Tunnelling in periodically driven systems

Tunnelling in periodically driven bistable symmetric potential wells is investigated in an analytical approximation in a domain where the driving frequency is large compared to the tunnelling frequency and only the four lowest lying levels contribute significantly. The influence of finite level widths is taken into account, and a smooth variation of the amplitude of the driving field is allowed for.     

Noise-induced generation of saw-tooth type transitions between climate attractors and stochastic excitability of paleoclimate

Motivated by important paleoclimate applications we study a three dimensional model ofthe Quaternary climatic variations in the presence of stochastic forcing. It is shown thatthe deterministic system exhibits a limit cycle and two stable system equilibria. Wedemonstrate that the closer paleoclimate system to its bifurcation points (lying either inits monostable or bistable zone) the smaller noise generates small or large amplitudestochastic oscillations, respectively. In the bistable zone with two stable equilibria,noise induces a complex multimodal stochastic regime with intermittency of small and largeamplitude stochastic fluctuations. In the monostable zone, the small amplitude stochasticoscillations localized in the vicinity of unstable equilibrium appear along with the largeamplitude oscillations near the stable limit cycle. For the analysis of thesenoise-induced effects, we develop the stochastic sensitivity technique and use theMahalanobis metric in the three-dimensional case. To approximate the distribution ofrandom trajectories in Poincare sections, we use a method of confidence ellipses. Aspatial configuration of these ellipses is defined by the stochastic sensitivity and noiseintensity. The glaciation/deglaciation transitions going between two polar Earth’s stateswith the warm and cold climate become easier and quicker with increasing the noiseintensity. Our stochastic analysis demonstrates a near 100 ky saw-tooth type climate selffluctuations known from paleoclimate records. In addition, the enhancement of noiseintensity blurs the sharp climate cycles and reduces the glaciation-deglaciation periodsof the Earth’s paleoclimate.     

Activated escape of periodically driven systems

We discuss activated escape from a metastable state of a system driven by a time-periodic force. We show that the escape probabilities can be changed very strongly even by a comparatively weak force. In a broad parameter range, the activation energy of escape depends linearly on the force amplitude. This dependence is described by the logarithmic susceptibility, which is analyzed theoretically and through analog and digital simulations. A closed-form explicit expression for the escape rate of an overdamped Brownian particle is presented and shown to be in quantitative agreement with the simulations. We also describe experiments on a Brownian particle optically trapped in a double-well potential. A suitable periodic modulation of the optical intensity breaks the spatio-temporal symmetry of an otherwise spatially symmetric system. This has allowed us to localize a particle in one of the symmetric wells. (c) 2001 American Institute of Physics.     

Energy transduction in periodically driven non-hermitian systems

We show a new mechanism to extract energy from nonequilibrium fluctuations typical of periodically driven non-Hermitian systems. The transduction of energy between the driving force and the system is revealed by an anomalous behavior of the susceptibility, leading to a diminution of the dissipated power and consequently to an improvement of the transport properties. The general framework is illustrated by the analysis of some relevant cases.     

Long-lasting exponential spreading in periodically driven quantum systems

Using a dynamical model relevant to cold-atom experiments, we show that long-lasting exponential spreading of wave packets in momentum space is possible. Numerical results are explained via a pseudoclassical map, both qualitatively and quantitatively. Possible applications of our findings are also briefly discussed.     

Strong-coupling theory of periodically driven two-level systems

We present a simple but highly efficient iterating approach for strong-coupling periodically driven two-level systems. The obtained explicit approximating analytical solution reproduces accurately the exact numerical solution in the strong-coupling regime for a wide frequency range including resonance, far-off resonance, harmonic, and subharmonic cases. Our theory is suitable for single- and multi-period periodic driving and for the periodic driving with a few-cycle pulse as well, and it gives a general formula for calculating the strong-field ac Stark effect in such diverse situations.     

Many-body energy localization transition in periodically driven systems

According to the second law of thermodynamics the total entropy of a system is increased during almost any dynamical process. The positivity of the specific heat implies that the entropy increase is associated with heating. This is generally true both at the single particle level, like in the Fermi acceleration mechanism of charged particles reflected by magnetic mirrors, and for complex systems in everyday devices. Notable exceptions are known in noninteracting systems of particles moving in periodic potentials. Here the phenomenon of dynamical localization can prevent heating beyond certain threshold. The dynamical localization is known to occur both at classical (Fermi–Ulam model) and at quantum levels (kicked rotor). However, it was believed that driven ergodic systems will always heat without bound. Here, on the contrary, we report strong evidence of dynamical localization transition in both classical and quantum periodically driven ergodic systems in the thermodynamic limit. This phenomenon is reminiscent of many-body localization in energy space.     

