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We present an exactly solvable model of a hybrid quantum-classical system of a Nitrogen-Vacancy (NV) center spin (quantum spin) coupled to a nanocantilever (classical) and analyze the enforcement of the regular or chaotic classical dynamics onto the quantum spin dynamics. The main problem we focus in this paper is whether the classical dynamical chaos may induce chaotic effects in the quantum spin dynamics or not. We explore several characteristic criteria of the quantum chaos, such as quantum Poincar\'{e} recurrences, generation of coherence and energy level distribution and observe interesting chaotic effects in the spin dynamics. Dynamical chaos imposed in the cantilever dynamics through the kicking pulses induces the stochastic dynamics on the quantum subsystem. We consider a quantum system of two and three levels and show that in a two-level case, type of stochasticity is not conforming all the characteristic features of the quantum chaos and is distinct from it. We also explore the effect of quantum feedback on dynamics of the cantilever and the entire system., Comment: Accepted in Physica D: Nonlinear Phenomena (2022) 13 pages, 7 figures

The Mathieu–Schrodinger equation, which describes the behavior of a quantum pendulum, depending on the value of the parameter l (pendulum filament length), can have the symmetry of the Klein’s four-group or its invariant subgroups. The paper shows that the mean values of z-components of the angular momentum of nondegenerate quantum states (the symmetry region of the four-group) tend to zero and their root mean square fluctuations are non-zero. Consequently, in this region of parameter values, the fluctuations overlap the mean values of the angular momentum and they become indistinguishable. Therefore, it can be argued that if, with an increase in the parameter, the system goes into a non-degenerate state, then after the inversion of the parameter change and the transition to the region of degenerate states, the initial states will not be restored. This behavior of the average values of angular momenta is caused by the combined actions of two factors: discontinuous change in the system at the points of change of its symmetry and the presence of quantum fluctuations in nondegenerate states.

The magnonic spin Seebeck effect is a key element of spin caloritronic, a field that exploits thermal effects for spintronic applications. Early studies were focused on investigating the steady-state nonequilibrium magnonic spin Seebeck current, and the underlying physics of the magnonic spin Seebeck effect is now relatively well established. However, the initial steps of the formation of the spin Seebeck current are in the scope of recent interest. To address this dynamical aspect theoretically we propose here a new approach to the time-resolved spin Seebeck effect. Our method exploits the supersymmetric theory of stochastics and Ito - Stratonovich integration scheme. We found that in the early step the spin Seebeck current has both nonzero transversal and longitudinal components. As the magnetization dynamics approaches the steady-state, the transversal components decay through dephasing over the dipole-dipole reservoir. The time scale for this process is typically in the sub-nanoseconds pointing thus to the potential of an ultrafast control of the dynamical spin Seebeck during its buildup., to appear in Phys. Rev. B

This study is focused on the quantum dynamics of a nitrogen-vacancy (NV) center coupled to a nonlinear, periodically driven mechanical oscillator. For a continuous periodic driving that depends on the position of the oscillator, the mechanical motion is described by Mathieu elliptic functions. This solution is employed to study the dynamics of the quantum spin system including environmental effects and to evaluate the purity and the von Neumann entropy of the NV-spin. The unitary generation of coherence is addressed. We observe that the production of coherence through a unitary transformation depends on whether the system is prepared initially in mixed state. Production of coherence is efficient when the system initially is prepared in the region of the separatrix (i.e., the region where classical systems exhibit dynamical chaos). From the theory of dynamical chaos, we know that phase trajectories of the system passing through the homoclinic tangle have limited memory, and therefore the information about the initial conditions is lost. We proved that quantum chaos and diminishing of information about the mixed initial state favors the generation of quantum coherence through the unitary evolution. We introduced quantum distance from the homoclinic tangle and proved that for the initial states permitting efficient generation of coherence, this distance is minimal., 22 pages, 12 figures

At low temperatures, the heat capacity of a superparamagnetic “ideal gas” determined by magnetic degrees of freedom can greatly exceed the lattice heat capacity. It is shown that in the presence of an external magnetic field, the temperature dependence of the magnetic part of the heat capacity has two maxima. The relations between the temperature at which these maxima are achieved, the magnetic moment of the nanoparticles and the magnetic anisotropy constant have been obtained. Measuring the heat capacity maxima temperatures by low-temperature calorimetry methods and using the obtained relations, we can obtain the numerical values both of the magnetic moment of nanoparticles and the magnetic anisotropy constants.

