A. Khamzin - Academia.edu (original) (raw)
Papers by A. Khamzin
ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expression... more ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expressions for correlation functions of Ising-type nanosystems is demonstrated.
ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expression... more ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expressions for correlation functions of Ising-type nanosystems is demonstrated.
New Journal of Chemistry
The results of a quantitative reading of the cyclic voltammetry behavior of the tryptophan (Trp) ... more The results of a quantitative reading of the cyclic voltammetry behavior of the tryptophan (Trp) enantiomers deposited on an electrochemically activated glassy carbon electrode (GCE) are presented.
Physical Chemistry Chemical Physics
A microscopic model of the dielectric relaxation of ice at low temperatures is proposed.
Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Isin... more Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Ising model (n ϭ 1, 2, 3) is studied within the so-called static fluctuation approximation (SFA). The underlying physical picture is that the local field operator z f with quadratic fluctuations is replaced with its mean value
Mathematical Methods in the Applied Sciences, 2016
International Journal of Modern Physics E, 2010
The collective moment of inertia is derived analytically within the cranking model in the adiabat... more The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.
Bulletin of the Russian Academy of Sciences: Physics, 2008
ABSTRACT The cranking model taking into account the residual neutron-proton correlations with Gau... more ABSTRACT The cranking model taking into account the residual neutron-proton correlations with Gaussian interaction in the Hartree-Fock-Bogolyubov approximation has been formulated. The behavior of quasi-particle levels as a function of the rotation frequency of even-even and odd-odd nuclei with A = 158 has been investigated within this approach.
![Research paper thumbnail of Dielectric spectroscopy study of low-concentration aqueous solutions of a calix[4]resorcinarene derivative](https://attachments.academia-assets.com/41914461/thumbnails/1.jpg)
](Doklady Physical Chemistry, 2014
Bulletin of the Russian Academy of Sciences: Physics, 2012
ABSTRACT The algebra of canonical commutation relations is constructed in the Weyl form and a loc... more ABSTRACT The algebra of canonical commutation relations is constructed in the Weyl form and a locally covariant formulation of a charged scalar field is presented in terms of the covariant functor. The symplectic space of solutions of the Klein-Gordon-Fock equation is represented as a direct sum of symplectic spaces of positively and negatively charged π mesons. In each of the spaces, these fields satisfy the conditions of the locally covariant quantum field theory. Using natural transformation, the equivalence of two functors describing the π+ and π− mesons is shown. From the physical viewpoint, the equivalence corresponds to the equality of the mesons’ masses.
Russian Physics Journal, 2010
A method of calculating the equilibrium correlation functions of any arbitrary order for the Bald... more A method of calculating the equilibrium correlation functions of any arbitrary order for the Baldwin-Kolesnikov-Shelah (BKSh) model is suggested based on the static fluctuational approach. The method based on only one controllable approach allows the so-called equations of long-range coupling to be obtained which contain all information on the sought-after equilibrium correlation functions within the scope of the BKSh model. Calculations of the sought-after equilibrium correlation functions allow one to go beyond the scope of the conventional molecular field approach and to take into account the effect of field fluctuations on the gap behavior and the heat capacity to the left and right of the critical point. For the simplest case disregarding a dependence of the potential on the wave vector, temperature dependences of the energy gap and heat capacity with allowance for the fluctuations are presented. It is demonstrated that in this case, the fluctuations are small for three-dimensional systems, but sharply increase with decreasing dimensionality of the system.
Bulletin of the Russian Academy of Sciences: Physics, 2010
ABSTRACT Quasiparticle and collective characteristics of the isotopic triplet of 74RB, 74Kr and 7... more ABSTRACT Quasiparticle and collective characteristics of the isotopic triplet of 74RB, 74Kr and 74Se were studied in the Hartree-Fock-Bogolyubov approximation, in combination with a forced-rotation model depending on the rotation frequency at moderate spins. It was shown that for 74Rb, the first intersection in yrast occurs due to an aligning of the spins of the n-p pair, which leads to backbending in the behavior of the moment of inertia at ħΩ ≃ 0.25 MeV. In the last two even-even nuclei, the smooth behavior of the moment of inertia is explained by an enhancement of the competition between the T = 1 and T = 0 modes at ħΩ > 0.5 MeV.
