Vadim Ohanyan | Yerevan State University (original) (raw)
Papers by Vadim Ohanyan
Теоретическая и математическая физика, 2008
Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the mo... more Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere S^3 in the field of n fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on S^3.
We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechan... more We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-1/2 XY chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic or/and electric field.
An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling... more An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at M=0,1/4 and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A novel mechanism of magnetization plateau stabilization corresponding to M=1/4 state is reported.
A spin-1/2 XY chain model of magnetoelectric on a zigzag chain is considered rigorously. The magn... more A spin-1/2 XY chain model of magnetoelectric on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. By non-uniform spin-rotations the model is reduced to a dimerized XY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model, zero and finite temperature magnetoelectric effect, obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellip... more We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various two-dimensional surfaces listed above we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution with the magnetic filed conserving the symmetry of the two-dimensional surface(Landau problem). For each case we figure out at which values of parameters the qualitative character of the moving coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories (ellipsoid) we construct also the action-angle variables.
The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenbe... more The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenberg model and mixed-spin (1,1/2) double sawtooth Ising-Heisenberg model on the distorted ladders are rigorously investigated under an adiabatic demagnetization process using the quantum transfer-matrix technique. The models include the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. Close to field-induced quantum phase transitions, we compare both models together in the ability of cooling/heating near the quantum critical points. However, we observe a large magnetocaloric effect for both models, the mixed-spin double sawtooth ladder shows much more magneticaloric efficiency than the spin-1/2 double sawtooth ladder. During an adiabatic demagnetization process it can be seen a temperature dropping in the vicinity...
The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each sec... more The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground stated properties are also investigated, the corresponding ground state phase diagram is presented.
Fluorides in general are characterized by big variety of crystal structures, whereas those contai... more Fluorides in general are characterized by big variety of crystal structures, whereas those containing transition metals also often show sizable magnetic properties. The tendency of fluorine to form linear chain structures in many cases results in low-dimensional magnetism. Despite the plethora of magnetic phenomena in fluorides, their magnetoelectric properties are less studied than those of oxides. In the present work we theoretically study the magnetic and magnetoelectric properties of spin-chain compounds CaFeF_5 and SrFeF_5. The density functional theory is employed for determination of magnetic exchange constants, which are then used in Monte Carlo calculations. The symmetry analysis reveals that CaFeF_5 does not show magnetoelectric properties, whereas SrFeF_5 is a multiferroic.
We consider the spin-1/2 isotropic XY chain in an external magnetic field directed along z axis w... more We consider the spin-1/2 isotropic XY chain in an external magnetic field directed along z axis with periodically varying g-factors. To reveal the effects of regularly alternating g-factors, we calculate various static and dynamic equilibrium quantities in the ground state and at finite temperatures. We demonstrate that because of the regularly alternating g-factors the saturation field may disappear and the field dependence of the susceptibility in the ground state has additional logarithmic singularity at zero field. Moreover, the zero-field susceptibility has a logarithmic singularity as T→ 0. Furthermore, the dynamic structure factors exhibit much more structure in the "wave vector – frequency" plane that can be traced out to modifications of the two-fermion excitation continua which exclusively determine S_zz(κ,ω) and dominate the properties of S_xx(κ,ω). We discuss what changes can be observed in dynamic experiments on the corresponding substances.
The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction ... more The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits separation of variables in the Schrödinger equation and is integrable at the classical level. In the physical context this system describes the charge–dyon system subjected to homogeneous electric and magnetic fields parallel to each other. Another important feature which guarantees the separation of variables is the additional potential terms, oscillator like and proportional to cos θ. The first order corrections to the unperturbed spectrum of the ordinary MICZ–Kepler system are calculated. Particularly, the linear Zeeman–effect and effects of MICZ-terms are analyzed. The possible realizations of the system in some quantum dots are considered. 1
We propose the multi-center generalization of the MICZ-Kepler system (describing the motion of th... more We propose the multi-center generalization of the MICZ-Kepler system (describing the motion of the charged particle in the field of Dirac dyon) on the arbitrary conformally flat space. When the background dyons have the same ratio of the electric and magnetic charges the system admits N = 4 supersymmetric extension. We show that the twocenter MICZ-Kepler system on the Euclidean space is classically integrable; when one of the background dyons is located at the infinity the system results in the integrable generalization of the one-center MICZ-Kepler system in the parallel constant uniform electric and magnetic fields with some specific potential field. Moreover, any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates could be extended to the integrable system with the Dirac monopoles located in the foci of these coordinate systems. We also construct the integrable system describing the particle in parabolic quantum dot in the pre...