The effect of electron-electron interactions on the energy spectrum of surface electrons in a three-dimensional topological insulator is studied theoretically. The interaction includes both charge- and spin-dependent correlations. Using the Green's function method, we calculate the electron self-energy and determine the renormalized spin-orbit coupling strength. We find that the energy spectrum renormalized by spin-dependent electronic correlation turns nonlinear with respect to the wave vector $k$ measured from the perfect Dirac cone (in the absence of electron-electron interactions). We also discuss charge screening contributions from surface and bulk electrons.

We study the spin transport theoretically in heterostructures consisting of a ferromagnetic metallic thin film sandwiched between heavy-metal and oxide layers. The spin current in the heavy-metal layer is generated via the spin Hall effect, whereas the oxide layer induces at the interface with the ferromagnetic layer a spin-orbital coupling of the Rashba type. Impact of the spin-Hall effect and Rashba spin-orbit coupling on the spin-Seebeck current is explored with a particular emphasis on nonlinear effects. Technically, we employ the Fokker-Planck approach and contrast the analytical expressions with full numerical micromagnetic simulations. We show that, when an external magnetic field ${H}_{0}$ is aligned parallel (antiparallel) to the Rashba field, the spin-orbit coupling enhances (reduces) the spin pumping current. In turn, the spin-Hall effect and the Dzyaloshinskii-Moriya interaction are shown to increase the spin pumping current.

A non-uniform temperature profile may generate a pure spin current in magnetic films, as observed for instance in the spin Seebeck effect. In addition, thermally induced elastic deformations may set in that could affect the spin current. A self-consistent theory of the magnonic spin Seebeck effect including thermally activated magneto-elastic effects is presented and analytical expressions for the thermally activated deformation tensor and dispersion relations for coupled magneto-elastic modes are obtained. We derived analytical results for bulk (3D) systems and thin magnetic (2D) films. We observed that the displacement vector and the deformation tensor in bulk systems decay asymptotically as $u\sim1/R^{2}$ and $\varepsilon\sim1/R^{3}$, respectively, while the decays in thin magnetic films proceed slower following $u\sim1/R$ and $\varepsilon\sim1/R^{2}$. The dispersion relations evidence a strong anisotropy in the magnetic excitations. We observed that a thermoelastic steady state deformation may lead to both an enchantment or a reduction of the gap in the magnonic spectrum. The reduction of the gap increases the number of magnons contributing to the spin Seebeck effect and offers new possibilities for the thermoelastic control of the Spin Seebeck effect., to appear in Phys. Rev. B

The influence of an asymmetric in-plane magnetic anisotropy K x ≠ K y on the thermally activated spin current is studied theoretically for two different systems: (i) the F | N system consisting of a ferromagnetic insulator ( F ) in a direct contact with a nonmagnetic metal ( N ) and (ii) the sandwich structure N | F | N consisting of a ferromagnetic insulating part sandwiched between two nonmagnetic metals. It is shown that when the difference between the temperatures of the two nonmagnetic metals in a N | F | N structure is not large, the spin pumping currents from the magnetic part to the nonmagnetic ones are equal in amplitude and have opposite directions, so only the spin torque current contributes to the total spin current. The spin current flows then from the nonmagnetic metal with the higher temperature to the nonmagnetic metal having a lower temperature. Its amplitude varies linearly with the difference in temperatures. In addition, we have found that if the magnetic anisotropy is in the layer plane, then the spin current increases with the magnon temperature, while in the case of an out-of-plane magnetic anisotropy the spin current decreases when the magnon temperature enhances. Enlarging the difference between the temperatures of the nonmagnetic metals, the linear response becomes important, as confirmed by analytical expressions inferred from the Fokker–Planck approach and by the results obtained upon a full numerical integration of the stochastic Landau–Lifshitz–Gilbert equation.

