Jasmina Tekic - Academia.edu (original) (raw)
Papers by Jasmina Tekic
Physica Scripta, Mar 2, 2020
Waves in Random and Complex Media, May 28, 2018
An overdamped three-layer model with incommensurate structure consisting of two harmonic chains w... more An overdamped three-layer model with incommensurate structure consisting of two harmonic chains which both move over the substrate potential is studied in the presence of an external dc + ac driving force. The force is applied only on the upper harmonic chain, and dynamics of the middle layer is examined. The results show that the dynamical mode-locking appears not only in the upper layer but also in the middle one. The behavior of the middle layer is strongly determined by the amplitude and frequency of the ac force, and the phase diagram which presents pinned, dynamical mode-locking and sliding regimes as a function of system parameters are given. Contrary to the standard case, critical depinning force and steps exhibit anomalous behavior. Particles trajectories have been analyzed which showed very different motion of particles from the one which usually appears in systems under dc + ac forces.
Scientific Reports, Jul 2, 2020
Waves in Random and Complex Media, Apr 28, 2016
Hysteretic phenomenon is studied for an underdampedcommensurate three layers model consisting of ... more Hysteretic phenomenon is studied for an underdampedcommensurate three layers model consisting of two harmonic chains that both move over the substrate. In the depinning process, two critical points and are found. In the pinning process, two critical points and are also found. The dependence of four critical forces on the system parameters is investigated. The analytical result of critical force is obtained which is in good agreement with the numerical one.
13th Chaotic Modeling and Simulation International Conference, 2021
Physical review, Jan 21, 2020
Examination of an annular system of underdamped Josephson junctions in the presence of external r... more Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristics only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation.
Physical review, Jun 26, 2023
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is ... more Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. I. INTRODUCTION Synchronization effects have been a subject of intensive theoretical and experimental studies in charge density wave transport [1-7], vortex matter [8-10], irradiated Josephson junctions [11-15], superconducting nanowires [16, 17] and driven colloidal systems [18]. One of the models used for investigation of synchronization phenomena (modelocking, i.e. Shapiro steps), starting from microscopic dynamics, is the dissipative Frenkel-Kontorova (FK) model under external periodic forces [19-22]. Recently, it has been shown that dc-driven FK model with a lateral periodic excitation to the substrate potential can be used to generate Shapiro steps as well [23]. The one-dimensional FK model represents a chain of coupled particles which are subjected to the substrate potential. For the standard FK model, the particles are harmonically coupled to their nearest neighbors and the substrate potential is sinusoidal. To capture certain phenomena in Josephson junction arrays [24-26], charge density wave systems [5-7] and tribology [27-29] different generalizations of the FK model are used. Due to competition between the length scales of interparticle and substrate potential, many nontrivial ground states of the model are possible. They can be classified into two categories-commensurate (for which the interparticle average distance, i.e. winding number, is rational) or incommensurate (for which the winding number is irrational) [19, 22, 30]. If an external dc driving force is applied, there exists a critical threshold value, i.e. critical depinning force F c , which separates two dynamical regimes-pinning and sliding regime. The latter regime is defined by collective motion of the particles along with non-zero average velocity, whereas in the pinning regime the particles are pinned to the static configurations with zero average velocity. When both external dc and ac forces are applied to the FK model, modelocking appears due to locking between the frequency of particle motion and frequency of external ac force, which results in the staircase-like response function [21, 31-36]. A new class of nonlinear periodic deformable potentials, which could be specified by suitable choice of parameters, was introduced in [37, 38]. By fixing parameters, different periodic potentials, such as assymetric deformable potential, which are relevant for studying Josephson junctions, charge density waves, heat conduction in low dimensional lattices, and crystals with dislocations, can be obtained. Unlike the case of the standard FK model, when the subharmonic steps