The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction ... more The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits separation of variables in the Schrödinger equation and is integrable at the classical level. The first order corrections to the unperturbed spectrum of the ordinary MICZ–Kepler system are calculated. Particularly, the linear Zeeman–effect and effects of MICZ-terms are analyzed. The possible realizations of the system in some quantum dots are considered. 1
We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. T... more We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with so(3)-invariant conformal flat metrics. 1
Exactly solvable model of Ising-Heisenberg diamond-chain with S = 1 XXZ vertical dimers with addi... more Exactly solvable model of Ising-Heisenberg diamond-chain with S = 1 XXZ vertical dimers with additional biquadratic interactions and single-ion anisotropy ... Onofre Rojas1 SM de Souza1, Vadim Ohanyan2,3 and Martiros Khurshudyan2 ... 1Departamento de Ciencias ...
Condensed Matter Physics
A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in ... more A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric suscept...
The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each s... more The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground stated properties are also investigated, the corresponding ground state phase diagram is presented. 1 Introduction. The sawtooth chain or delta chain is a one-dimensional lattice spin system with a topology of corner-sharing triangles (Fig. 1). This system is famous for a number of important features. Physically, magnetic lattices corresponding to the sawtooth chain are found in a number of compounds, in delafossite YCuO2.5 [1, 2] and olivines with structures ZnL2S4 (L=Er,Tm,Yb) [3] to cite a couple of examples. Antiferromagnetic Heisenberg model on sawtooth chain is
A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assemb... more A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration–iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined. 1
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellip... more We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various two-dimensional surfaces listed above we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution with the magnetic filed conserving the symmetry of the two-dimensional surface(Landau problem). For each case we figure out at which values of parameters the qualitative character of the moving coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories (ellipsoid) we construct also the action-angle variables.
![Research paper thumbnail of 0 70 5 . 07 27 v 1 [ m at hph ] 5 M ay 2 00 7 Multi-center MICZ-Kepler systems](https://attachments.academia-assets.com/76745140/thumbnails/1.jpg)
](We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. T... more We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with so(3)-invariant conformal flat metrics.
Теоретическая и математическая физика, 2008
Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the mo... more Proceeding from the superfield action for N=4, d=1 nonlinear supermultiplet, equipped with the most general potential term, we find the action describing a charged particle on the sphere S^3 in the field of n fixed Dirac dyons. We construct the supercharges and Hamiltonian and analyze some particulary interesting potentials corresponding to the N=4 supersymmetric extension of the integrable one- and two-center McIntosh--Cisneros--Zwanziger--Kepler (MICZ-Kepler) systems on S^3.
We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechan... more We illustrate the magnetoelectric effect conditioned by the Katsura-Nagaosa-Balatsky (KNB) mechanism within the frames of exactly solvable spin-1/2 XY chains. Due to three-spin interactions which are present in our consideration, the magnetization (polarization) is influenced by the electric (magnetic) field even in the absence of the magnetic (electric) field. We also discuss a magnetoelectrocaloric effect examining the entropy changes under the isothermal varying of the magnetic or/and electric field.
An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling... more An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at M=0,1/4 and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A novel mechanism of magnetization plateau stabilization corresponding to M=1/4 state is reported.
A spin-1/2 XY chain model of magnetoelectric on a zigzag chain is considered rigorously. The magn... more A spin-1/2 XY chain model of magnetoelectric on a zigzag chain is considered rigorously. The magnetoelectric coupling is described within the Katsura-Nagaosa-Balatsky mechanism. In the zigzag geometry it leads to the staggered Dzyaloshinskii-Moriya interaction. By non-uniform spin-rotations the model is reduced to a dimerized XY chain and solved exactly using the Jordan-Wigner transformation. We analyze the ground-state phase diagram of the model, zero and finite temperature magnetoelectric effect, obtain the magnetization and polarization curves versus magnetic and electric fields, as well as the parameters of anisotropic dielectric and magnetoelectric response. It is also shown that the electric field may enhance the magnetocaloric effect in the model.