This study demonstrates how the spin quantum dynamics of a single Fe atom adsorbed on Cu(001) can be controlled and manipulated by the vibrations of a nearby copper tip attached to a nano cantilever by virtue of the dynamic magnetic anisotropy. The magnetic properties of the composite system are obtained from \emph{ab initio} calculations in completely relaxed geometries and turned out to be dependent considerably on the tip-iron distance that changes as the vibrations set in. The level populations, the spin dynamics interrelation with the driving frequency, as well as quantum information related quantities are exposed and analyzed., accepted in New Journal of Physics

In this paper we study the time evolution of the entanglement between two remote NV Centers (nitrogen vacancy in diamond) connected by a dual-mode nanomechanical resonator with magnetic tips on both sides. Calculating the negativity as a measure for the entanglement, we find that the entanglement between two spins oscillates with time and can be manipulated by varying the parameters of the system. We observed the phe- nomenon of a sudden death and the periodic revivals of entanglement in time. For the study of quantum deco- herence, we implement a Lindblad master equation. In spite of its complexity, the model is analytically solvable under fairly reasonable assumptions, and shows that the decoherence influences the entanglement, the sudden death, and the revivals in time., to appear in J.Phys. B

A quantum thermodynamic cycle with a chiral multiferroic working substance such as $\textrm{LiCu}_{2}\textrm{O}_{2}$ is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite time quantum thermodynamic cycle which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e. the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between of the spin and the electric polarization, the cycle performs an electro-magnetic work. We determine this work's mean square fluctuations, the irreversible work, and the output power of the cycle. We observe that the work mean square fluctuations are increased with the duration of the adiabatic strokes while the irreversible work and the output power of the cycle show a non-monotonic behavior. In particular the irreversible work vanishes at the end of the quantum adiabatic strokes. This fact confirms that the cycle is reversible. Our theoretical findings evidence the existence of a system inherent maximal output power. By implementing a Lindblad master equation we quantify the role of thermal relaxations on the cycle efficiency. We also discuss the role of entanglement encoded in the non-collinear spin order as a resource to affect the quantum thermodynamic cycle., Comment: 13pages, 15 figures, submitted in Phys. Rev. E

The time dependence of the entanglement for two Tavis–Cummings atoms with dynamical Stark shift is studied. It is shown that the influence of the dynamical Stark shift is not equivalent for different Bell states. Namely for the states ϕ = 1 2 ( | 00 〉 ± | 11 〉 ) sudden death of entanglement happens, while for the states ψ = 1 2 ( | 01 〉 ± | 10 〉 ) we still have a rest of entanglement. A direct relation between the sudden death of entanglement and the values of the dynamical Stark shift is shown. The fidelity of the system is evaluated.

We consider the controlled switching of individual spins in a nonlinear, interacting spin chain by means of external magnetic fields. We show analytically and by full numerical simulations that stochastic switching is achievable when the driving fields are such that the underlying semi-classical dynamics is chaotic. On the basis of random matrix theory and the geometry of quantum evolution we confirm the quantum case to follow qualitatively the semi-classical behavior.

One of the main models used to study problems of ferromagnetic resonance is the Landau–Lifshitz phenomenological model. According to this model, the dynamics of the magnetization in a ferromagnet is described by a nonlinear Landau–Lifshitz equation. Because of the nonlinearity of this equation the physical properties described by it are extremely diverse. Depending on the physical situation, a system is characterized by soliton or chaotic solutions. Usually it is assumed that a necessary condition for obtaining a chaotic solution is that the system be acted upon by a random field due to fluctuations of the local magnetization. It is shown here that chaotic dynamics can also be obtained in the case of a regular external force. The conditions for the appearance of Hamiltonian chaos are determined, and numerical estimates are made for concrete substances. A kinetic equation describing the dynamics of the magnetization under conditions of stochasticity is obtained. It is shown that the solution of the kinetic...