either do not exist or they are too small, for the FK model with asymmetric deformable substrate potential large subharmonic steps can be observed in the response function plot [31, 32, 34]. Aside from the response function, the largest Lyapunov exponent (LE) also provides certain insight into the dynamics of dissipatively driven FK model. It has been shown that the largest LE can be viewed as a tool to characterize chaotic, periodic, and quasiperiodic motion (see [39, 40] and references therein). Furthermore, the LEs are also used for observation of dynamical phase transitions (pinning to sliding regime and unlocking transition) [14, 15, 21, 41, 42] and thermally induced phase transitions [43-46]. Specifically, the largest LE calculated for the standard overdamped FK model in the sliding regime takes on negative values on the steps, determining the trajectories periodic in time, while it reaches zero outside the steps, characterizing the unlocking transition to the quasiperiodic regime [21, 41]. On the other hand, in the underdamped regime chaos sometimes appears at the edges of the Shapiro steps and system exhibits structural chaotic behavior [15, 23]. Moreover, according to [47] calculating the largest LE presents the most
arXiv (Cornell University), Aug 7, 2023
The unique resonance and locking phenomena in the superconductor-ferromagnet-superconductor φ0 Jo... more The unique resonance and locking phenomena in the superconductor-ferromagnet-superconductor φ0 Josephson junction under external electromagnetic radiation are demonstrated when not just the electric but also the magnetic component of external radiation is taken into account. Due to the coupling of superconductivity and magnetism in this system, the magnetic moment precession of the ferromagnetic layer caused by the magnetic component of external radiation can lock the Josephson oscillations, which results in the appearance of a particular type of steps in the currentvoltage characteristics, completely different from the well-known Shapiro steps. We call these steps the Buzdin steps in the case when the system is driven only by the magnetic component and the Chimera steps in the case when both magnetic and electric components are present. Unlike the Shapiro steps where the magnetization remains constant along the step, here it changes though the system is locked. The spin-orbit coupling substantially contributes to the amplitude, i.e., the size of these steps. Dramatic changes in their amplitudes are also observed at frequencies near the ferromagnetic resonance. Combinations of the Josephson and Kittel ferromagnetic resonances together with different types of locking pronounced in dynamics and current-voltage characteristics make the physics of this system very interesting and open up a series of new applications.
Physical review, Feb 10, 2023
The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in... more The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the ϕ 0 junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I-G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (I S −→ I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.
Physical Review E
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is ... more Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. I. INTRODUCTION Synchronization effects have been a subject of intensive theoretical and experimental studies in charge density wave transport [1-7], vortex matter [8-10], irradiated Josephson junctions [11-15], superconducting nanowires [16, 17] and driven colloidal systems [18]. One of the models used for investigation of synchronization phenomena (modelocking, i.e. Shapiro steps), starting from microscopic dynamics, is the dissipative Frenkel-Kontorova (FK) model under external periodic forces [19-22]. Recently, it has been shown that dc-driven FK model with a lateral periodic excitation to the substrate potential can be used to generate Shapiro steps as well [23]. The one-dimensional FK model represents a chain of coupled particles which are subjected to the substrate potential. For the standard FK model, the particles are harmonically coupled to their nearest neighbors and the substrate potential is sinusoidal. To capture certain phenomena in Josephson junction arrays [24-26], charge density wave systems [5-7] and tribology [27-29] different generalizations of the FK model are used. Due to competition between the length scales of interparticle and substrate potential, many nontrivial ground states of the model are possible. They can be classified into two categories-commensurate (for which the interparticle average distance, i.e. winding number, is rational) or incommensurate (for which the winding number is irrational) [19, 22, 30]. If an external dc driving force is applied, there exists a critical threshold value, i.e. critical depinning