Vitaly Kocharovsky | Texas A&M University (original) (raw)

Papers by Vitaly Kocharovsky

Journal of Physics: Conference Series

A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with ... more A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with a bound state in the continuum (BIC) is revealed analytically. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.

Journal of Physics: Conference Series

A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with ... more A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with a bound state in the continuum (BIC) is revealed analytically. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.

2021 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), 2021

Numerical simulations and qualitative analysis of the predicted simultaneous generation of differ... more Numerical simulations and qualitative analysis of the predicted simultaneous generation of different quasiperiodic pulse trains [1] - [3] in a CW multimode class C quantum-dot heterolaser with self-locking of some of the modes are carried out on the basis of the Maxwell-Bloch equations. For the class C lasers, a photon (cavity) lifetime is of the order of a lifetime of a polarization (a density of the quantum-dot optical dipoles). We consider the combined low-Q Fabry-Perot cavities with distributed feedback of counter-propagating waves, where higher-Q modes are situated close to the ends of a photonic bandgap and lower-Q quasi-equidistant modes occupy the adjacent wings.

Journal of Statistical Physics, 2015

We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and ... more We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and thermodynamics in the critical region of Bose-Einstein condensation. It is valid for an arbitrary trap, loaded with an ideal gas, in the thermodynamic limit. We show that for the quantities, changing by a finite amount across the critical region, the exact GCE result differs from the corresponding canonical-ensemble result by a factor on the order of unity even in the thermodynamic limit. Thus, a widely used GCE approach does not describe correctly the critical phenomena at the phase transition for the actual systems with a fixed number of particles and yields only an asymptotics far outside the critical region.

AIP Conference Proceedings, 2001

ABSTRACT We develope a self-consistent theory of the synchrotron-self-Compton emission for optica... more ABSTRACT We develope a self-consistent theory of the synchrotron-self-Compton emission for optically thin sources with a stationary injection of relativistic monoenergetic electrons. We investigate the electron distribution function, synchrotron and inverse Compton spectra and find their analytical asymptotics. The steady-state electron distribution entangled with synchrotron radiation via Compton losses is shown to produce spectral indices ranging from 1/2 to 1. Possible ways of addressing steep low-energy slopes in some bursts are pointed out. .

Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, 2000

El objetivo es analizar la tasa de interés ofrecida por los intermediarios financieros para el fi... more El objetivo es analizar la tasa de interés ofrecida por los intermediarios financieros para el financiamiento de las actividades económicas de las Pequeñas y Medianas Empresas (Pymes) en Costa Rica, mediante escenarios donde se evidencian los efectos de estas variaciones, originados por una Tasa Básica Pasiva variable, tasa de referencia, y cómo estas fluctuaciones afectan los resultados económicos y financieros de estos negocios. El diseño de esta investigación es esencialmente de carácter descriptivo y comparativo, ya que pretende contribuir con la ampliación del conocimiento sobre el efecto negativo de las tasas de interés en los resultados financieros y económicos de las Pymes en Costa Rica, específicamente aquellas que han requerido financiamientos del Sistema Financiero. Por lo tanto, se realiza un análisis de los efectos de las tasas de interés en los resultados operacionales pertenecientes a las pymes, a partir del cálculo de intereses, variación en las cuotas, flujo de caja libre, capacidad de pago y conclusiones financieras. Este análisis se situa dentro del marco de administración financiera y económica de las pymes y de su efecto en la economía productiva del país..

Radiophysics and Quantum Electronics, 2020

We perform qualitative physical analysis and particle-in-cell two-dimensional numerical simulatio... more We perform qualitative physical analysis and particle-in-cell two-dimensional numerical simulation of the Weibel mechanism of magnetic-field generation due to the self-consistent formation of filaments of the hot-electron current with anisotropic velocity distribution, which occurs in the process of decay of a strong discontinuity in a collisionless plasma with a great difference in the number density and temperature of electrons. Anisotropy of the electron distribution is mainly stipulated by their quasiadiabatic expansion and a significant decrease in the thermal velocities in the normal direction to the front of the formed electrostatic shock wave at a weak decrease in the thermal velocities in the transverse directions. A strong magnetic field is formed in a layer with the maximum anisotropy under the front, covers the entire region of the expanding plasma, and, at the nonlinear evolution stage, acquires quasiperiodic modulation along the normal to the front, which correlates with the modulation of the electron anisotropy degree. The considered scenario of development of the Weibel instability is of interest for analysis of experiments with femtosecond laser plasma and interpretation of such phenomena in the case of a decay of strong discontinuities in a nonequilibrium space plasma.

