Pavlo Shyhorin | Volyn National University of Lesya Ukrainka (original) (raw)
Papers by Pavlo Shyhorin
Starting from first principles of the statistical mechanics we construct a dynamics of the conden... more Starting from first principles of the statistical mechanics we construct a dynamics of the condensed Bose gas at the nonzero temperatures. In particular, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. Obtained generalized Gross-Pitaevskii equation for condensate include effect of collisions with thermal cloud atoms (non-condensate). The Boltzmann quantum kinetic equation for non-condensate was obtained using Zubarev’s method of nonequilibrium statistical operator. Therefore was obtained a complete dynamics of the condensed Bose gas at the nonzero temperatures.
A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in th... more A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in the ideal approximation is represented. The starting point in our formalism is a system of Heisen-berg's equation of motion for both normal and anomalous correlation functions. The use of a mixed Wigner representation allows us to perform the expansion of the equations of motion for correlation functions in gradients directly, very easily, and with a rigorous mathematics. To find the hydrodynamic flows, we have constructed a local equilibrium statistical operator for superfluid helium in the reference frame, where the condensate is at rest.
Low Temperature Physics
In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify ... more In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify the Wang Chang and Uhlenbeck method for description of the sounds in a Maxwell gas for the case of a degenerate quantum gas. Using this approach, we constructed a dispersion relation for sound waves in a condensed Bose gas at finite temperatures, and calculate the velocities of first and second sounds in the first approximation. The possibility of the theoretical investigation for sound damping is discussed.
Ukrainian Journal of Physics
The Josephson current through a two-barrier SISIS tunnel junction has been calculated analyticall... more The Josephson current through a two-barrier SISIS tunnel junction has been calculated analytically in the quasiclassical approximation for the microscopic theory of superconductivity. Green's functions for a SISIS tunnel junction and an expression for the Josephson current through a point contact are obtained. The dependence of the tunnel current on the order parameter phase is determined, and the current dependence on the distance between the barriers is analyzed. The presence of resonance peaks in the Josephson current is demonstrated.
The Journal of Chemical Physics, 2003
The hydrodynamic equations of a phase-separating fluid mixture are derived from the underlying mi... more The hydrodynamic equations of a phase-separating fluid mixture are derived from the underlying microscopic dynamics of the system. A projection operator method is used in the GENERIC form ͓H. C. Ö ttinger, Phys. Rev. E 57, 1416 ͑1998͔͒. In this way, the thermodynamic consistency of the final equations is apparent. The microscopic potential is separated into short-and long-range parts, in the spirit of the original work of van der Waals. Explicit expressions for surface tension terms in the hydrodynamic equations are obtained. These terms describe diffuse interfaces in the system. Miscible-immiscible and gas-liquid phase transitions are possible, nonisothermal situations can be studied, and explicit account of cross effects is taken.
Condensed Matter Physics, 2009
Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlati... more Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlation functions a two-fluid hydrodynamics for superfluid helium-4 was constructed. The method is based on a gradient expansion of the exact equations of motion for correlation functions about a local equilibrium together with explicit use of the local equilibrium statistical operator for superfluid helium in the frame of reference, where condensate is in the state of rest.
The Josephson current through a two-barrier SISIS tunnel junction has been calculated analyticall... more The Josephson current through a two-barrier SISIS tunnel junction has been calculated analytically in the quasiclassical approximation for the microscopic theory of superconductivity. Green's functions for a SISIS tunnel junction and an expression for the Josephson current through a point contact are obtained. The dependence of the tunnel current on the order parameter phase is determined, and the current dependence on the distance between the barriers is analyzed. The presence of resonance peaks in the Josephson current is demonstrated. K e y w o r d s: Josephson effect, tunnel junction, critical current.
In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify ... more In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify the Wang Chang and Uhlenbeck method for description of the sounds in a Maxwell gas for the case of a degenerate quantum gas. Using this approach, we constructed a dispersion relation for sound waves in a condensed Bose gas at finite temperatures, and calculate the velocities of first and second sounds in the first approximation. The possibility of the theoretical investigation for sound damping is discussed. PACS: 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow; 67.40.Pm Transport processes, second and other sounds, and thermal counterflow; Kapitza resistance; 67.57.Jj Collective modes.
Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlati... more Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlation functions a two-fluid hydrodynamics for superfluid helium-4 was constructed. The method is based on a gradient expansion of the exact equations of motion for correlation functions about a local equilibrium together with explicit use of the local equilibrium statistical operator for superfluid helium in the frame of reference, where condensate is in the state of rest.
A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in th... more A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in the ideal approximation is represented. The starting point in our formalism is a system of Heisen-berg's equation of motion for both normal and anomalous correlation functions. The use of a mixed Wigner representation allows us to perform the expansion of the equations of motion for correlation functions in gradients directly, very easily, and with a rigorous mathematics. To find the hydrodynamic flows, we have constructed a local equilibrium statistical operator for superfluid helium in the reference frame, where the condensate is at rest.
We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases ... more We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases of the first principles of statistical mechanics. We derived the equation of motion for the con-densate wavefunction and the quantum kinetic equation for the distribution function of excited atoms. The obtained generalized Gross–Pitaevskii equation for a condensate includes the effect of collisions with thermal cloud atoms (non-condensate). The Boltz-mann quantum kinetic equation for a non-condensate was obtained by means of Zubarev's method of nonequilibrium statistical operator .
Starting from the first principles of statistical mechanics, the two-fluid hy-drodynamics of supe... more Starting from the first principles of statistical mechanics, the two-fluid hy-drodynamics of superconductor in ideal approximation is constructed. The system of equations of motion for normal and anomalous correlation functions is used for hydrodynamic description. Transition to equations of hy-drodynamics is performed using an expansion of equations of motion for correlation functions in terms of a small parameter. PACS: 05.30.Fk, 47.37.+q
Starting from first principles of the statistical mechanics we construct a dynamics of the conden... more Starting from first principles of the statistical mechanics we construct a dynamics of the condensed Bose gas at the nonzero temperatures. In particular, we derive an equation of motion for the condensate wavefunction and a quantum kinetic equation for the distribution function for the excited atoms. Obtained generalized Gross-Pitaevskii equation for condensate include effect of collisions with thermal cloud atoms (non-condensate). The Boltzmann quantum kinetic equation for non-condensate was obtained using Zubarev’s method of nonequilibrium statistical operator. Therefore was obtained a complete dynamics of the condensed Bose gas at the nonzero temperatures.
A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in th... more A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in the ideal approximation is represented. The starting point in our formalism is a system of Heisen-berg's equation of motion for both normal and anomalous correlation functions. The use of a mixed Wigner representation allows us to perform the expansion of the equations of motion for correlation functions in gradients directly, very easily, and with a rigorous mathematics. To find the hydrodynamic flows, we have constructed a local equilibrium statistical operator for superfluid helium in the reference frame, where the condensate is at rest.
Low Temperature Physics
In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify ... more In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify the Wang Chang and Uhlenbeck method for description of the sounds in a Maxwell gas for the case of a degenerate quantum gas. Using this approach, we constructed a dispersion relation for sound waves in a condensed Bose gas at finite temperatures, and calculate the velocities of first and second sounds in the first approximation. The possibility of the theoretical investigation for sound damping is discussed.
Ukrainian Journal of Physics
The Josephson current through a two-barrier SISIS tunnel junction has been calculated analyticall... more The Josephson current through a two-barrier SISIS tunnel junction has been calculated analytically in the quasiclassical approximation for the microscopic theory of superconductivity. Green's functions for a SISIS tunnel junction and an expression for the Josephson current through a point contact are obtained. The dependence of the tunnel current on the order parameter phase is determined, and the current dependence on the distance between the barriers is analyzed. The presence of resonance peaks in the Josephson current is demonstrated.