force F c , which separates two dynamical regimes-pinning and sliding regime. The latter regime is defined by collective motion of the particles along with non-zero average velocity, whereas in the pinning regime the particles are pinned to the static configurations with zero average velocity. When both external dc and ac forces are applied to the FK model, modelocking appears due to locking between the frequency of particle motion and frequency of external ac force, which results in the staircase-like response function [21, 31-36]. A new class of nonlinear periodic deformable potentials, which could be specified by suitable choice of parameters, was introduced in [37, 38]. By fixing parameters, different periodic potentials, such as assymetric deformable potential, which are relevant for studying Josephson junctions, charge density waves, heat conduction in low dimensional lattices, and crystals with dislocations, can be obtained. Unlike the case of the standard FK model, when the subharmonic steps either do not exist or they are too small, for the FK model with asymmetric deformable substrate potential large subharmonic steps can be observed in the response function plot [31, 32, 34]. Aside from the response function, the largest Lyapunov exponent (LE) also provides certain insight into the dynamics of dissipatively driven FK model. It has been shown that the largest LE can be viewed as a tool to characterize chaotic, periodic, and quasiperiodic motion (see [39, 40] and references therein). Furthermore, the LEs are also used for observation of dynamical phase transitions (pinning to sliding regime and unlocking transition) [14, 15, 21, 41, 42] and thermally induced phase transitions [43-46]. Specifically, the largest LE calculated for the standard overdamped FK model in the sliding regime takes on negative values on the steps, determining the trajectories periodic in time, while it reaches zero outside the steps, characterizing the unlocking transition to the quasiperiodic regime [21, 41]. On the other hand, in the underdamped regime chaos sometimes appears at the edges of the Shapiro steps and system exhibits structural chaotic behavior [15, 23]. Moreover, according to [47] calculating the largest LE presents the most
Springer proceedings in complexity, 2021
Chaos, Solitons & Fractals, 2022
Physical Review E, 2019
The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were ex... more The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction.
Journal of Research in Physics, 2015
Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate ... more Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate structures with integer values of winding number in the dc- and ac-driven overdamped Frenkel-Kontorova model. While in the standard case with sinusoidal substrate potential, the system reduces to the single particles model in which only harmonic steps exist and analytical form for the step size can be revealed, in the case of deformable potential, the presence of many degrees of freedom strongly influences the Shapiro steps. Whole series of subharmonic steps appear, and the two types of response functions, the one for the commensurate structures with odd and the one for the commensurate structures with even winding number have been observed.
International Journal of Modern Physics B, 2007
The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova m... more The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova model are studied. The particular attention has been focused on, the variations of the step width and critical depinning force with the ac amplitude. The amplitude dependence is strongly influenced by the frequency of ac force where at the higher frequencies, the oscillations have the Bessel like form.
Journal of Physics: Condensed Matter, 1993
ABSTRACT The possibility of the creation of the bound state of a domain wall and surrounding latt... more ABSTRACT The possibility of the creation of the bound state of a domain wall and surrounding lattice distortion was investigated in the framework of the one-dimensional Ising model with transverse field. It was found that the existence of such an entity is very sensitive to the mutual ratio of the basic physical parameters of the system. The authors obtain that, in the weak-coupling regime, such a 'dressed' excitation can arise in the so-called unadiabatic limit when the maximal photon energy greatly exceeds the nearest-neighbour exchange energy. In that case, the 'dressing' effect can significantly modify domain-wall properties, causing the increase of its effective mass and lowering of the ground-state energy, while the domain-wall velocity cannot exceed the speed of sound.
Frontiers of Physics, 2015
Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova m... more Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.
