersion of conductivity in one-dimensional conductors // ZhETF – 1984 – T. 86, no. 1 – P. 287-301.
- Kaner E.A., Chebotarev L.V. The spatial dispersion of conductivity in one-dimensional disordered metals // Phys. Rep. – 1987 – V. 150, Ns. 3 & 4 – P. 179-261.
- Kaner E.A., Tarasov Yu.V., Chebotarev L.V. Temperature effects in the spatial dispersion of the conductivity of one-dimensional systems // ZhETF – 1986 – V. 90, no. 4 – P. 1392-1398.
- Kaner E.A., Tarasov Yu.V. A theory of sound propagation in disordered one-dimensional metals // Phys. Rep. – 1988 – V. 150, Ns. 3 & 4 – P. 179-261.
- Tarasov Yu.V. Low-temperature conductivity of 1D disordered metals: adiabatic approximation for the electron-phonon interaction // Phys. Rev. B – 1992 – V. 45, No. 16 – P. 8873â8886.

*Nonlinear electromagnetic phenomena in hard superconductors*

This direction was led by N.M. Makarov and V.A. Yampolsky (1990 – 1995), V.A. Yampolsky (1995 – up to the present).

- Prediction and construction of the theory of transport current collapse and static magnetization in hard superconductors (Baltaga I.V., Makarov N.M., Yampolsky V.A., Ilienko K.V., Saveliev S.E., Perez Rodriguez F., and Levchenko A.A., 1990-2003)
- Creation of a contactless method for determining the magnetic field dependence of the critical current density in superconductors (Makarov N.M., Yampolsky V.A., Fisher L.M. and Voloshin I.F., 1990-1992)
- Prediction of the effect of stimulated transparency of superconducting plates (Lyubimov O.I., Lyubimova I.O., Derevianko S.A. and Yampolsky V.A., 1997-2001)
- Theory of macroturbulent instability in hard superconductors (Yampolsky V.A., Rakhmanov A.L., Fisher L.M. and Levchenko A.A., 2001-2003).

- Baltaga I.V., Makarov N.M., Yampol’skii V.A., Fisher L.M., Voloshin I.F., and Il’in N.V.Â Collapse of superconducting current in high-ĐąŃ ceramics in alternating magnetic field // Phys. Lett. A. â 1990. â V. 148, No. 3&4. â P. 213-216.
- Fisher L.M., Gorbachev V.S., Il’in N.V., Makarov N.M., Voloshin I.F., Yampol’skii V.A., et. al.Â Effect of microstructure on the magnetic-field dependence of the local critical current density in YBa2Cu3O7-ÎŽÂ superconductors // Phys. Rev. B. â 1992. â V. 46, No. 17. â P. 10986.
- Fisher L.M., Il’enko K.V., Kalinov A.V., LeBlanc M.A.R., Perez Rodriguez F., Savel’ev S.E., Voloshin I.F., and Yampol’skii V.A.Â Suppression of the magnetic moment under the action of a transverse magnetic field in hard superconductors // Phys. Rev. B. â 2000. â V. 61, No. 22. â P. 15382.
- Derev’anko S.A., Lyubimov O.I., Yampol’skii V.A., Perez-Rodriguez F.Â Effect of the stimulated transparency of a superconducting plate due to the nonlinear wave interaction // Physica C. â 2001. â V. 353. â P. 38-48.
- Fisher L.M., Goa P.E., Baziljevich M., Johansen T.H., Rakhmanov A.L., Yampol’skii V.A.Â Hydrodynamic Instability of the Flux-Antiflux Interface in Type-II Superconductors // Phys. Rev. Lett. â 2001. â V. 87, No. 24. â P. 247005 (1-4).
- Grant 1050 E 9112 CONACyT (Mexico), 1992, N.Đ. Makarov.
- Grant 3004 E 9306 CONACyT (Mexico), 1994, N.M. Makarov.
- Grant INTAS, project IR-97-1394, 1997, V.Đ. Yampolsky.
- Grant INTAS, project 02-2282, 2002, V.Đ. Yampolsky.

*Localization phenomena in disordered classical and quantum systems*

This direction is led by Tarasov Yu.V. (1989 – up to now).

