# Dynamical analysis of bounded and unbounded orbits in a generalized Hénon-Heiles system [CL]

The H\’enon-Heiles potential was first proposed as a simplified version of the gravitational potential experimented by a star in the presence of a galactic center. Currently, this system is considered a paradigm in dynamical systems because despite its simplicity exhibits a very complex dynamical behavior. In the present paper, we perform a series expansion up to the fifth-order of a potential with axial and reflection symmetries, which after some transformations, leads to a generalized H\’enon-Heiles potential. Such new system is analyzed qualitatively in both regimes of bounded and unbounded motion via the Poincar\’e sections method and plotting the exit basins. On the other hand, the quantitative analysis is performed through the Lyapunov exponents and the basin entropy, respectively. We find that in both regimes the chaoticity of the system decreases as long as the test particle energy gets far from the critical energy. Additionally, we may conclude that despite the inclusion of higher order terms in the series expansion, the new system shows wider zones of regularity (islands) than the ones present in the H\’enon-Heiles system.

F. Dubeibe, A. Riano-Doncel and E. Zotos
Thu, 7 Dec 17
10/72

# Quantum chaos of dark matter in the Solar System [CL]

We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution.

D. Shepelyansky
Thu, 23 Nov 17
48/52

# Quantum chaos of dark matter in the Solar System [CL]

We perform time-dependent analysis of quantum dynamics of dark matter particles in the Solar System. It is shown that this problem has similarities with a microwave ionization of Rydberg atoms studied previously experimentally and analytically. On this basis it is shown that the quantum effects for chaotic dark matter dynamics become significant for dark matter mass ratio to electron mass being smaller than $2 \times 10^{-15}$. Below this border multiphoton diffusion over Rydberg states of dark matter atom becomes exponentially localized in analogy with the Anderson localization in disordered solids. The life time of dark matter in the Solar System is determined in dependence on mass ratio in the localized phase and a few photon ionization regime. Various implications of these quantum results are discussed for the capture of dark matter from Galaxy and its steady-state density distribution.

D. Shepelyansky
Thu, 23 Nov 17
25/52

# Negative magnetic eddy diffusivity due to oscillatory $α$-effect [CL]

We study large-scale kinematic dynamo action of steady mirror-antisymmetric flows of incompressible fluid, that involve small spatial scales only, by asymptotic methods of the multiscale stability theory. It turns out that, due to the magnetic $\alpha$-effect in such flows, mean field experiences harmonic oscillations in time on the scale $T_1=\varepsilon t$ without growth or decay. Here $\varepsilon$ is the spatial scale ratio and $t$ is the fast time of the order of the flow turnover time. The interaction of the accompanying fluctuating magnetic field with the flow gives rise to an anisotropic magnetic eddy diffusivity, whose dependence on the direction of the large-scale wave vector generically exhibits a singular behaviour, and thus to negative eddy diffusivity for whichever molecular magnetic diffusivity. Consequently, such flows always act as kinematic dynamos on the time scale $T_2=\varepsilon^2t$. We investigate numerically this dynamo mechanism for two sample flows.

A. Andrievsky, R. Chertovskih and V. Zheligovsky
Fri, 10 Nov 17
3/55

# Chaotic dynamics in the (47171) Lempo triple system [EPA]

We investigate the dynamics of the (47171) Lempo triple system, also known by 1999TC$_{36}$. We derive a full 3D $N$-body model that takes into account the orbital and spin evolution of all bodies, which are assumed triaxial ellipsoids. We show that, for reasonable values of the shapes and rotational periods, the present best fitted orbital solution is chaotic and unstable in short time-scales. The formation mechanism of this system is unknown, but the orbits can be stabilised when tidal dissipation is taken into account. The dynamics of this system is very rich, but depends on many parameters that are presently unknown. A better understanding of this systems thus requires more observations, which also need to be fitted with a complete model like the one presented here.

A. Correia
Tue, 24 Oct 17
55/68

# On multiplicative Lie invariants and two-fluid plasma Cauchy invariants equation [CL]

To understand and model non-ideal flows, we use the simple result $(\partial_t + L_v) (\omega_1 \wedge \omega_2) = S_1 \wedge \omega_2 + \omega_1 \wedge S_2$ from the Lie-varying forms $(\partial_t + L_v) \omega_i = S_i: \ i = 1, 2$. If the (Lie-)sources/sinks satisfy $S_1 \wedge \omega_2 + \omega_1 \wedge S_2 = 0$, a multiplicative' Lie invariant follows, extending the classical approaches offinding new invariants from known ones of ideal flows’ and of modeling non-ideal flows constrained by invariant(s), beyond the traditional ones, the Gauss method, say. Precise relations, such as the generalised Cauchy invariants equation, as found here for two-fluid plasma dynamics, also extend to wider application space.

J. Zhu
Tue, 12 Sep 17
65/71

Large-scale turbulence in fluid layers and other quasi two-dimensional compressible systems consists of planar vortices and waves. Separately, wave turbulence usually produces direct energy cascade, while solenoidal planar turbulence transports energy to large scales by an inverse cascade. Here we consider turbulence at finite Mach numbers when interaction between acoustic waves and vortices is substantial. We employ solenoidal pumping at intermediate scales and show how both direct and inverse energy cascades are formed starting from the pumping scale. We show that there is an inverse cascade of kinetic energy up to a scale, $\ell$, where typical velocity reaches the speed of sound; that creates shock waves which provide for a compensating direct cascade. When the system size is less than $\ell$, the steady state contains a system-size pair of long-living condensate vortices connected by a system of shocks. Thus turbulence in fluid layers processes energy via a loop: most energy first goes to large scales via vortices and is then transported by waves to small-scale dissipation.