Spin systems are one of the most promising candidates for quantum computation. At the same time, control of a system's quantum state during time evolution is one of the main problems. It is usually considered that in magnetic resonance the so-called resonance condition is sufficient to control the spin system. However, because of the nonlinearity of the system, obstructions to the control of the system's quantum state may emerge. In particular, the quantum dynamics of coupled two-level atoms in the optical cavity are studied in this work. The problem under consideration is a generalization of the paradigmatic model for Cavity Quantum Electrodynamics of the Jaynes-Cummings model in the case of interacting spins. In this work, it is shown that the dynamics are chaotic when taking into account the center-of-mass motion of the system and the recoil effect. Furthermore, even in the case of zero detuning, chaotic dynamics emerge in the system. It is also shown in this work that, because of the chaotic dynamics the system executes an irreversible transition from a pure quantum-mechanical state to a mixed one. Irreversibility, in turn, is an obstacle for controlling the state of the quantum-mechanical system.

The possibility of chaos formation is studied in terms of a generalized Jaynes-Cummings model which is a key model in the quantum electrodynamics of resonators. In particular, the dynamics of a three-level optical atom which is under the action of the resonator field is considered. The specific feature of the considered problem consists in that not all transitions between the atom levels are permitted. This asymmetry of the system accounts for the complexity of the problem and makes it different from the three-level systems studied previously. We consider the most general case, where the interaction of the system with the resonator depends on the system coordinate inside the resonator. It is shown that, contrary to the commonly accepted opinion, the absence of resonance detuning does not guarantee the system state controllability. In the course of evolution the system performs an irreversible transition from the purely quantum-mechanical state to the mixed state. It is shown that the asymmetry of the system levels accounts for the fact that the upper excited level turns out to be the most populated one.

The nonlinear system of Bloch equations describing the dynamics of the magnetization is investigated in the cases of weak and strong nonlinearity. Nonlinearity appears as a consequence of the influence of the oscillator circuit. It is shown that in the case of weak nonlinearity one can use perturbation theory to obtain an analytical solution that agrees well with the results of numerical calculations. In the case of strong nonlinearity the motion of the magnetization can have a stochastic character, similar to a strange attractor. The fractal dimension of the stochastic attractor is estimated.

Following the theoretical approach by Xiao et al [Phys. Rev. B 81, 214418 (2010)] to the spin Seebeck effect, we calculate the mean value of the total spin current flowing through a normalmetal/ ferromagnet interface. The spin current emitted from the ferromagnet to the normal metal is evaluated in the framework of the Fokker-Planck approach for the stochastic Landau-Lifshitz-Gilbert equation. We show that the total spin current depends not only on the temperature difference between the electron and the magnon baths, but also on the external magnetic field and magnetic anisotropy. Apart from this, the spin current is shown to saturate with increasing magnon temperature, and the saturation temperature increases with increasing magnetic field and/or magnetic anisotropy., 7 pages, 3 figures

We study the dynamics of an electron confined in a one-dimensional double-well potential in the presence of driving external magnetic fields. The orbital motion of the electron is coupled to the spin dynamics by spin–orbit interaction of the Dresselhaus type. We derive an effective time-dependent model Hamiltonian for the orbital motion of the electron and obtain a condition for synchronization of the orbital and the spin dynamics. We find an analytical expression for the Arnold ‘tongue’ and propose an experimental scheme for realizing the proposed synchronization.

We study a chain of non-linear, interacting spins driven by a static and a time-dependent magnetic field. The aim is to identify the conditions for the locally and temporally controlled spin switching. Analytical and full numerical calculations show the possibility of stochastic control if the underlying semi-classical dynamics is chaotic. This is achievable by tuning the external field parameters according to the method described in this paper. We show analytically for a finite spin chain that Arnold diffusion is the underlying mechanism for the present stochastic control. Quantum mechanically we consider the regime where the classical dynamics is regular or chaotic. For the latter we utilize the random matrix theory. The efficiency and the stability of the non-equilibrium quantum spin-states are quantified by the time-dependence of the Bargmann angle related to the geometric phases of the states., Journal-ref: to appear in J.Phys.C