- Predicted the phenomenon of interference channeling of electromagnetic, acoustic and internal gravitational waves in randomly stratified media (Tarasov Yu.V., Freilikher V.D. and Lyubitsky A.A., 1989 – 2001)
- Theory of Anderson localization of quantum waves due to their scattering on random roughnesses of the boundaries of waveguide-type systems was constructed (Makarov N.M. and Tarasov Yu.V., 1998 – 2001)
- The phenomenon of quantum dephasing caused by elastic scattering of waves and particles was predicted, and a theory of conductivity and metal-insulator transition in two-dimensional disordered electronic systems was constructed (Tarasov Yu.V., 2000 – 2006)
- Theory of the spectrum of quasi-optical volume cylindrical resonators with a randomly rough lateral surface was constructed (Tarasov Yu.V., 2006)
- The effect of “floating” of resonances in frequency was predicted with an increase in the degree of roughness sharpness in resonators with randomly rough boundaries (Ganapolskiy E.M., Tarasov Yu.V. and Shostenko L.D., 2013)
- The effect of entropy localization in waveguide systems with randomly and regularly rough lateral boundaries was predicted (Ganapolskiy E.M., Tarasov Yu.V. and Shostenko L.D., 2015).

- Tarasov Yu.V.Â Elastic scattering as a cause of quantum dephasing: the conductance of two-dimensional imperfect conductors // Waves Random Media â 2000 â V. 10, No. 4 â P. 395â415.
- Makarov N.M., Tarasov Yu.V.Â Electron localization in narrow surface-corrugated conducting channels: manifestation of competing scattering mechanisms // Phys. Rev. B â 2001 â V. 64 â P. 235306-1â235306-14.
- Freilikher V.D., Tarasov Yu.V.Â Propagation of wave packets in randomly stratified media // Phys. Rev. E â 2001 â P. 056620-1â056620-9.
- Tarasov Yu.V.Â One-particle conductance of an open quasi-two-dimensional Fermi system: Evidence of the parallel-magnetic-field-induced mode reduction effect // Rev. B â 2006 â V. 73 â P. 014202-1â014202-7.
- Tarasov Yu.V., Shostenko L.D.Â Dual nature of localization in guiding systems with randomly corrugated boundaries: Anderson-type versus entropic // Annals of Physics â 2015 â V.Â 356 â P.Â 95-127.

*Propagation of nonlinear waves and solitons. Nonlinear electromagnetic phenomena in hard superconductors.*

This direction is led by V.E. Vekslerchik.

- New exact solutions of the Gross-Pitaevsky equation were obtained and a method was proposed for using the Feshbach resonance for the generation, stabilization and control of localized soliton-type excitations in Bose-Einstein condensates (Vekslerchik V.E., 2008)
- A new class of solutions of the sinusoidal Gordon equation corresponding to excitations with an arbitrary profile propagating along a Josephson vortex in a two-dimensional Josephson junction was found (Yampolsky V.A., 2008)
- New N-soliton solutions were obtained for a nonlinear model with logarithmic interaction on a cubic lattice (Vekslerchik V.E., 2017)

- New N-soliton solutions were obtained for the generalized Toda lattice (Vekslerchik V.E., 2019).
- Gulevich D.R., Kusmartsev F.V., Savel’ev S., Yampolâskii V.A., Nori F.Â Shape and wobbling wave excitations in Josephson junctions: Exact solutions of the (2+1)-dimensional sine-Gordon model // Phys. Rev. B â 2009 â 80, P. 094509-1â094509-13.
- Belmonte-Beitia J., Konotop V.V., Perez-Garcia V. M., Vekslerchik V.Â Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices // Chaos, Solitons, & Fractals â 2009 â V. 41, No. 2 â P. 197â203.
- Pritula G.M., Vekslerchik V.E.Â KdVâVolterra chain // J. Phys. A â 2010 â V. 43, 365203.
- Pritula G.M., Vekslerchik V.E.Â Toda-Heisenberg chain: interacting sigma-fields in two dimensions // Journal of Nonlinear Mathematical Physics â 2011 â V. 18 â P. 443.
- Vekslerchik V.E.Â Explicit solutions for a (2+ 1)-dimensional Toda-like chain // J. Phys. A â 2013 â V. 46, No. 5, 055202.
- E. Vekslerchik Solitons of a simple nonlinear model on the cubic lattice // Journal of Physics A â2017 âV. 50, No. 47, 475201.
- E. Vekslerchik Solitons of the (2+2)-dimensional Toda lattice // Journal of Physics A â2019 âV. 52, No. 4, 045202.

State Prize of Ukraine (V.A.Yampolsky, 2013).

*Â Linear and nonlinear electromagnetic phenomena in layered superconductors*

This direction is led by V.A. Yampolsky.