Bulletin of the Russian Academy of Sciences: Physics, 2011
The algebra of canonical commutation relations is constructed in the Weyl form and a locally cova... more The algebra of canonical commutation relations is constructed in the Weyl form and a locally covariant formulation of a charged scalar field is presented in terms of the covariant functor. The symplectic space of solutions of the Klein-Gordon-Fock equation is represented as a direct sum of symplectic spaces of positively and negatively charged π mesons. In each of the spaces, these fields satisfy the conditions of the locally covariant quantum field theory. Using natural transformation, the equivalence of two functors describ ing the π + and πmesons is shown. From the physical viewpoint, the equivalence corresponds to the equality of the mesons' masses.
We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary o... more We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so called far dis tance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high density limit were obtained. All expres sions are given in the units of r s , where r s determines the ratio of a mean distance between electrons to the Bohr radius a 0 . In these expressions, we calculate terms of the respective order r s and . It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r s .
Physical Review E, 2014
Based on the supposition related to fractal nature of transport processes in ion-conducting mater... more Based on the supposition related to fractal nature of transport processes in ion-conducting materials, an expression for the low-frequency ac conductivity dependence was derived. This expression for the ac conductivity generalizes the power-law dependence and gives a possibility to take into account the influence of the electrode polarization effect. The ac conductivity expression obtained is in excellent agreement with experimental data for a wide frequency range.
Optics and Spectroscopy, 2014
The authors obtain the closed self consistent system of equations for calculation of the desired ... more The authors obtain the closed self consistent system of equations for calculation of the desired thermody namic values of the Ising magnet with arbitrary spin and in presence of the single ion anisotropy in the frame of the original static fluctuation approach (SFA). The essence of the SFA is based on accurate calculations of fluctuations of a molecular field. As an example the complete analysis of the critical behavior of the Ising magnet with spin S = 1 (Blume Capiel model) is shown. The expressions for the phase transitions lines of the first and the second order are found. In addition, the coordinates of the tricritical point for some types of cu bic lattices are found also.
Physical Review E, 2000
The transverse Ising model is considered in the static fluctuation approximation. This hinges on ... more The transverse Ising model is considered in the static fluctuation approximation. This hinges on the replacement of the local field operator with its mean value; only the quadratic fluctuations of the local field are retained. The model is applied to ferroelectrics of the order-disorder type, such as monoaxial crystalline threeglycinsulfate. Analytic expressions are derived for the spontaneous polarization, the specific heat, the pair correlation function, and the static susceptibility of this ferroelectric. Its main characteristics are then determined numerically as functions of the temperature. In particular, its critical behavior is obtained automatically for a specific value of some ''control'' parameter. It is predicted that, with respect to this parameter, the specific heat exhibits a logarithmic behavior to the right of the critical point; this is interpreted as a consequence of the long range and axial anisotropy of the dipole-dipole interaction. In passing, the behavior of the lattice Green function for the anisotropic dipole-dipole potential near the critical point is thoroughly examined.
Theoretical and Mathematical Physics, 2011
We obtain an expression for the NMR line at low temperatures for a system of nuclear spins descri... more We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of "easy axis" anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing highfrequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of "easy plane" anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system.
Theoretical and Mathematical Physics, 2005
For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spi... more For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration.
ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expression... more ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expressions for correlation functions of Ising-type nanosystems is demonstrated.
ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expression... more ABSTRACT Using a four-spin nanocluster as an example, a technique for developing exact expressions for correlation functions of Ising-type nanosystems is demonstrated.
New Journal of Chemistry
The results of a quantitative reading of the cyclic voltammetry behavior of the tryptophan (Trp) ... more The results of a quantitative reading of the cyclic voltammetry behavior of the tryptophan (Trp) enantiomers deposited on an electrochemically activated glassy carbon electrode (GCE) are presented.
Physical Chemistry Chemical Physics
A microscopic model of the dielectric relaxation of ice at low temperatures is proposed.
Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Isin... more Viewed as a prototype for strongly interacting many-body systems, the spin-1/2 n-dimensional Ising model (n ϭ 1, 2, 3) is studied within the so-called static fluctuation approximation (SFA). The underlying physical picture is that the local field operator z f with quadratic fluctuations is replaced with its mean value
Mathematical Methods in the Applied Sciences, 2016
International Journal of Modern Physics E, 2010
The collective moment of inertia is derived analytically within the cranking model in the adiabat... more The collective moment of inertia is derived analytically within the cranking model in the adiabatic mean-field approximation at finite temperature. Using the nonperturbative periodic-orbit theory the semiclassical shell-structure components of the collective moment of inertia are obtained for any potential well. Their relation to the free-energy shell corrections are found semiclassically as being given through the shell-structure components of the rigid-body moment of inertia of the statistically equilibrium rotation in terms of short periodic orbits. Shell effects in the moment of inertia disappear exponentially with increasing temperature. For the case of the harmonic-oscillator potential one observes a perfect agreement between semiclassical and quantum shell-structure components of the free energy and the moment of inertia for several critical bifurcation deformations and several temperatures.
Bulletin of the Russian Academy of Sciences: Physics, 2008
ABSTRACT The cranking model taking into account the residual neutron-proton correlations with Gau... more ABSTRACT The cranking model taking into account the residual neutron-proton correlations with Gaussian interaction in the Hartree-Fock-Bogolyubov approximation has been formulated. The behavior of quasi-particle levels as a function of the rotation frequency of even-even and odd-odd nuclei with A = 158 has been investigated within this approach.
Doklady Physical Chemistry, 2014
Bulletin of the Russian Academy of Sciences: Physics, 2012
ABSTRACT The algebra of canonical commutation relations is constructed in the Weyl form and a loc... more ABSTRACT The algebra of canonical commutation relations is constructed in the Weyl form and a locally covariant formulation of a charged scalar field is presented in terms of the covariant functor. The symplectic space of solutions of the Klein-Gordon-Fock equation is represented as a direct sum of symplectic spaces of positively and negatively charged π mesons. In each of the spaces, these fields satisfy the conditions of the locally covariant quantum field theory. Using natural transformation, the equivalence of two functors describing the π+ and π− mesons is shown. From the physical viewpoint, the equivalence corresponds to the equality of the mesons’ masses.
Russian Physics Journal, 2010
A method of calculating the equilibrium correlation functions of any arbitrary order for the Bald... more A method of calculating the equilibrium correlation functions of any arbitrary order for the Baldwin-Kolesnikov-Shelah (BKSh) model is suggested based on the static fluctuational approach. The method based on only one controllable approach allows the so-called equations of long-range coupling to be obtained which contain all information on the sought-after equilibrium correlation functions within the scope of the BKSh model. Calculations of the sought-after equilibrium correlation functions allow one to go beyond the scope of the conventional molecular field approach and to take into account the effect of field fluctuations on the gap behavior and the heat capacity to the left and right of the critical point. For the simplest case disregarding a dependence of the potential on the wave vector, temperature dependences of the energy gap and heat capacity with allowance for the fluctuations are presented. It is demonstrated that in this case, the fluctuations are small for three-dimensional systems, but sharply increase with decreasing dimensionality of the system.
Bulletin of the Russian Academy of Sciences: Physics, 2010
ABSTRACT Quasiparticle and collective characteristics of the isotopic triplet of 74RB, 74Kr and 7... more ABSTRACT Quasiparticle and collective characteristics of the isotopic triplet of 74RB, 74Kr and 74Se were studied in the Hartree-Fock-Bogolyubov approximation, in combination with a forced-rotation model depending on the rotation frequency at moderate spins. It was shown that for 74Rb, the first intersection in yrast occurs due to an aligning of the spins of the n-p pair, which leads to backbending in the behavior of the moment of inertia at ħΩ ≃ 0.25 MeV. In the last two even-even nuclei, the smooth behavior of the moment of inertia is explained by an enhancement of the competition between the T = 1 and T = 0 modes at ħΩ > 0.5 MeV.