We carry out 3D and 2D PIC-simulations of the expansion of a magnetized plasma that initially uni... more We carry out 3D and 2D PIC-simulations of the expansion of a magnetized plasma that initially uniformly fills a half-space and contains a semi-cylindrical region of heated electrons elongated along the surface of the plasma boundary. This geometry is related, for instance, to the ablation of a plane target by a femtosecond laser beam under quasi-cylindrical focusing. We find that the decay of the inhomogeneous plasma–vacuum discontinuity is strongly affected by an external magnetic field parallel to its boundary. We observe various transient phenomena, including the anisotropic scattering of electrons and the accompanying Weibel instability, and reveal various spatial structures of the arising magnetic field and current, including multiple flying apart filaments of a zpinch type and slowly evolving current sheets with different orientations. The magnitude of the self-generated magnetic field can be of the order of or significantly exceed that of the external one. Such phenomena are ...

We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-con... more We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial contractions of creation and annihilation operators for constrained spin bosons in a Holstein-Primakoff representation. In particular, we calculate analytically the total irreducible self-energy, the order parameter, the correlation functions, and the joined occupation probabilities of spin bosons. The developed regular microscopic quantum-field-theory method has a potential for a full solution of a long-standing and still open problem of 3D critical phenomena.

JETP Letters, 2016

The analytical theory of Bose-Einstein condensation of an ideal gas in mesoscopic systems has bee... more The analytical theory of Bose-Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose-Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose-Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose-Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose-Einstein condensation has been given.

Monthly Notices of the Royal Astronomical Society, 2016

We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres ... more We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres of compact stars, which are simple enough to allow practical implementation and still preserve all important physical effects. We take into account a frequency redistribution of radiation within the cyclotron line as well as the relativistic and quantum-electrodynamic effects. Our analysis is valid for the magnetic fields up to 10 13 G and for temperatures well below 500 keV. We present and compare two forms of the radiation transfer equations. The first form, for the intensities of ordinary and extraordinary modes, is applicable for the compact stars with a moderate magnetic field strength up to 10 11 G for typical neutron star and up to 10 9 G for magnetic white dwarfs. The second form, for the Stokes parameters, is more complex, but applicable even if a linear mode coupling takes place somewhere in the scattering-dominated atmosphere. Analysing dispersion properties of a magnetized plasma in the latter case, we describe a range of parameters where the linear mode coupling is possible and essential.

Radiophysics and Quantum Electronics, 1998

Radiophysics and Quantum Electronics, 2011

ABSTRACT We numerically model the frequency redistribution of gyroresonant photons in a plane-par... more ABSTRACT We numerically model the frequency redistribution of gyroresonant photons in a plane-parallel semi-infinite plasma atmosphere of a compact star by means of the Monte-Carlo method. We calculate the mean frequency shift and the mean number of scatterings for photons leaving the atmosphere as functions of the optical depth at emission, plasma temperature, and magnetic field strength. The probability of the escape of cyclotron-radiation photons from the atmosphere as a function of their optical depth at birth is calculated. The influence of the frequency redistribution effects on the spectrum of emergent radiation is studied.

NATO Science Series

Generalization of the self-similar solution for ultrarelativistic shock waves (Blandford & McKee,... more Generalization of the self-similar solution for ultrarelativistic shock waves (Blandford & McKee, 1976) is obtained in presence of losses localized on the shock front or distributed in the downstream medium. It is shown that there are two qualitatively different regimes of shock deceleration, corresponding to small and large losses. We present the temperature, pressure and density distributions in the downstream fluid as well as Lorentz factor as a function of distance from the shock front.

Radiophysics and Quantum Electronics, 2011

ABSTRACT Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars... more ABSTRACT Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars with various distributions of temperature over the star surface is carried out. General and special relativity effects are taken into account in the radiation transfer calculations. A novel method of analysis based on the Fourier series expansion of the observed spectra over rotation frequencies is proposed. It is shown that the mutual influence of the gravitational bending of light rays and rotation of the star leads to the formation of strong features (sometimes several features at once) in the Fourier-harmonic spectrum, whereas these features remain almost invisible in both the integrated and dynamic spectra. Possible application of the obtained results to the interpretation of absorption features in the spectrum of the single neutron star 1E 1207.4 − 5209 is discussed.

Physics Letters A, 2015

Abstract We find the exact solutions for the main steps in the analysis of the three-dimensional ... more Abstract We find the exact solutions for the main steps in the analysis of the three-dimensional Ising model. A method is based on a recently found rigorous theory of magnetic phase transitions in a mesoscopic lattice of spins, described as the constrained spin bosons in a Holstein–Primakoff representation.