Scaling and decay in periodically driven scattering systems

We investigate irregular scattering in a periodically driven Hamiltonian system of one degree of freedom. The potential is asymptotically attracting, so there exist parabolically escaping scattering orbits, i.e. orbits with asymptotic energy E(out)=0. The scattering functions (i.e. the asymptotic out-variables as functions of an asymptotic in-variable) show a characteristic algebraic scaling in the vicinity of these orbits. This behavior is explained by asymptotic properties of the interaction. As a consequence, the number N(Deltat) of temporarily bound particles decays algebraically with the delay time Deltat, although no KAM scenario can be found in phase space. On the other hand, we find the number N(n) of temporarily bound particles to decay exponentially with the number n of zeros of x(t).     

Theory of many-body localization in periodically driven systems

We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.     

Quantum mechanics of rapidly and periodically driven systems

This review deals with the dynamics of quantum systems that are subject to high frequency external perturbations. Though the problem may look hopelessly time-dependent, and poised on the extreme opposite side of adiabaticity, there exists a ‘Kapitza Window’ over which the dynamics can be treated in terms of effective time-independent Hamiltonians. The consequent results are important in the context of atomic traps as well as quantum optic properties of atoms in intense and high-frequency electromagnetic fields.      

Hopping and phase shifts in noisy periodically driven bistable systems

We consider a periodically driven bistable system in the presence of fluctuations. In a number of recent papers it has been shown that the amplitude of the response of the noisy system to periodic modulations exhibits stochastic resonance, i.e. a resonance-like behavior as a function of the noise intensity. In this paper, we consider the phase shift between the response and the periodic driving. For weak periodic driving, the phase shift also shows a resonance like behaviour as a function of the noise strength, but this effect is shown to be of different origin than the one responsible for stochastic resonance. Furthermore, the phase shift is demonstrated to exhibit a resonance-like behavior as a function of the driving frequency.     

Survival probability and saturation energy in periodically driven quantum chaotic systems

We study characteristics of the steady state of a random-matrix model with periodical pumping, where the energy increase saturates by quantum localization. We study the dynamics by making use of the survival probability. We found that Floquet eigenstates are separated into the localized and extended states, and the former governs the dynamics.     

Hopping between localized Floquet states in periodically driven quantum dots

The dynamic localization in energy space, suppression of the absorption of energy from an external microwave field due to quantum interference, was analyzed recently for a closed quantum dot in the absence of electron-electron interactions. Here a weak interaction is shown to lead to a finite absorption and heating, which may be viewed as hopping between localized Floquet states. The heating rate grows together with the electronic temperature, eventually destroying the localization.     

Domain walls and ising-BLOCH transitions in parametrically driven systems

Parametrically driven systems sustaining sech solitons are shown to support a new kind of localized state. These structures are walls connecting two regions oscillating in antiphase that form in the parameter domain where the sech soliton is unstable. Depending on the parameter set the oppositely phased domains can be either spatially uniform or patterned. Both chiral (Bloch) and nonchiral (Ising) walls are found, which bifurcate one into the other via an Ising-Bloch transition. While Ising walls are at rest Bloch walls move and may display secondary bifurcations leading to chaotic wall motion.     

Chaotic atomic tunneling between two periodically driven Bose-Einstein condensates

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.     

Random organization in periodically driven gliding dislocations

We numerically examine dynamical irreversible to reversible transitions and random organization for periodically driven gliding dislocation assemblies using the stroboscopic protocol developed to identify random organization in periodically driven dilute colloidal suspensions. We find that the gliding dislocations exhibit features associated with random organization and evolve into a dynamically reversible state after a transient time extending over a number of cycles. At a critical shearing amplitude, the transient time diverges. When the dislocations enter the reversible state they organize into patterns with fragmented domain wall type features.     

Boundary-driven phase transitions in open driven systems with an umbilic point

Different phases in open driven systems are governed by either shocks or rarefaction waves. A presence of an isolated umbilic point in bidirectional systems of interacting particles stabilizes an unusual large scale excitation, an umbilic shock (U-shock). We show that in open systems the U-shock governs a large portion of phase space, and drives a new discontinuous transition between the two rarefaction-controlled phases. This is in contrast to strictly hyperbolic case where such a transition is always continuous. Also, we describe another robust phase which takes place at the phase governed by the U-shock, if the umbilic point is not isolated.