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellip... more We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various two-dimensional surfaces listed above we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution with the magnetic filed conserving the symmetry of the two-dimensional surface(Landau problem). For each case we figure out at which values of parameters the qualitative character of the moving coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories (ellipsoid) we construct also the action-angle variables.
The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenbe... more The entropy and cooling rate of the both antiferromagnetic spin-1/2 double sawtooth IsingHeisenberg model and mixed-spin (1,1/2) double sawtooth Ising-Heisenberg model on the distorted ladders are rigorously investigated under an adiabatic demagnetization process using the quantum transfer-matrix technique. The models include the XXZ interaction between the interstitial Heisenberg dimers, the Ising coupling between nearest-neighbor spins of the legs and rungs, and additional cyclic four-spin exchange (ring exchange) in the square plaquette of each block. Close to field-induced quantum phase transitions, we compare both models together in the ability of cooling/heating near the quantum critical points. However, we observe a large magnetocaloric effect for both models, the mixed-spin double sawtooth ladder shows much more magneticaloric efficiency than the spin-1/2 double sawtooth ladder. During an adiabatic demagnetization process it can be seen a temperature dropping in the vicinity...
The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each sec... more The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground stated properties are also investigated, the corresponding ground state phase diagram is presented.
Fluorides in general are characterized by big variety of crystal structures, whereas those contai... more Fluorides in general are characterized by big variety of crystal structures, whereas those containing transition metals also often show sizable magnetic properties. The tendency of fluorine to form linear chain structures in many cases results in low-dimensional magnetism. Despite the plethora of magnetic phenomena in fluorides, their magnetoelectric properties are less studied than those of oxides. In the present work we theoretically study the magnetic and magnetoelectric properties of spin-chain compounds CaFeF_5 and SrFeF_5. The density functional theory is employed for determination of magnetic exchange constants, which are then used in Monte Carlo calculations. The symmetry analysis reveals that CaFeF_5 does not show magnetoelectric properties, whereas SrFeF_5 is a multiferroic.
We consider the spin-1/2 isotropic XY chain in an external magnetic field directed along z axis w... more We consider the spin-1/2 isotropic XY chain in an external magnetic field directed along z axis with periodically varying g-factors. To reveal the effects of regularly alternating g-factors, we calculate various static and dynamic equilibrium quantities in the ground state and at finite temperatures. We demonstrate that because of the regularly alternating g-factors the saturation field may disappear and the field dependence of the susceptibility in the ground state has additional logarithmic singularity at zero field. Moreover, the zero-field susceptibility has a logarithmic singularity as T→ 0. Furthermore, the dynamic structure factors exhibit much more structure in the "wave vector – frequency" plane that can be traced out to modifications of the two-fermion excitation continua which exclusively determine S_zz(κ,ω) and dominate the properties of S_xx(κ,ω). We discuss what changes can be observed in dynamic experiments on the corresponding substances.
The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction ... more The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits separation of variables in the Schrödinger equation and is integrable at the classical level. In the physical context this system describes the charge–dyon system subjected to homogeneous electric and magnetic fields parallel to each other. Another important feature which guarantees the separation of variables is the additional potential terms, oscillator like and proportional to cos θ. The first order corrections to the unperturbed spectrum of the ordinary MICZ–Kepler system are calculated. Particularly, the linear Zeeman–effect and effects of MICZ-terms are analyzed. The possible realizations of the system in some quantum dots are considered. 1
We propose the multi-center generalization of the MICZ-Kepler system (describing the motion of th... more We propose the multi-center generalization of the MICZ-Kepler system (describing the motion of the charged particle in the field of Dirac dyon) on the arbitrary conformally flat space. When the background dyons have the same ratio of the electric and magnetic charges the system admits N = 4 supersymmetric extension. We show that the twocenter MICZ-Kepler system on the Euclidean space is classically integrable; when one of the background dyons is located at the infinity the system results in the integrable generalization of the one-center MICZ-Kepler system in the parallel constant uniform electric and magnetic fields with some specific potential field. Moreover, any system (without monopoles) admitting the separation of variables in the elliptic or parabolic coordinates could be extended to the integrable system with the Dirac monopoles located in the foci of these coordinate systems. We also construct the integrable system describing the particle in parabolic quantum dot in the pre...