Solid State Phenomena, 1998
Within the framework of the sine-Gordon model, the phenomenon of magnetoacoustic resonance has be... more Within the framework of the sine-Gordon model, the phenomenon of magnetoacoustic resonance has been analyzed. It was found that MAR arises on account of the common motion of magnetic and lattice solitons
Physical Review E, 1999
The Fokker-Planck equation for multivibron solitons interacting with lattice vibrations in a mole... more The Fokker-Planck equation for multivibron solitons interacting with lattice vibrations in a molecular chain has been derived by means of the nonequilibrium statistical operator method. It was shown that a soliton undergoes diffusive motion characterized by two substantially different diffusion coefficients. The first one corresponds to the ordinary ͑Einsteinian or dissipative͒ diffusion and characterizes the soliton Brownian motion, while the second one corresponds to the anomalous diffusion connected with frictionless displacement of the soliton center of mass coordinate due to the interaction with phonons. Both processes are the consequence of the Cherenkov-like radiation of phonon quanta arising when soliton velocity approaches the phase speed of sound. ͓S1063-651X͑99͒01707-9͔
Physica Scripta, Mar 2, 2020
Waves in Random and Complex Media, May 28, 2018
An overdamped three-layer model with incommensurate structure consisting of two harmonic chains w... more An overdamped three-layer model with incommensurate structure consisting of two harmonic chains which both move over the substrate potential is studied in the presence of an external dc + ac driving force. The force is applied only on the upper harmonic chain, and dynamics of the middle layer is examined. The results show that the dynamical mode-locking appears not only in the upper layer but also in the middle one. The behavior of the middle layer is strongly determined by the amplitude and frequency of the ac force, and the phase diagram which presents pinned, dynamical mode-locking and sliding regimes as a function of system parameters are given. Contrary to the standard case, critical depinning force and steps exhibit anomalous behavior. Particles trajectories have been analyzed which showed very different motion of particles from the one which usually appears in systems under dc + ac forces.
Scientific Reports, Jul 2, 2020
Waves in Random and Complex Media, Apr 28, 2016
Hysteretic phenomenon is studied for an underdampedcommensurate three layers model consisting of ... more Hysteretic phenomenon is studied for an underdampedcommensurate three layers model consisting of two harmonic chains that both move over the substrate. In the depinning process, two critical points and are found. In the pinning process, two critical points and are also found. The dependence of four critical forces on the system parameters is investigated. The analytical result of critical force is obtained which is in good agreement with the numerical one.
13th Chaotic Modeling and Simulation International Conference, 2021
Physical review, Jan 21, 2020
Examination of an annular system of underdamped Josephson junctions in the presence of external r... more Examination of an annular system of underdamped Josephson junctions in the presence of external radiation showed that the ability of the system to lock with some external radiation was determined not only by the number but also by the type of rotating excitations (fluxons or antifluxons). Shapiro steps can be observed in the current-voltage characteristics only in the system with trapped fluxons or in the system with fluxon-antifluxon pairs. If the trapped fluxons circulate simultaneously with fluxon-antifluxon pairs, there are no Shapiro steps regardless of the amplitude or frequency of the applied external radiation.
Physical review, Jun 26, 2023
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is ... more Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. I. INTRODUCTION Synchronization effects have been a subject of intensive theoretical and experimental studies in charge density wave transport [1-7], vortex matter [8-10], irradiated Josephson junctions [11-15], superconducting nanowires [16, 17] and driven colloidal systems [18]. One of the models used for investigation of synchronization phenomena (modelocking, i.e. Shapiro steps), starting from microscopic dynamics, is the dissipative Frenkel-Kontorova (FK) model under external periodic forces [19-22]. Recently, it has been shown that dc-driven FK model with a lateral periodic excitation to the substrate potential can be used to generate Shapiro steps as well [23]. The one-dimensional FK model represents a chain of coupled particles which are subjected to the substrate potential. For the standard FK model, the particles are harmonically coupled to their nearest neighbors and the substrate potential is sinusoidal. To capture certain phenomena in Josephson junction arrays [24-26], charge density wave systems [5-7] and tribology [27-29] different generalizations of the FK model are used. Due to competition between the length scales of interparticle and substrate potential, many nontrivial ground states of the model are possible. They can be classified into two categories-commensurate (for which the interparticle average distance, i.e. winding number, is rational) or incommensurate (for which the winding number is irrational) [19, 22, 30]. If an external dc driving force is applied, there exists a critical threshold value, i.e. critical depinning force F c , which separates two dynamical regimes-pinning and sliding