The rapid points of a complex oscillation

By considering a counting-type argument on Brownian sample paths, we prove a result similar to that of Orey and Taylor on the exact Hausdorff dimension of the rapid points of Brownian motion. Because of the nature of the proof we can then apply the concepts to so-called complex oscillations (or 'algorithmically random Brownian motion'), showing that their rapid points have the same dimension.Comment: 11 page

Dynamics of Coupled Adaptive Elements : Bursting and Intermittent Oscillations Generated by Frustration in Networks

Adaptation to environmental change is a common property of biological systems. Cells initially respond to external changes in the environment, but after some time, they regain their original state. By considering an element consisting of two variables that show such adaptation dynamics, we studied a coupled dynamical system containing such elements to examine the diverse dynamics in the system and classified the behaviors on the basis of the network structure that determined the interaction among elements. For a system with two elements, two types of behaviors, perfect adaptation and simple oscillation, were observed. For a system with three elements, in addition to these two types, novel types of dynamics, namely, rapid burst-type oscillation and a slow cycle, were discovered; depending on the initial conditions, these novel types of dynamics coexisted. These behaviors are a result of the characteristic dynamics of each element, i.e., fast response and slow adaptation processes. The behaviors depend on the network structure (in specific, a combination of positive or negative feedback among elements). Cooperativity among elements due to a positive feedback loop leads to simple oscillation, whereas frustration involving alternating positive and negative interactions among elements leads to the coexistence of rapid bursting oscillation and a slow cycle. These behaviors are classified on the basis of the frustration indices defined by the network structure. The period of the slow cycle is much longer than the original adaptation time scale, while the burst-type oscillation is a continued response that does not involve any adaptation. We briefly discuss the universal applicability of our results to a network of a larger number of elements and their possible relevance to biological systems.Comment: 12 pages, 13 figure

Approaching the adiabatic timescale with machine-learning

The control and manipulation of quantum systems without excitation is challenging, due to the complexities in fully modeling such systems accurately and the difficulties in controlling these inherently fragile systems experimentally. For example, while protocols to decompress Bose-Einstein condensates (BEC) faster than the adiabatic timescale (without excitation or loss) have been well developed theoretically, experimental implementations of these protocols have yet to reach speeds faster than the adiabatic timescale. In this work, we experimentally demonstrate an alternative approach based on a machine learning algorithm which makes progress towards this goal. The algorithm is given control of the coupled decompression and transport of a metastable helium condensate, with its performance determined after each experimental iteration by measuring the excitations of the resultant BEC. After each iteration the algorithm adjusts its internal model of the system to create an improved control output for the next iteration. Given sufficient control over the decompression, the algorithm converges to a novel solution that sets the current speed record in relation to the adiabatic timescale, beating out other experimental realizations based on theoretical approaches. This method presents a feasible approach for implementing fast state preparations or transformations in other quantum systems, without requiring a solution to a theoretical model of the system. Implications for fundamental physics and cooling are discussed.Comment: 7 pages main text, 2 pages supporting informatio

Nonlinear wave propagation and reconnection at magnetic X-points in the Hall MHD regime

The highly dynamical, complex nature of the solar atmosphere naturally implies the presence of waves in a topologically varied magnetic environment. Here, the interaction of waves with topological features such as null points is inevitable and potentially important for energetics. The low resistivity of the solar coronal plasma implies that non-MHD effects should be considered in studies of magnetic energy release in this environment. This paper investigates the role of the Hall term in the propagation and dissipation of waves, their interaction with 2D magnetic X-points and the nature of the resulting reconnection. A Lagrangian remap shock-capturing code (Lare2d) is used to study the evolution of an initial fast magnetoacoustic wave annulus for a range of values of the ion skin depth in resistive Hall MHD. A magnetic null-point finding algorithm is also used to locate and track the evolution of the multiple null-points that are formed in the system. Depending on the ratio of ion skin depth to system size, our model demonstrates that Hall effects can play a key role in the wave-null interaction. In particular, the initial fast-wave pulse now consists of whistler and ion-cyclotron components; the dispersive nature of the whistler wave leads to (i) earlier interaction with the null, (ii) the creation of multiple additional, transient nulls and, hence, an increased number of energy release sites. In the Hall regime, the relevant timescales (such as the onset of reconnection and the period of the oscillatory relaxation) of the system are reduced significantly, and the reconnection rate is enhanced.Comment: 13 pages, 10 figure