Physica Scripta, 2015

The problem of finding a microscopic theory of phase transitions across a critical point is a cen... more The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation in an interacting gas and ferromagnetism in a lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For Bose-Einstein condensation, we present the exact, valid for the entire critical region, equations for the Green's functions and order parameter, that is a critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations. For the magnetic phase transition, we find an exact theory in terms of constrained bosons in a lattice and obtain similar equations for the Green's functions and order parameter. In particular, we outline an exact solution for the three-dimensional Ising model.

The properties of the plasma state of matter are determined by the motion and the electromagnetic... more The properties of the plasma state of matter are determined by the motion and the electromagnetic emission of the non-bound electrically charged particles --- electrons, positrons, protons and ions. It is not easy to create plasma in a laboratory. However this state is typical for the cosmic conditions --- at the stars and in the interstellar space. The properties of the laboratory as well as the space plasma are investigated at the Institute of Applied Physics of the Russian Academy of Sciences. The research is focused on the mechanisms of generation and propagation of the electromagnetic radiation --- from the radio waves to the gamma-rays --- in the planetary and stellar atmospheres and at the other astrophysical objects. The extreme physical conditions for a plasma are realized near the compact objects like black holes, neutron stars and collapsing nuclei of the massive stars. The plasma could be strongly non-equlibrium and can produce strong electromagnetic fields. Its bulk mot...

Journal of Physics: Conference Series

A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with ... more A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with a bound state in the continuum (BIC) is revealed analytically. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.

Journal of Physics: Conference Series

A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with ... more A phenomenon of a solitary narrow high-Q resonance in a planar grating waveguide associated with a bound state in the continuum (BIC) is revealed analytically. BICs appear when dispersion curves of the leaking even-parity and non-leaking odd-parity infinite-grating eigenmodes intersect. These intersections engender a parity symmetry break of the leaking eigenmode, causing it to decouple from a spatial Fourier harmonic that is emitted out of the waveguide. As a result, the otherwise low-Q waveguide eigenmode, comprised of those two aforementioned and some other infinite-grating eigenmodes, acquires a very high quality factor in a narrow vicinity of the mode-crossing frequency. Implementation of such a mechanism can be instructive for designing BICs in other photonic crystals and structures.

2021 Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC), 2021

Numerical simulations and qualitative analysis of the predicted simultaneous generation of differ... more Numerical simulations and qualitative analysis of the predicted simultaneous generation of different quasiperiodic pulse trains [1] - [3] in a CW multimode class C quantum-dot heterolaser with self-locking of some of the modes are carried out on the basis of the Maxwell-Bloch equations. For the class C lasers, a photon (cavity) lifetime is of the order of a lifetime of a polarization (a density of the quantum-dot optical dipoles). We consider the combined low-Q Fabry-Perot cavities with distributed feedback of counter-propagating waves, where higher-Q modes are situated close to the ends of a photonic bandgap and lower-Q quasi-equidistant modes occupy the adjacent wings.

Journal of Statistical Physics, 2015

We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and ... more We find a self-similar analytical solution for the grand-canonical-ensemble (GCE) statistics and thermodynamics in the critical region of Bose-Einstein condensation. It is valid for an arbitrary trap, loaded with an ideal gas, in the thermodynamic limit. We show that for the quantities, changing by a finite amount across the critical region, the exact GCE result differs from the corresponding canonical-ensemble result by a factor on the order of unity even in the thermodynamic limit. Thus, a widely used GCE approach does not describe correctly the critical phenomena at the phase transition for the actual systems with a fixed number of particles and yields only an asymptotics far outside the critical region.

AIP Conference Proceedings, 2001

ABSTRACT We develope a self-consistent theory of the synchrotron-self-Compton emission for optica... more ABSTRACT We develope a self-consistent theory of the synchrotron-self-Compton emission for optically thin sources with a stationary injection of relativistic monoenergetic electrons. We investigate the electron distribution function, synchrotron and inverse Compton spectra and find their analytical asymptotics. The steady-state electron distribution entangled with synchrotron radiation via Compton losses is shown to produce spectral indices ranging from 1/2 to 1. Possible ways of addressing steep low-energy slopes in some bursts are pointed out. .