regime. The latter regime is defined by collective motion of the particles along with non-zero average velocity, whereas in the pinning regime the particles are pinned to the static configurations with zero average velocity. When both external dc and ac forces are applied to the FK model, modelocking appears due to locking between the frequency of particle motion and frequency of external ac force, which results in the staircase-like response function [21, 31-36]. A new class of nonlinear periodic deformable potentials, which could be specified by suitable choice of parameters, was introduced in [37, 38]. By fixing parameters, different periodic potentials, such as assymetric deformable potential, which are relevant for studying Josephson junctions, charge density waves, heat conduction in low dimensional lattices, and crystals with dislocations, can be obtained. Unlike the case of the standard FK model, when the subharmonic steps either do not exist or they are too small, for the FK model with asymmetric deformable substrate potential large subharmonic steps can be observed in the response function plot [31, 32, 34]. Aside from the response function, the largest Lyapunov exponent (LE) also provides certain insight into the dynamics of dissipatively driven FK model. It has been shown that the largest LE can be viewed as a tool to characterize chaotic, periodic, and quasiperiodic motion (see [39, 40] and references therein). Furthermore, the LEs are also used for observation of dynamical phase transitions (pinning to sliding regime and unlocking transition) [14, 15, 21, 41, 42] and thermally induced phase transitions [43-46]. Specifically, the largest LE calculated for the standard overdamped FK model in the sliding regime takes on negative values on the steps, determining the trajectories periodic in time, while it reaches zero outside the steps, characterizing the unlocking transition to the quasiperiodic regime [21, 41]. On the other hand, in the underdamped regime chaos sometimes appears at the edges of the Shapiro steps and system exhibits structural chaotic behavior [15, 23]. Moreover, according to [47] calculating the largest LE presents the most
arXiv (Cornell University), Aug 7, 2023
The unique resonance and locking phenomena in the superconductor-ferromagnet-superconductor φ0 Jo... more The unique resonance and locking phenomena in the superconductor-ferromagnet-superconductor φ0 Josephson junction under external electromagnetic radiation are demonstrated when not just the electric but also the magnetic component of external radiation is taken into account. Due to the coupling of superconductivity and magnetism in this system, the magnetic moment precession of the ferromagnetic layer caused by the magnetic component of external radiation can lock the Josephson oscillations, which results in the appearance of a particular type of steps in the currentvoltage characteristics, completely different from the well-known Shapiro steps. We call these steps the Buzdin steps in the case when the system is driven only by the magnetic component and the Chimera steps in the case when both magnetic and electric components are present. Unlike the Shapiro steps where the magnetization remains constant along the step, here it changes though the system is locked. The spin-orbit coupling substantially contributes to the amplitude, i.e., the size of these steps. Dramatic changes in their amplitudes are also observed at frequencies near the ferromagnetic resonance. Combinations of the Josephson and Kittel ferromagnetic resonances together with different types of locking pronounced in dynamics and current-voltage characteristics make the physics of this system very interesting and open up a series of new applications.
Physical review, Feb 10, 2023
The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in... more The ordinary (superconductor-insulator-superconductor) Josephson junction cannot exhibit chaos in the absence of an external ac drive, whereas in the superconductor-ferromagnet-superconductor Josephson junction, known as the ϕ 0 junction, the magnetic layer effectively provides two extra degrees of freedom that can facilitate chaotic dynamics in the resulting four-dimensional autonomous system. In this work, we use the Landau-Lifshitz-Gilbert model for the magnetic moment of the ferromagnetic weak link, while the Josephson junction is described by the resistively capacitively shunted-junction model. We study the chaotic dynamics of the system for parameters surrounding the ferromagnetic resonance region, i.e., for which the Josephson frequency is reasonably close to the ferromagnetic frequency. We show that, due to the conservation of magnetic moment magnitude, two of the numerically computed full spectrum Lyapunov characteristic exponents are trivially zero. One-parameter bifurcation diagrams are used to investigate various transitions that occur between quasiperiodic, chaotic, and regular regions as the dc-bias current through the junction, I, is varied. We also compute two-dimensional bifurcation diagrams, which are similar to traditional isospike diagrams, to display the different periodicities and synchronization properties in the I-G parameter space, where G is the ratio between the Josephson energy and the magnetic anisotropy energy. We find that as I is reduced the onset of chaos occurs shortly before the transition to the superconducting state. This onset of chaos is signaled by a rapid rise in supercurrent (I S −→ I) which corresponds, dynamically, to increasing anharmonicity in phase rotations of the junction.