The Journal of Chemical Physics, 2003
The hydrodynamic equations of a phase-separating fluid mixture are derived from the underlying mi... more The hydrodynamic equations of a phase-separating fluid mixture are derived from the underlying microscopic dynamics of the system. A projection operator method is used in the GENERIC form ͓H. C. Ö ttinger, Phys. Rev. E 57, 1416 ͑1998͔͒. In this way, the thermodynamic consistency of the final equations is apparent. The microscopic potential is separated into short-and long-range parts, in the spirit of the original work of van der Waals. Explicit expressions for surface tension terms in the hydrodynamic equations are obtained. These terms describe diffuse interfaces in the system. Miscible-immiscible and gas-liquid phase transitions are possible, nonisothermal situations can be studied, and explicit account of cross effects is taken.
Condensed Matter Physics, 2009
Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlati... more Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlation functions a two-fluid hydrodynamics for superfluid helium-4 was constructed. The method is based on a gradient expansion of the exact equations of motion for correlation functions about a local equilibrium together with explicit use of the local equilibrium statistical operator for superfluid helium in the frame of reference, where condensate is in the state of rest.
The Josephson current through a two-barrier SISIS tunnel junction has been calculated analyticall... more The Josephson current through a two-barrier SISIS tunnel junction has been calculated analytically in the quasiclassical approximation for the microscopic theory of superconductivity. Green's functions for a SISIS tunnel junction and an expression for the Josephson current through a point contact are obtained. The dependence of the tunnel current on the order parameter phase is determined, and the current dependence on the distance between the barriers is analyzed. The presence of resonance peaks in the Josephson current is demonstrated. K e y w o r d s: Josephson effect, tunnel junction, critical current.
In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify ... more In this work the propagation of sound waves in a degenerate quantum gas is considered. We modify the Wang Chang and Uhlenbeck method for description of the sounds in a Maxwell gas for the case of a degenerate quantum gas. Using this approach, we constructed a dispersion relation for sound waves in a condensed Bose gas at finite temperatures, and calculate the velocities of first and second sounds in the first approximation. The possibility of the theoretical investigation for sound damping is discussed. PACS: 03.75.Kk Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow; 67.40.Pm Transport processes, second and other sounds, and thermal counterflow; Kapitza resistance; 67.57.Jj Collective modes.
Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlati... more Using a system of Heisenberg's equation of motion for both the normal and the anomalous correlation functions a two-fluid hydrodynamics for superfluid helium-4 was constructed. The method is based on a gradient expansion of the exact equations of motion for correlation functions about a local equilibrium together with explicit use of the local equilibrium statistical operator for superfluid helium in the frame of reference, where condensate is in the state of rest.
A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in th... more A consistent microscopic derivation of the two-fluid hydrodynam-ics for superfluid helium-4 in the ideal approximation is represented. The starting point in our formalism is a system of Heisen-berg's equation of motion for both normal and anomalous correlation functions. The use of a mixed Wigner representation allows us to perform the expansion of the equations of motion for correlation functions in gradients directly, very easily, and with a rigorous mathematics. To find the hydrodynamic flows, we have constructed a local equilibrium statistical operator for superfluid helium in the reference frame, where the condensate is at rest.
We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases ... more We constructed equations of the condensed Bose gas dynamics at nonzero temperatures on the bases of the first principles of statistical mechanics. We derived the equation of motion for the con-densate wavefunction and the quantum kinetic equation for the distribution function of excited atoms. The obtained generalized Gross–Pitaevskii equation for a condensate includes the effect of collisions with thermal cloud atoms (non-condensate). The Boltz-mann quantum kinetic equation for a non-condensate was obtained by means of Zubarev's method of nonequilibrium statistical operator .
Starting from the first principles of statistical mechanics, the two-fluid hy-drodynamics of supe... more Starting from the first principles of statistical mechanics, the two-fluid hy-drodynamics of superconductor in ideal approximation is constructed. The system of equations of motion for normal and anomalous correlation functions is used for hydrodynamic description. Transition to equations of hy-drodynamics is performed using an expansion of equations of motion for correlation functions in terms of a small parameter. PACS: 05.30.Fk, 47.37.+q