- The existence of surface and waveguide Josephson plasma waves in bounded layered superconductors is predicted, the spectra of natural waves and methods of their excitation are studied; a number of resonance effects associated with the excitation of Josephson plasma eigenmodes have been predicted. In particular, a theory of a significant increase in the transparency coefficient of thick plates of layered superconductors under resonant excitation of waveguide eigenmodes has been developed (Yampolsky V.A., Kats A.V., Nikitin A.Yu., Nesterov M.L., Slipchenko T.M., Kadygrob D.V., Saveliev S. and Nori F., 2005 – 2014)
- A number of nonlinear phenomena in layered superconductors have been predicted, such as the formation of self-localized light beams, a strong hysteresis amplitude dependence of the transparency coefficient of superconducting plates, pumping of a weak Josephson plasma wave due to the energy of a strong wave, stopping of terahertz electromagnetic waves, etc. (Yampolsky V.A., Rakhmanov A.L., Maizelis Z.A., Apostolov S.S., Saveliev S., Rokhmanova T.N. and Nori F., 2006 – 2014)
- The theory of transformation of the polarization of terahertz waves during their reflection and passage through the plates of layered superconductors has been developed (Yampolsky V.A., Maizelis Z.A., Apostolov S.S., Rokhmanova T.N. and Nori F., 2013)
- The theory of transition and Cherenkov radiation of terahertz waves when an electron crosses the boundary of a layered superconductor was developed (Averkov Yu.O., Yakovenko V.M., Yampolsky V.A. and Nori F., 2014)
- A theory was developed for the transmission of terahertz waves through a plate of a layered superconductor in the presence of a DC magnetic field. It is shown that an external DC magnetic field transforms a layered superconductor into an inhomogeneous medium with a spatial and frequency-dependent dielectric constant. Even a relatively weak DC magnetic field, when the superconductor is in the Meissner state, significantly affects the transmittance of the layered superconductor. Thus, the magnetic field can effectively control the transparency of layered superconductors. (Apostolov S.S., Maizelis Z.A., Rokhmanova T.N., Yampolâskii V.A., Franco Nori, 2015-2017)
- It is shown that layered superconductors, due to their specific nonlinear response to a weak DC magnetic field, behave like tunable hyperbolic media in a wide frequency range. In particular, using the transfer matrix method, the resonant transparency of a layered superconductor, induced by the excitation of localized waves with nonmonotonic dispersion, is studied. (Kvitka N.M., Mazanov M.V., Apostolov S.S., Maizelis Z.A., Makarov N.M., Rokhmanova T.N., Shmatko A.A. and Yampolâskii V.A., 2018 -2021)

- Savel’ev S.,Â Yampolâskii V., Nori F.Â Surface Josephson plasma waves in layered superconductors // Phys. Rev. Lett. â 2005. â V. 95. â P. 187002.
- Savelâev S., Rakhmanov A.L., Yampolâskii V.A., Nori F.Â Analogues of nonlinear optics using terahertz Josephson plasma waves in layered superconductors // Nature Phys. â 2006 â V. 2, P. 521.
- Savelâev S., Yampolâskii V.A., Rakhmanov A.L., and Nori F. Terahertz Josephson plasma waves in layered superconductors: spectrum, generation, nonlinear and quantum phenomena // Rep. Prog. Phys. â 2010 â V. 73. â P. 026501.
- Golick V.A., Kadygrob D.V., Yampolâskii V.A., Ivanov B.A., Nori F.Â Surface Josephson plasma waves in layered superconductors above the plasma frequency: evidence for a negative index of refraction // Phys. Rev. Lett. â 2010. â V. 104. â P. 187003.
- Rokhmanova T.N., Apostolov S.S., Maizelis Z.A., Yampol’skii V.A., Nori F.Â Self-induced terahertz-wave transmissivity of waveguides with finite-length layered superconductors // Phys. Rev. B â 2013 â V. 88 â P. 014506.
- N. Rokhmanova, S. S. Apostolov, Z. A. Maizelis, V. A. Yampol’skii, Franco Nori Superposition principle for nonlinear Josephson plasma waves in layered superconductors // Phys. Rev. B â 2014 â V. 90 â P. 184503.
- S. Apostolov, Z. A. Maizelis, N. M. Makarov, F. PĂ©rez-RodrĂguez, T. N. Rokhmanova, V. A. Yampol’skii Transmission of terahertz waves through layered superconductors controlled by a dc magnetic field // Phys. Rev. B â 2016 â V. 94 â P. 024513.
- S. Apostolov, N. M. Makarov, V. A. Yampol’skii Excitation of terahertz modes localized on a layered superconductor: Anomalous dispersion and resonant transmission // Phys. Rev. BÂ -2018 – V. 97 â P. 024510.
- V. Mazanov, S. S. Apostolov, Z. A. Maizelis, N. M. Makarov, A. A. Shmat’ko, V. A. Yampol’skii Resonant absorption of terahertz waves in layered superconductors: Wood’s anomalies and anomalous dispersion // Phys. Rev. BÂ – 2020 – V. 101 â P. 024504.
- Kvitka, S. S. Apostolov, N. M. Makarov, T. Rokhmanova, A. A. Shmat’ko, V. A. Yampol’skii Resonant transparency of a layered superconductor: Hyperbolic material in the terahertz range tuned by dc magnetic field // Phys. Rev. BÂ – 2021 – V. 103 â P. 104512.