Physical Review E
Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is ... more Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step. I. INTRODUCTION Synchronization effects have been a subject of intensive theoretical and experimental studies in charge density wave transport [1-7], vortex matter [8-10], irradiated Josephson junctions [11-15], superconducting nanowires [16, 17] and driven colloidal systems [18]. One of the models used for investigation of synchronization phenomena (modelocking, i.e. Shapiro steps), starting from microscopic dynamics, is the dissipative Frenkel-Kontorova (FK) model under external periodic forces [19-22]. Recently, it has been shown that dc-driven FK model with a lateral periodic excitation to the substrate potential can be used to generate Shapiro steps as well [23]. The one-dimensional FK model represents a chain of coupled particles which are subjected to the substrate potential. For the standard FK model, the particles are harmonically coupled to their nearest neighbors and the substrate potential is sinusoidal. To capture certain phenomena in Josephson junction arrays [24-26], charge density wave systems [5-7] and tribology [27-29] different generalizations of the FK model are used. Due to competition between the length scales of interparticle and substrate potential, many nontrivial ground states of the model are possible. They can be classified into two categories-commensurate (for which the interparticle average distance, i.e. winding number, is rational) or incommensurate (for which the winding number is irrational) [19, 22, 30]. If an external dc driving force is applied, there exists a critical threshold value, i.e. critical depinning force F c , which separates two dynamical regimes-pinning and sliding regime. The latter regime is defined by collective motion of the particles along with non-zero average velocity, whereas in the pinning regime the particles are pinned to the static configurations with zero average velocity. When both external dc and ac forces are applied to the FK model, modelocking appears due to locking between the frequency of particle motion and frequency of external ac force, which results in the staircase-like response function [21, 31-36]. A new class of nonlinear periodic deformable potentials, which could be specified by suitable choice of parameters, was introduced in [37, 38]. By fixing parameters, different periodic potentials, such as assymetric deformable potential, which are relevant for studying Josephson junctions, charge density waves, heat conduction in low dimensional lattices, and crystals with dislocations, can be obtained. Unlike the case of the standard FK model, when the subharmonic steps either do not exist or they are too small, for the FK model with asymmetric deformable substrate potential large subharmonic steps can be observed in the response function plot [31, 32, 34]. Aside from the response function, the largest Lyapunov exponent (LE) also provides certain insight into the dynamics of dissipatively driven FK model. It has been shown that the largest LE can be viewed as a tool to characterize chaotic, periodic, and quasiperiodic motion (see [39, 40] and references therein). Furthermore, the LEs are also used for observation of dynamical phase transitions (pinning to sliding regime and unlocking transition) [14, 15, 21, 41, 42] and thermally induced phase transitions [43-46]. Specifically, the largest LE calculated for the standard overdamped FK model in the sliding regime takes on negative values on the steps, determining the trajectories periodic in time, while it reaches zero outside the steps, characterizing the unlocking transition to the quasiperiodic regime [21, 41]. On the other hand, in the underdamped regime chaos sometimes appears at the edges of the Shapiro steps and system exhibits structural chaotic behavior [15, 23]. Moreover, according to [47] calculating the largest LE presents the most
Springer proceedings in complexity, 2021
Chaos, Solitons & Fractals, 2022
Physical Review E, 2019
The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were ex... more The effects of inertial terms on the dynamics of the dc+ac driven Frenkel-Kontorova model were examined. As the mass of particles was varied, the response of the system to the driving forces and appearance of the Shapiro steps were analyzed in detail. Unlike in the overdamped case, the increase of mass led to the appearance of the whole series of subharmonic steps in the staircase of the average velocity as a function of average driving force in any commensurate structure. At certain values of parameters, the subharmonic steps became separated by chaotic windows while the whole structure retained scaling similar to the original staircase. The mass of the particles also determined their sensitivity to the forces governing their dynamics. Depending on their mass, they were found to exhibit three types of dynamics, from dynamical mode-locking with chaotic windows, through to a typical dc response, to essentially a free-particle response. Examination of this dynamics in both the upforce and downforce directions showed that the system may not only exhibit hysteresis, but also that large Shapiro steps may appear in the downforce direction, even in cases for which no dynamical mode-locking occurred in the upforce direction.
