Non-stationary resonance dynamics of weakly coupled pendula

In this paper we fill the gap in understanding the non-stationary resonance dynamics of the weakly coupled pendula model, having significant applications in numerous fields of physics such as super- conducting Josephson junctions, Bose-Einstein condensates, DNA, etc.. While common knowledge of the problem is based on two alternative limiting asymptotics, namely the quasi-linear approach and the approximation of independent pendula, we present a unified description in the framework of new concept of Limiting Phase Trajectories (LPT), without any restriction on the amplitudes of oscillation. As a result the conditions of intense energy exchange between the pendula and transition to energy localization are revealed in all possible diapason of initial conditions. By doing so, the roots and the domain of chaotic behavior are clarified as they are associated with this transition while simultaneously approaching the pendulum separatrix. The analytical findings are corrobo- rated by numerical simulations. By considering the simplest case of two weakly coupled pendula, we pave the ground for new opening possibilities of significant extensions in both fundamental and applied directions.Comment: 7 pages, 7 figure

Non-stationary resonance dynamics of the harmonically forced pendulum

The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only existence of slow time scale, permits one to avoid any restriction on the oscillation amplitudes. The main results relating to the dynamical bifurcation thresholds are represented in a closed form. The small parameter defining the separation of the time scales is naturally identified in the ana- lytical procedure. Considering the pendulum frequency as the control parameter we reveal two qualitative tran- sitions. One of them corresponding to stationary instability with formation of two additional stationary states, the other, associated with the most intense energy drawing from the source, at which the amplitude of pendulum oscillations abruptly grows. Analytical predictions of both bifurcations are verified by numerical integration of original equation. It is also shown that occurrence of chaotic domains may be strongly connected with the second transition

Nonequilibrium properties of an atomic quantum dot coupled to a Bose-Einstein condensate

We study nonequilibrium properties of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensate (BEC) within Keldysh-Green's function formalism when the AQD level is varied harmonically in time. Nonequilibrium features in the AQD energy absorption spectrum are the side peaks that develop as an effect of photon absorption and emission. We show that atoms can be efficiently transferred from the BEC into the AQD for the parameter regime of current experiments with cold atoms.Comment: 8 pages, 2 figures, to appear in the special issue "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases" of The European Physical Journal - Special Topic

Stationary and non-stationary resonance dynamics of the finite chain of weakly coupled pendula

We discuss new phenomena of energy localization and transition to chaos in the finite system of coupled pendula (which is a particular case of the Frenkel-Kontorova model), without any restrictions on the amplitudes of oscillations. The direct significant applications of this fundamental model comprise numerous physical systems. In the infinite and continuum limit the considered model is reduced to integrable sine-Gordon equation or certain non-integrable generalizations of it. In this limit, the chaotization is absent, and the energy localization is indicated by the existence of soliton-like solutions (kinks and breathers). As for more realistic finite models, analytical approaches are lacking, with the exception of cases limited to two and three pendula. We propose a new approach to the problem based on the recently developed Limiting Phase Trajectory (LPT) concept in combination with a semi-inverse method. The analytical predictions of the con-ditions providing transition to energy localization are confirmed by numerical simulation. It is shown that strongly nonlinear effects in finite chains tend to disap- pear in the infinite limit