Nuclear Physics B-proceedings Supplements - NUCL PHYS B-PROC SUPPL, 2000

El objetivo es analizar la tasa de interés ofrecida por los intermediarios financieros para el fi... more El objetivo es analizar la tasa de interés ofrecida por los intermediarios financieros para el financiamiento de las actividades económicas de las Pequeñas y Medianas Empresas (Pymes) en Costa Rica, mediante escenarios donde se evidencian los efectos de estas variaciones, originados por una Tasa Básica Pasiva variable, tasa de referencia, y cómo estas fluctuaciones afectan los resultados económicos y financieros de estos negocios. El diseño de esta investigación es esencialmente de carácter descriptivo y comparativo, ya que pretende contribuir con la ampliación del conocimiento sobre el efecto negativo de las tasas de interés en los resultados financieros y económicos de las Pymes en Costa Rica, específicamente aquellas que han requerido financiamientos del Sistema Financiero. Por lo tanto, se realiza un análisis de los efectos de las tasas de interés en los resultados operacionales pertenecientes a las pymes, a partir del cálculo de intereses, variación en las cuotas, flujo de caja libre, capacidad de pago y conclusiones financieras. Este análisis se situa dentro del marco de administración financiera y económica de las pymes y de su efecto en la economía productiva del país..

Radiophysics and Quantum Electronics, 2020

We perform qualitative physical analysis and particle-in-cell two-dimensional numerical simulatio... more We perform qualitative physical analysis and particle-in-cell two-dimensional numerical simulation of the Weibel mechanism of magnetic-field generation due to the self-consistent formation of filaments of the hot-electron current with anisotropic velocity distribution, which occurs in the process of decay of a strong discontinuity in a collisionless plasma with a great difference in the number density and temperature of electrons. Anisotropy of the electron distribution is mainly stipulated by their quasiadiabatic expansion and a significant decrease in the thermal velocities in the normal direction to the front of the formed electrostatic shock wave at a weak decrease in the thermal velocities in the transverse directions. A strong magnetic field is formed in a layer with the maximum anisotropy under the front, covers the entire region of the expanding plasma, and, at the nonlinear evolution stage, acquires quasiperiodic modulation along the normal to the front, which correlates with the modulation of the electron anisotropy degree. The considered scenario of development of the Weibel instability is of interest for analysis of experiments with femtosecond laser plasma and interpretation of such phenomena in the case of a decay of strong discontinuities in a nonequilibrium space plasma.

We carry out 3D and 2D PIC-simulations of the expansion of a magnetized plasma that initially uni... more We carry out 3D and 2D PIC-simulations of the expansion of a magnetized plasma that initially uniformly fills a half-space and contains a semi-cylindrical region of heated electrons elongated along the surface of the plasma boundary. This geometry is related, for instance, to the ablation of a plane target by a femtosecond laser beam under quasi-cylindrical focusing. We find that the decay of the inhomogeneous plasma–vacuum discontinuity is strongly affected by an external magnetic field parallel to its boundary. We observe various transient phenomena, including the anisotropic scattering of electrons and the accompanying Weibel instability, and reveal various spatial structures of the arising magnetic field and current, including multiple flying apart filaments of a zpinch type and slowly evolving current sheets with different orientations. The magnitude of the self-generated magnetic field can be of the order of or significantly exceed that of the external one. Such phenomena are ...

We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-con... more We find an exact general solution to the three-dimensional (3D) Ising model via an exact self-consistency equation for nearest-neighbors' correlations. It is derived by means of an exact solution to the recurrence equations for partial contractions of creation and annihilation operators for constrained spin bosons in a Holstein-Primakoff representation. In particular, we calculate analytically the total irreducible self-energy, the order parameter, the correlation functions, and the joined occupation probabilities of spin bosons. The developed regular microscopic quantum-field-theory method has a potential for a full solution of a long-standing and still open problem of 3D critical phenomena.

JETP Letters, 2016

The analytical theory of Bose-Einstein condensation of an ideal gas in mesoscopic systems has bee... more The analytical theory of Bose-Einstein condensation of an ideal gas in mesoscopic systems has been briefly reviewed in application to traps with arbitrary shapes and dimension. This theory describes the phases of the classical gas and the formed Bose-Einstein condensate, as well as the entire vicinity of the phase transition point. The statistics and thermodynamics of Bose-Einstein condensation have been studied in detail, including their self-similar structure in the critical region, transition to the thermodynamic limit, effect of boundary conditions on the properties of a system, and nonequivalence of the description of Bose-Einstein condensation in different statistical ensembles. The complete classification of universality classes of Bose-Einstein condensation has been given.