In this paper we study the dynamics in the general case for a Tavis Cummings atom in a non-uniform cavity. In addition to the dynamical Stark shift, the center-of-mass motion of the atom and the recoil effect are considered in both - the weak and the strong cavity atom coupling regimes. It is shown that the spatial motion of the atom inside the cavity in the resonant case leads to a transition between topologically different solutions. This effect is manifested by a singularity in the inter-level transition spectrum. In the non-resonant case, the spatial motion of the atom leads to a switching of the spin orientation. In both effects, the key factor is the relation between the values of the Stark shift and the cavity field coupling constant. We also investigate the entanglement of an atom in the cavity with the radiation field. It is shown that the entanglement between the atom and the field, usually quantified in terms of purity, decreases with increasing the Stark shift., Comment: to appear in Phys. Rev. A

We study a chain of coupled nanomagnets in a classical approximation. We show that the infinitely long chain of coupled nanomagnets can be equivalently mapped onto an effective one-dimensional Hamiltonian with a fictitious time-dependent perturbation. We establish a connection between the dynamical characteristics of the classical system and spin correlation time. The decay rate for the spin correlation functions turns out to depend logarithmically on the maximal Lyapunov exponent. Furthermore, we discuss the non-trivial role of the exchange anisotropy within the chain., to appear in Phys.Rev.B

The influence of the dynamical Stark shift on the thermal entanglement and the efficiency of the quantum Otto cycle is studied for the su(1,1) Tavis-Cummings system. It is shown that the degree of the thermal entanglement becomes larger as the dynamical Stark shift increases. In contrast, the efficiency of the Otto cycle is degraded with an increase of the values of dynamical Stark shift. Expressions for the efficiency coefficient are derived. Using those expressions we identify the maximal efficiency of the quantum Otto cycle from the experimentally measured values of the dynamical Stark shift, Comment: to appear in J.Phys. A

We study the excitation dynamics of a single molecular nanomagnet by static and pulsed magnetic fields. Based on a stability analysis of the classical magnetization dynamics we identify analytically the fields parameters for which the energy is stochastically pumped into the system in which case the magnetization undergoes diffusively and irreversibly a large angle deflection. An approximate analytical expression for the diffusion constant in terms of the fields parameters is given and assessed by full numerical calculations., 5 pages, 4 figures, to appear in Phys. Rev. B

Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain values of the parameters from this domain, form of the classical power spectrum is in a good agreement with the quantum band profile. Local density of states is calculated. The range in which application of perturbation theory is correct has been defined., Comment: 9 figures. to be published in Mod.Phys.Lett.B

We study the role of thermal fluctuations on the spin dynamics of a thin permalloy film with a focus on the behavior of spin torque and find that the thermally assisted spin torque results in new aspects of the magnetization dynamics. In particular, we uncover the formation of a finite, spin torque-induced, in-plane magnetization component. The orientation of the in-plane magnetization vector depends on the temperature and the spin-torque coupling. We investigate and illustrate that the variation of the temperature leads to a thermally-induced rotation of the in-plane magnetization., Comment: 9 pages, 12 figures

The process of rotational isomerism of linear triatomic molecules is described by the potential with two different-depth minima and one barrier between them. The corresponding quantum-mechanical equation is represented in the form that is a special case of the Hill equation. It is shown that the Hill-Schrodinger equation has a Klein's quadratic group symmetry which, in its turn, contains three invariant subgroups. The presence of these subgroups makes it possible to create a picture of energy spectrum which depends on a parameter and has many merging and branch points. The parameter-dependent energy spectrum of the Hill-Schrodinger equation, like Mathieu-characteristics, contains branch points from the left and from the right of the demarcation line. However, compared to the Mathieu-characteristics, in the Hill-Schrodinger equation spectrum the “right” points are moved away even further for some distance that is the bigger, the bigger is the less deep well. The asymptotic wave functions of the Hill-Schrodinger equation for the energy values near the potential minimum contain two isolated sharp peaks indicating a possibility of the presence of two stable isomers. At high energy values near the potential maximum, the height of two peaks decreases, and between them there appear chaotic oscillations. This form of the wave functions corresponds to the process of isomerization.