Bulletin of the Russian Academy of Sciences: Physics, 2011
The algebra of canonical commutation relations is constructed in the Weyl form and a locally cova... more The algebra of canonical commutation relations is constructed in the Weyl form and a locally covariant formulation of a charged scalar field is presented in terms of the covariant functor. The symplectic space of solutions of the Klein-Gordon-Fock equation is represented as a direct sum of symplectic spaces of positively and negatively charged π mesons. In each of the spaces, these fields satisfy the conditions of the locally covariant quantum field theory. Using natural transformation, the equivalence of two functors describ ing the π + and πmesons is shown. From the physical viewpoint, the equivalence corresponds to the equality of the mesons' masses.
We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary o... more We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi gas model in the framework of the static fluctuation approximation method. This method based only on a single and controllable approximation allows obtaining the so called far dis tance equations. These equations connecting the quantum states of a Fermi particle with variables of the local field operator contain all necessary information related to the calculation of the desired correlation functions and basic thermodynamic parameters of the many body system. The basic expressions for the mean energy and heat capacity for the electron gas at low temperatures in the high density limit were obtained. All expres sions are given in the units of r s , where r s determines the ratio of a mean distance between electrons to the Bohr radius a 0 . In these expressions, we calculate terms of the respective order r s and . It is also shown that the static fluctuation approximation allows finding the terms related to higher orders of the decomposition with respect to the parameter r s .
Physical Review E, 2014
Based on the supposition related to fractal nature of transport processes in ion-conducting mater... more Based on the supposition related to fractal nature of transport processes in ion-conducting materials, an expression for the low-frequency ac conductivity dependence was derived. This expression for the ac conductivity generalizes the power-law dependence and gives a possibility to take into account the influence of the electrode polarization effect. The ac conductivity expression obtained is in excellent agreement with experimental data for a wide frequency range.
Optics and Spectroscopy, 2014
The authors obtain the closed self consistent system of equations for calculation of the desired ... more The authors obtain the closed self consistent system of equations for calculation of the desired thermody namic values of the Ising magnet with arbitrary spin and in presence of the single ion anisotropy in the frame of the original static fluctuation approach (SFA). The essence of the SFA is based on accurate calculations of fluctuations of a molecular field. As an example the complete analysis of the critical behavior of the Ising magnet with spin S = 1 (Blume Capiel model) is shown. The expressions for the phase transitions lines of the first and the second order are found. In addition, the coordinates of the tricritical point for some types of cu bic lattices are found also.
Physical Review E, 2000
The transverse Ising model is considered in the static fluctuation approximation. This hinges on ... more The transverse Ising model is considered in the static fluctuation approximation. This hinges on the replacement of the local field operator with its mean value; only the quadratic fluctuations of the local field are retained. The model is applied to ferroelectrics of the order-disorder type, such as monoaxial crystalline threeglycinsulfate. Analytic expressions are derived for the spontaneous polarization, the specific heat, the pair correlation function, and the static susceptibility of this ferroelectric. Its main characteristics are then determined numerically as functions of the temperature. In particular, its critical behavior is obtained automatically for a specific value of some ''control'' parameter. It is predicted that, with respect to this parameter, the specific heat exhibits a logarithmic behavior to the right of the critical point; this is interpreted as a consequence of the long range and axial anisotropy of the dipole-dipole interaction. In passing, the behavior of the lattice Green function for the anisotropic dipole-dipole potential near the critical point is thoroughly examined.
Theoretical and Mathematical Physics, 2011
We obtain an expression for the NMR line at low temperatures for a system of nuclear spins descri... more We obtain an expression for the NMR line at low temperatures for a system of nuclear spins described by a Hamiltonian with equal spin-spin coupling constants. We show that in the case of "easy axis" anisotropy, the line has a logarithmic low-frequency singularity and an exponentially decreasing highfrequency asymptotic behavior at the temperature of an anomalous peak of heat capacity. In the case of "easy plane" anisotropy, the line has the traditional Gaussian form. We discuss the possibility of using NMR data to discover specific thermodynamic and magnetic properties of the considered model system.
Theoretical and Mathematical Physics, 2005
For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spi... more For the model of equal spin-spin interactions, we obtain exact Heisenberg expressions for the spin operator components and use them to find the relations that hold for spin operators appearing in the thermodynamic mean. We use the obtained exact relations for the means to describe the thermodynamics of the model under consideration.