Chaotic oscillations in nonlinear system of interacting oscillators with the interaction of the fourth order

Dynamics of two anharmonic oscillators with interaction of the fourth order has been investigated. The conditions at realization of which system is integrable are established. The exact analytical solution of the nonlinear equations in the case of adiabatic isolation of a system of oscillators has been obtainedComment: 7 pages, 5 figure

Non-Reversible Evolution of Quantum Chaotic System. Kinetic Description

Time dependent dynamics of the chaotic quantum-mechanical system has been studied. Irreversibility of the dynamics is shown. It is shown, that being in the initial moment in pure quantum-mechanical state, system makes irreversible transition into mixed state. Original mechanism of mixed state formation is offered. Quantum kinetic equation is obtained. Growth of the entropy during the evolution process is estimated

Chaotic dynamics of two 1/2 spin-qubit system in the optical cavity

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 actual problems. It is usually considered that to hold well-known resonance condition in magnetic resonance is sufficient to control spin system. But because of nonlinearity of the system, obstructions of control of system's quantum state may emerge. In particular quantum dynamics of two 1/2 spin-qubit system in the optical cavity is studied in this work. The problem under study is a generalization of paradigmatic model for Cavity Quantum Electrodynamics of James-Cummings model in case of interacting spins. In this work it is shown that dynamics is chaotic when taking into account center-of-mass motion of the qubit and recoil effect. And besides even in case of zero detuning chaotic dynamics emerges in the system. It is also shown in this work that because of the chaotic dynamics the system execute irreversible transition from pure quantum-mechanical state to mixed one. Irreversibility in its turn is an obstacle for controlling state of quantum-mechanical system

Quantum chaos at the Kinetic Stage of Evolution

It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighbourhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states, the system gets self-chaotized and passes from the pure state to the mixed one. Chaotization involves the states, the branch points of whose levels participate in a slow "drift" of the system along the Mathieu characteristics this "drift" being caused by a slowly changing variable field. Recurrent relations are obtained for populations of levels participating in the irreversible evolution process. It is shown that the entropy of the system first grows and, after reaching the equilibrium state, acquires a constant value.Comment: 10 figure

Paul Trap and the Problem of Quantum Stability

This work is devoted to the investigation of possibility of controlling of ions motion inside Paul trap. It has been shown that by proper selection of the parameters of controlling electric fields, stable localization of ions inside Paul trap is possible. Quantum consideration of this problem is reduced to the investigation of the Mathieu-Schrodinger equation. It has been shown that quantum consideration is appreciably different from classical one that leads to stronger limitations of the values of the parameters of stable motion. Connection between the problem under study and the possibility of experimental observation of quantum chaos has been shown

Spectral characteristics of time resolved magnonic spin Seebeck effect

Spin Seebeck effect (SSE) holds promise for new spintronic devices with low-energy consumption. The underlying physics, essential for a further progress, is yet to be fully clarified. This study of the time resolved longitudinal SSE in the magnetic insulator yttrium iron garnet (YIG) concludes that a substantial contribution to the spin current stems from small wave-vector subthermal exchange magnons. Our finding is in line with the recent experiment by S. R. Boona and J. P. Heremans, Phys. Rev. B 90, 064421 (2014). Technically, the spin-current dynamics is treated based on the Landau-Lifshitz-Gilbert (LLG) equation also including magnons back-action on thermal bath, while the formation of the time dependent thermal gradient is described self-consistently via the heat equation coupled to the magnetization dynamicsComment: 5 pages, 5 figure

Chaos, Fractal and Quantum Poincare Recurrences in Diamagnetic Kepler Problem

The statistics of quantum Poincare recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in a good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincare recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to the mixed one

Zitterbewegung and symmetry switching in Klein's four-group

Zitterbewegung is the exotic phenomenon associated either with the relativistic electron-positron rapid oscillation or to the electron-hole transitions in the narrow gap semiconductors. In the present work, we enlarge concept of Zitterbewegung and show that the trembling motion may occur due to the dramatic changes in the symmetry of the system. In particular, we exploit a paradigmatic model of quantum chaos, quantum mathematical pendulum (universal Hamiltonian). The symmetry group of this system is the Klein's four-group that possess three invariant subgroups. The energy spectrum of the system parametrically depends on the height of the potential barrier, and contains degenerate and non-degenerate areas, corresponding to the different symmetry subgroups. Change in the height of the potential barrier switches the symmetry subgroup and leads to the trembling motion. We analyzed mean square fluctuations of the velocity operator and observed that trembling enhances for the highly excited states. We observed the link between the phenomena of trembling motion and uncertainty relations of noncommutative operators of the system.Comment: accepted in Journal of Physics A: Mathematical and Theoretica

Quantum heat engines with multiferroic working substance

The work provides an overview on some recent advances in the area of quantum thermodynamics and quantum heat engines. A particular emphasis is put on the possibility of constructing finite time quantum cycles and adiabatic shortcuts. We discuss in details the particular quantum heat engines operating with a multiferroic working substance.Comment: Lecture Notes of the 12th International School on Theoretical Physics Symmetry, Spin Dynamics and the Properties of Nanostructure

Chaotic dynamics and spin correlation functions in a chain of nanomagnets

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.Comment: to appear in Phys.Rev.