Birhythmicity, Synchronization, and Turbulence in an Oscillatory System with Nonlocal Inertial Coupling

We consider a model where a population of diffusively coupled limit-cycle oscillators, described by the complex Ginzburg-Landau equation, interacts nonlocally via an inertial field. For sufficiently high intensity of nonlocal inertial coupling, the system exhibits birhythmicity with two oscillation modes at largely different frequencies. Stability of uniform oscillations in the birhythmic region is analyzed by means of the phase dynamics approximation. Numerical simulations show that, depending on its parameters, the system has irregular intermittent regimes with local bursts of synchronization or desynchronization.Comment: 21 pages, many figures. Paper accepted on Physica

Observations of Rapid Disk-Jet Interaction in the Microquasar GRS 1915+105

We present evidence that ~ 30 minute episodes of jet formation in the Galactic microquasar GRS 1915+105 may sometimes entirely be a superposition of smaller, faster phenomena. We base this conclusion on simultaneous X-ray and infrared observations in July 2002, using the Rossi X-ray Timing Explorer and the Palomar 5 meter telescope. On two nights, we observed quasi-periodic infrared flares from GRS 1915+105, each accompanied by a set of fast oscillations in the X-ray light curve (indicating an interaction between the jet and accretion disk). In contrast to similar observations in 1997, we find that the duration of each X-ray cycle matches the duration of its accompanying infrared flare, and we observed one instance in which an isolated X-ray oscillation occurred at the same time as a faint infrared "subflare" (of duration ~ 150 seconds) superimposed on one of the main flares. From these data, we are able to conclude that each X-ray oscillation had an associated faint infrared flare and that these flares blend together to form, and entirely comprise, the ~ 30 minute events we observed. Part of the infrared emission in 1997 also appears to be due to superimposed small flares, but it was overshadowed by infrared-bright ejections associated with the appearance of a sharp "trigger" spike in each X-ray cycle that were not present in 2002. We also study the evolution of the X-ray spectrum and find significant differences in the high energy power law component, which was strongly variable in 1997 but not in 2002. Taken together, these observations reveal the diversity of ways in which the accretion disk and jet in black hole systems are capable of interacting and solidify the importance of the trigger spike for large ejections to occur on ~ 30 minute timescales in GRS 1915+105.Comment: 17 pages, 9 figures; accepted for publication in The Astrophysical Journa

Electron-positron pair oscillation in spatially inhomogeneous electric fields and radiation

It is known that strong electric fields produce electron and positron pairs from the vacuum, and due to the back-reaction these pairs oscillate back and forth coherently with the alternating electric fields in time. We study this phenomenon in spatially inhomogeneous and bound electric fields by integrating the equations of energymomentum and particle-number conservations and Maxwell equations. The space and time evolutions of the pair-induced electric field, electric charge- and currentdensities are calculated. The results show that non-vanishing electric charge-density and the propagation of pair-induced electric fields, differently from the case of homogeneous and unbound electric fields. The space and time variations of pair-induced electric charges and currents emit an electromagnetic radiation. We obtain the narrow spectrum and intensity of this radiation, whose peak {\omega}peak locates in the region around 4 KeV for electric field strength \sim Ec. We discuss their relevances to both the laboratory experiments for electron and positron pair-productions and the astrophysical observations of compact stars with an electromagnetic structure.Comment: 15 pages, 8 figures. Accepted by Phys. Lett.

Rapidly-oscillating scatteringless non-Hermitian potentials and the absence of Kapitza stabilization

In the framework of the ordinary non-relativistic quantum mechanics, it is known that a quantum particle in a rapidly-oscillating bound potential with vanishing time average can be scattered off or even trapped owing to the phenomenon of dynamical (Kapitza) stabilization. A similar phenomenon occurs for scattering and trapping of optical waves. Such a remarkable result stems from the fact that, even though the particle is not able to follow the rapid external oscillations of the potential, these are still able to affect the average dynamics by means of an effective -albeit small- nonvanishing potential contribution. Here we consider the scattering and dynamical stabilization problem for matter or classical waves by a bound potential with oscillating ac amplitude $f(t)$ in the framework of a non-Hermitian extension of the Schr\"odinger equation, and predict that for a wide class of imaginary amplitude modulations $f(t)$ possessing a one-sided Fourier spectrum the oscillating potential is effectively canceled, i.e. it does not have any effect to the particle dynamics, contrary to what happens in the Hermitian caseComment: 7 pages, 3 figure