Monthly Notices of the Royal Astronomical Society, 2016

We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres ... more We find the forms of the transfer equations for polarized cyclotron radiation in the atmospheres of compact stars, which are simple enough to allow practical implementation and still preserve all important physical effects. We take into account a frequency redistribution of radiation within the cyclotron line as well as the relativistic and quantum-electrodynamic effects. Our analysis is valid for the magnetic fields up to 10 13 G and for temperatures well below 500 keV. We present and compare two forms of the radiation transfer equations. The first form, for the intensities of ordinary and extraordinary modes, is applicable for the compact stars with a moderate magnetic field strength up to 10 11 G for typical neutron star and up to 10 9 G for magnetic white dwarfs. The second form, for the Stokes parameters, is more complex, but applicable even if a linear mode coupling takes place somewhere in the scattering-dominated atmosphere. Analysing dispersion properties of a magnetized plasma in the latter case, we describe a range of parameters where the linear mode coupling is possible and essential.

Radiophysics and Quantum Electronics, 1998

Radiophysics and Quantum Electronics, 2011

ABSTRACT We numerically model the frequency redistribution of gyroresonant photons in a plane-par... more ABSTRACT We numerically model the frequency redistribution of gyroresonant photons in a plane-parallel semi-infinite plasma atmosphere of a compact star by means of the Monte-Carlo method. We calculate the mean frequency shift and the mean number of scatterings for photons leaving the atmosphere as functions of the optical depth at emission, plasma temperature, and magnetic field strength. The probability of the escape of cyclotron-radiation photons from the atmosphere as a function of their optical depth at birth is calculated. The influence of the frequency redistribution effects on the spectrum of emergent radiation is studied.

NATO Science Series

Generalization of the self-similar solution for ultrarelativistic shock waves (Blandford & McKee,... more Generalization of the self-similar solution for ultrarelativistic shock waves (Blandford & McKee, 1976) is obtained in presence of losses localized on the shock front or distributed in the downstream medium. It is shown that there are two qualitatively different regimes of shock deceleration, corresponding to small and large losses. We present the temperature, pressure and density distributions in the downstream fluid as well as Lorentz factor as a function of distance from the shock front.

Radiophysics and Quantum Electronics, 2011

ABSTRACT Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars... more ABSTRACT Modeling of atomic and cyclotron lines in the emergent spectra of rotating neutron stars with various distributions of temperature over the star surface is carried out. General and special relativity effects are taken into account in the radiation transfer calculations. A novel method of analysis based on the Fourier series expansion of the observed spectra over rotation frequencies is proposed. It is shown that the mutual influence of the gravitational bending of light rays and rotation of the star leads to the formation of strong features (sometimes several features at once) in the Fourier-harmonic spectrum, whereas these features remain almost invisible in both the integrated and dynamic spectra. Possible application of the obtained results to the interpretation of absorption features in the spectrum of the single neutron star 1E 1207.4 − 5209 is discussed.

Physics Letters A, 2015

Abstract We find the exact solutions for the main steps in the analysis of the three-dimensional ... more Abstract We find the exact solutions for the main steps in the analysis of the three-dimensional Ising model. A method is based on a recently found rigorous theory of magnetic phase transitions in a mesoscopic lattice of spins, described as the constrained spin bosons in a Holstein–Primakoff representation.

Physica Scripta, 2015

The problem of finding a microscopic theory of phase transitions across a critical point is a cen... more The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation in an interacting gas and ferromagnetism in a lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For Bose-Einstein condensation, we present the exact, valid for the entire critical region, equations for the Green's functions and order parameter, that is a critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations. For the magnetic phase transition, we find an exact theory in terms of constrained bosons in a lattice and obtain similar equations for the Green's functions and order parameter. In particular, we outline an exact solution for the three-dimensional Ising model.

The properties of the plasma state of matter are determined by the motion and the electromagnetic... more The properties of the plasma state of matter are determined by the motion and the electromagnetic emission of the non-bound electrically charged particles --- electrons, positrons, protons and ions. It is not easy to create plasma in a laboratory. However this state is typical for the cosmic conditions --- at the stars and in the interstellar space. The properties of the laboratory as well as the space plasma are investigated at the Institute of Applied Physics of the Russian Academy of Sciences. The research is focused on the mechanisms of generation and propagation of the electromagnetic radiation --- from the radio waves to the gamma-rays --- in the planetary and stellar atmospheres and at the other astrophysical objects. The extreme physical conditions for a plasma are realized near the compact objects like black holes, neutron stars and collapsing nuclei of the massive stars. The plasma could be strongly non-equlibrium and can produce strong electromagnetic fields. Its bulk mot...