The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction ... more The quantum two-center MICZ–Kepler system is considered in the limit when one of the interaction centers is situated at infinity, which leads to homogeneous electric and magnetic fields appearing in the system. The emerging system admits separation of variables in the Schrödinger equation and is integrable at the classical level. The first order corrections to the unperturbed spectrum of the ordinary MICZ–Kepler system are calculated. Particularly, the linear Zeeman–effect and effects of MICZ-terms are analyzed. The possible realizations of the system in some quantum dots are considered. 1
We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. T... more We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with so(3)-invariant conformal flat metrics. 1
Exactly solvable model of Ising-Heisenberg diamond-chain with S = 1 XXZ vertical dimers with addi... more Exactly solvable model of Ising-Heisenberg diamond-chain with S = 1 XXZ vertical dimers with additional biquadratic interactions and single-ion anisotropy ... Onofre Rojas1 SM de Souza1, Vadim Ohanyan2,3 and Martiros Khurshudyan2 ... 1Departamento de Ciencias ...
Condensed Matter Physics
A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in ... more A magnetoelectric effect according to Katsura-Nagaosa-Balatsky mechanism in spin-1/2 XY chain in transverse magnetic field is considered. A spatial orientation of the electric field is chosen to provide an exact solution of the model in terms of free spinless fermions. The simplest model of quantum spin chain demonstrating a magnetoelectric effect, a zero temperature case of the spin-1/2 XX chain in a transverse magnetic field with Katsura-Nagaosa-Balatsky mechanism, is considered. The model has the simplest possible form of the magnetization, polarization and susceptibility functions, depending on electric and magnetic fields in a most simple form. For the case of arbitrary XY anisotropy, a non-monotonous dependence of magnetization on the XY anisotropy parameter is figured out. This non-uniform behaviour is governed by the critical point which is connected with the possibility to drive the system gapless or gapped by the electric field. Singularities of the magnetoelectric suscept...
The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each s... more The sawtooth chain with pairs of S = 1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground stated properties are also investigated, the corresponding ground state phase diagram is presented. 1 Introduction. The sawtooth chain or delta chain is a one-dimensional lattice spin system with a topology of corner-sharing triangles (Fig. 1). This system is famous for a number of important features. Physically, magnetic lattices corresponding to the sawtooth chain are found in a number of compounds, in delafossite YCuO2.5 [1, 2] and olivines with structures ZnL2S4 (L=Er,Tm,Yb) [3] to cite a couple of examples. Antiferromagnetic Heisenberg model on sawtooth chain is
A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assemb... more A mixed Ising-Heisenberg spin system consisting of triangular XXZ-Heisenberg spin clusters assembled into a chain by alternating with Ising spins interacting to all three spins in the triangle is considered. The exact solution of the model is given in terms of the generalized decoration–iteration map and within the transfer-matrix technique. Exact expressions for thermodynamic functions are derived. Ground state phase diagrams, thermodynamic and magnetic properties of the system are examined. 1
We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellip... more We define the Landau problem on two-dimensional surfaces of revolution of the second order: ellipsoid, hyperboloid and paraboloid. We start form the two-center MICZ-Kepler system Hamiltonian and then making the reduction into the various two-dimensional surfaces listed above we obtain the Hamiltonians of the charged particle moving on the corresponding surface of revolution with the magnetic filed conserving the symmetry of the two-dimensional surface(Landau problem). For each case we figure out at which values of parameters the qualitative character of the moving coincides with that of a free particle moving on the save two-dimensional surface. For the case of finite trajectories (ellipsoid) we construct also the action-angle variables.
We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. T... more We present the classical solutions of the two-center MICZ-Kepler and MICZ-Kepler-Stark systems. Then we suggest the model of multi-center MICZ-Kepler system on the curved spaces equipped with so(3)-invariant conformal flat metrics.