*Theory of random discrete systems with long-range correlations*

This direction is led by O.V. Usatenko.

- The theory of additive multistep Markov chains is constructed and their statistical equivalence to random discrete physical systems with long-range correlations is shown. A system of equations is obtained that one-to-one linking the main characteristic of the Markov chain (the so-called memory function) with the correlation function of the physical system (Usatenko O.V., Yampolsky V.A., Melnik S.S., Apostolov S.S. and Maizelis Z A., 2003 – 2005)
- The theory of propagation of electromagnetic waves along a one-dimensional chain of Josephson junctions and in a system of superconducting layers with random parameters has been developed. Similar to Anderson’s model, the transport properties of such systems are determined by correlations between random parameter values. It is shown that, by constructing these sequences in a certain way, it is possible to achieve the presence in the spectrum of the system of an abrupt conductor-insulator transition at a predetermined point (Usatenko O.V., Yampolsky V.A., Melnik S.S., Apostolov S.S. and Mayzelis Z.A., 2007)
- A method has been developed for constructing diffraction gratings with a random sequence of parameters with spectra of a given type, in particular, possessing the properties of simultaneously periodic, quasiperiodic and random gratings; studied linear antenna arrays with random intensities of dipole emitters and distances between them (Usatenko O.V., Yampolsky V.A., Melnik S.S., Apostolov S.S. and Maizelis Z.A., 2008)
- A method for solving the inverse problem of synthesis of random antennas for a given radiation pattern has been developed (Melnik S.S., Pritula G.M. and Usatenko O.V., 2012)
- Studied the differential entropy of systems with long-range weak correlations, which in the additive approximation can be expressed through the pair correlator of the sequence. The constructed theory makes it possible to calculate the entropy on a much larger scale than standard methods allow (Usatenko O.V. and Melnik S.S., 2014).

- RandomÂ finite-valued dynamical systems: additive Markov chain approach / O.V. Usatenko, S.S. Apostolov, Z.A. Mayzelis, and S.S. Melnik. â Cambridge: Cambridge Scientific Publisher, 2010. â 166 p.
- UsatenkoÂ and V. A. Yampol’skii // Binary N-Step Markov Chain as an Exactly Solvable Model of Long-Range Correlated Systems, Phys. Rev. Let. -2003. â 90, N 11,Â 110601 (4 Ń.).
- IzrailevMemory function versus binary correlator inÂ additive Markov chains /Â F.M. Izrailev, A.A. Krokhin, N.M. Makarov, S.S. Melnyk, O.V. Usatenko, and V.A. Yampolâskii // Physica A â 2006. â P. 372 – 279.
- Yampolâskii Controlled terahertz frequency response and transparency of Josephson chains and superconducting multilayers /Â V.A. Yampolâskii, S. Salvelâev, O.V. Usatenko, S.S. Melânik, F.V. Kusmartsev, A.A. Krokhin, and F. Nori //Â Phys. Rev. B â 2007.- 75 – 014527 (7 p.).
- Usatenko Spectral analysis and synthesis of 1D dichotomous long-range correlated systems: From diffraction gratings to quantum wires / O.V. Usatenko, S.S. Melnik, L. Kroon, M. Johansson, R. Riklund, and S.S. Apostolov // Physica A â 2008. â 387 â P. 4733-4739.

*Theory of electromagnetic phenomena in graphenes and other low-dimensional quantum systems*

This direction is led by S.S. Apostlov.

