Classical diffusion in double-delta-kicked particles

We investigate the classical chaotic diffusion of atoms subjected to {\em pairs} of closely spaced pulses (`kicks) from standing waves of light (the $2\delta$-KP). Recent experimental studies with cold atoms implied an underlying classical diffusion of type very different from the well-known paradigm of Hamiltonian chaos, the Standard Map. The kicks in each pair are separated by a small time interval $\epsilon \ll 1$, which together with the kick strength $K$, characterizes the transport. Phase space for the $2\delta$-KP is partitioned into momentum `cells' partially separated by momentum-trapping regions where diffusion is slow. We present here an analytical derivation of the classical diffusion for a $2\delta$-KP including all important correlations which were used to analyze the experimental data. We find a new asymptotic ($t \to \infty$) regime of `hindered' diffusion: while for the Standard Map the diffusion rate, for $K \gg 1$, $D \sim K^2/2[1- J_2(K)..]$ oscillates about the uncorrelated, rate $D_0 =K^2/2$, we find analytically, that the $2\delta$-KP can equal, but never diffuses faster than, a random walk rate. We argue this is due to the destruction of the important classical `accelerator modes' of the Standard Map. We analyze the experimental regime $0.1\lesssim K\epsilon \lesssim 1$, where quantum localisation lengths $L \sim \hbar^{-0.75}$ are affected by fractal cell boundaries. We find an approximate asymptotic diffusion rate $D\propto K^3\epsilon$, in correspondence to a $D\propto K^3$ regime in the Standard Map associated with 'golden-ratio' cantori.Comment: 14 pages, 10 figures, error in equation in appendix correcte

Anderson localization or nonlinear waves? A matter of probability

In linear disordered systems Anderson localization makes any wave packet stay localized for all times. Its fate in nonlinear disordered systems is under intense theoretical debate and experimental study. We resolve this dispute showing that at any small but finite nonlinearity (energy) value there is a finite probability for Anderson localization to break up and propagating nonlinear waves to take over. It increases with nonlinearity (energy) and reaches unity at a certain threshold, determined by the initial wave packet size. Moreover, the spreading probability stays finite also in the limit of infinite packet size at fixed total energy. These results are generalized to higher dimensions as well.Comment: 4 pages, 3 figure

Was Planet 9 captured in the Sun’s natal star-forming region?

The presence of an unseen ‘Planet 9’ on the outskirts of the Solar system has been invoked to explain the unexpected clustering of the orbits of several Edgeworth–Kuiper Belt Objects. We use N-body simulations to investigate the probability that Planet 9 was a free-floating planet (FFLOP) that was captured by the Sun in its birth star formation environment. We find that only 1–6 per cent of FFLOPs are ensnared by stars, even with the most optimal initial conditions for capture in star-forming regions (one FFLOP per star, and highly correlated stellar velocities to facilitate capture). Depending on the initial conditions of the star-forming regions, only 5–10 of 10 000 planets are captured on to orbits that lie within the constraints for Planet 9. When we apply an additional environmental constraint for Solar system formation – namely the injection of short-lived radioisotopes into the Sun’s protoplanetary disc from supernovae – we find the probability for the capture of Planet 9 to be almost zero

Position and velocity space diffusion of test particles in stochastic electromagnetic fields

The two--dimensional diffusive dynamics of test particles in a random electromagnetic field is studied. The synthetic electromagnetic fluctuations are generated through randomly placed magnetised ``clouds'' oscillating with a frequency $\omega$. We investigate the mean square displacements of particles in both position and velocity spaces. As $\omega$ increases the particles undergo standard (Brownian--like) motion, anomalous diffusion and ballistic motion in position space. Although in general the diffusion properties in velocity space are not trivially related to those in position space, we find that energization is present only when particles display anomalous diffusion in position space. The anomalous character of the diffusion is only in the non--standard values of the scaling exponents while the process is Gaussian.Comment: 10 pages, 4 figure

Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Controlling high-frequency collective electron dynamics via single-particle complexity

We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.Comment: 5 pages, 4 figure

Bose-Einstein Condensate Driven by a Kicked Rotor in a Finite Box

We study the effect of different heating rates of a dilute Bose gas confined in a quasi-1D finite, leaky box. An optical kicked-rotor is used to transfer energy to the atoms while two repulsive optical beams are used to confine the atoms. The average energy of the atoms is localized after a large number of kicks and the system reaches a nonequilibrium steady state. A numerical simulation of the experimental data suggests that the localization is due to energetic atoms leaking over the barrier. Our data also indicates a correlation between collisions and the destruction of the Bose-Einstein condensate fraction.Comment: 7 pages, 8 figure

CO2 ocean bistability on terrestrial exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub-systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear-sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean-bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G- and F-type stars (but not M-type stars) may display bistability between an Earth-like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO2 condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO2. At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO2-condensing and hot, non-condensing climates. CO2 bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide-condensing climates follow an opposite trend in pCO2 versus instellation compared to the weathering-stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories

CO2 Ocean Bistability on Terrestrial Exoplanets

Cycling of carbon dioxide between the atmosphere and interior of rocky planets can stabilize global climate and enable planetary surface temperatures above freezing over geologic time. However, variations in global carbon budget and unstable feedback cycles between planetary sub‐systems may destabilize the climate of rocky exoplanets toward regimes unknown in the Solar System. Here, we perform clear‐sky atmospheric radiative transfer and surface weathering simulations to probe the stability of climate equilibria for rocky, ocean‐bearing exoplanets at instellations relevant for planetary systems in the outer regions of the circumstellar habitable zone. Our simulations suggest that planets orbiting G‐ and F‐type stars (but not M‐type stars) may display bistability between an Earth‐like climate state with efficient carbon sequestration and an alternative stable climate equilibrium where CO(2) condenses at the surface and forms a blanket of either clathrate hydrate or liquid CO(2). At increasing instellation and with ineffective weathering, the latter state oscillates between cool, surface CO(2)‐condensing and hot, non‐condensing climates. CO(2) bistable climates may emerge early in planetary history and remain stable for billions of years. The carbon dioxide‐condensing climates follow an opposite trend in pCO(2) versus instellation compared to the weathering‐stabilized planet population, suggesting the possibility of observational discrimination between these distinct climate categories