Journal of Research in Physics, 2015
Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate ... more Dynamical mode locking phenomena and the appearance of Shapiro steps are studied in commensurate structures with integer values of winding number in the dc- and ac-driven overdamped Frenkel-Kontorova model. While in the standard case with sinusoidal substrate potential, the system reduces to the single particles model in which only harmonic steps exist and analytical form for the step size can be revealed, in the case of deformable potential, the presence of many degrees of freedom strongly influences the Shapiro steps. Whole series of subharmonic steps appear, and the two types of response functions, the one for the commensurate structures with odd and the one for the commensurate structures with even winding number have been observed.
International Journal of Modern Physics B, 2007
The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova m... more The existence and stability of the Shapiro steps in the ac driven dissipative Frenkel-Kontorova model are studied. The particular attention has been focused on, the variations of the step width and critical depinning force with the ac amplitude. The amplitude dependence is strongly influenced by the frequency of ac force where at the higher frequencies, the oscillations have the Bessel like form.
Journal of Physics: Condensed Matter, 1993
ABSTRACT The possibility of the creation of the bound state of a domain wall and surrounding latt... more ABSTRACT The possibility of the creation of the bound state of a domain wall and surrounding lattice distortion was investigated in the framework of the one-dimensional Ising model with transverse field. It was found that the existence of such an entity is very sensitive to the mutual ratio of the basic physical parameters of the system. The authors obtain that, in the weak-coupling regime, such a 'dressed' excitation can arise in the so-called unadiabatic limit when the maximal photon energy greatly exceeds the nearest-neighbour exchange energy. In that case, the 'dressing' effect can significantly modify domain-wall properties, causing the increase of its effective mass and lowering of the ground-state energy, while the domain-wall velocity cannot exceed the speed of sound.
Frontiers of Physics, 2015
Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova m... more Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel-Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.
Solid State Phenomena, 1998
Within the framework of the sine-Gordon model, the phenomenon of magnetoacoustic resonance has be... more Within the framework of the sine-Gordon model, the phenomenon of magnetoacoustic resonance has been analyzed. It was found that MAR arises on account of the common motion of magnetic and lattice solitons
Physical Review E, 1999
The Fokker-Planck equation for multivibron solitons interacting with lattice vibrations in a mole... more The Fokker-Planck equation for multivibron solitons interacting with lattice vibrations in a molecular chain has been derived by means of the nonequilibrium statistical operator method. It was shown that a soliton undergoes diffusive motion characterized by two substantially different diffusion coefficients. The first one corresponds to the ordinary ͑Einsteinian or dissipative͒ diffusion and characterizes the soliton Brownian motion, while the second one corresponds to the anomalous diffusion connected with frictionless displacement of the soliton center of mass coordinate due to the interaction with phonons. Both processes are the consequence of the Cherenkov-like radiation of phonon quanta arising when soliton velocity approaches the phase speed of sound. ͓S1063-651X͑99͒01707-9͔