- Predicted and theoretically investigated quantum oscillations of kinetic and thermodynamic quantities in graphene, controlled by an external electric field (Yampolsky V.A., Apostolov S.S., Maizelis Z.A., Saveliev S. and Nori F., 2011)
- The coexistence of terahertz TM- and TE-polarized waves localized near a graphene layer embedded in a dielectric photonic crystal was predicted (Averkov Yu.O., Yakovenko V.M., Yampolsky V.A. and Nori F., 2014)
- The theory of thermal transport in a nonlinear Luttinger fluid was developed, and the thermal conductivity and Coulomb thermal resistance of one-dimensional electronic systems were calculated (Apostolov S.S. and Maizelis Z.A., 2013)
- A theory of Coulomb drag in two-layer electronic systems has been developed, to which the hydrodynamic description of an electron liquid is applicable (Apostolov S.S. and Levchenko A., 2014)
- The theory of tunneling spectroscopy for electronic states at the boundary of a two-dimensional topological insulator was developed (Apostolov S.S. and Levchenko A., 2014)

- YampolâskiiÂ Voltage-driven quantum oscillations of conductance in graphene / V.A. Yampolâskii, S.S. Apostolov, Z.A. Maizelis, A. Levchenko, and F. Nori // EPL â 2011 â 96, â 67009 (5 p.).
- AverkovÂ Terahertz transverse-electric- and transverse-magnetic-polarized waves localized on graphene in photonic crystals / Yu.O. Averkov, V.M. Yakovenko, V.A. Yampol’skii, and F. Nori // Phys. Rev. B â 2014 â 90, â 045415 (7 p.).
- ApostolovÂ Thermal transport and quench relaxation in nonlinear Luttinger liquids / S. Apostolov, D.E. Liu, Z. Maizelis, and A. Levchenko // Phys. Rev. B. â 2013. â 88, â 045435 (5 p).
- ApostolovÂ Hydrodynamic Coulomb drag of strongly correlated electron liquids / S.S. Apostolov, A. Levchenko, and A.V. Andreev // Phys. Rev. B â 2014 â 89, â 121104(R) (5 p).
- ApostolovÂ Nonequilibrium spectroscopy of topological edge liquids // S.S. Apostolov and A. Levchenko // Phys. Rev. B. â 2014 â 89, â 201303(R) (5 p).
- Magnetodrag in the hydrodynamic regime: Effects of magnetoplasmon resonance and Hall viscosity / S. S. Apostolov, D. A. Pesin, A. Levchenko // Phys. Rev. B. â 2019. â 89. â 115401 (12 p).

*Resonant phenomena in metals associated with the excitation of localized eigenmodes*

This direction is led by A.V. Katz.

- A resonant perturbation theory has been developed, which allows to analytically solve the problems of diffraction of electromagnetic waves in periodically modulated systems, as well as to study resonance phenomena associated with the excitation of surface waves at the boundaries of conductors (Kats A.V. and Spevak S.I., 2000)
- The phenomenon of the appearance of spectral transparency windows of periodically modulated opaque metal films caused by the excitation of bilaterally localized surface waves was predicted and theoretically investigated (Kats A.V., Spevak S.I., Nikitin A.Yu. and Nesterov M.L., 2009. )
- The opposite effect was predicted and theoretically investigated – the appearance of spectral windows of opacity of films of transparent conductors, caused by periodic modulation of electromagnetic properties and excitation of surface modes (Kats A.V., Spevak S.I., Nikitin A.Yu., Nesterov M.L. and Timchenko, 2010).

- KatsÂ Polarization properties of a periodically-modulated metal film in regions of anomalous optical transparency / A.V. Kats, M.L. Nesterov, and A.Yu. Nikitin // Phys. Rev. B â 2005 â 72, â 193405 (R) (4 p).
- KatsÂ Energy redistribution and polarization transformation in conical mount diffraction under resonance excitation of surface waves / A.V. Kats, N.A. Balakhonova, and I.S. Spevak //Â Phys. Rev. B â 2007 â 76, â 045413 (23 p).
- AverkovÂ Electron beam excitation of left-handed surface electromagnetic waves at artificial interfaces / Yu.O. Averkov, A.V. Kats, and V.M. Yakovenko // Phys. Rev. B â 2009 â 79, â 193402 (R) (4 p).
- SpevakÂ Design of specific gratings operating under surface plasmon-polariton resonance / I.S. Spevak, M.A. Timchenko, and A.V. Kats // Opt. Lett â 2011 â 36 â P. 1419-1421.
- SpevakÂ High quality resonances for terahertz radiation at periodically corrugated semiconductor interfaces / I. S. Spevak, M.A. Timchenko, V.K. Gavrikov, V.M. Shulga, J. Feng, H.B. Sun, and A.V. Kats // Appl. Phys. B â 2011 â 104 â P. 925-930.
- V. Kats, I. S. Spevak. Diffraction of electromagnetic waves. Kharkiv, KhVU, 1998, 178 p.

*Â *

During the existence of the department, 8 monographs and more than 1000 articles have been published in peer-reviewed journals.