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A number of studies have shown that chaos occurs in scattering: the outgoing deflection angle is seen to be an erratic function of the impact parameter. We propose to extend this to quantum field theory, and to use erratic behavior of the…

High Energy Physics - Theory · Physics 2021-07-14 Vladimir Rosenhaus

Shilnikov's scenario in 3D consists of a vectorfield $V$ so that the equation $$ x'(t)=V(x(t))\in\mathbb{R}^3 $$ with $V(0)=0$ has a solution homoclinic to the origin and the eigenvalues of $DV(0)$ are $u>0$ and $\sigma\pm i\mu$,…

Dynamical Systems · Mathematics 2025-01-06 Hans-Otto Walther

We consider a version of the Vlasov equation on the circle under a periodic potential $V(x,t)$ and a repulsing smooth interaction $W$. We suppose that the Lagrangian for the single particle has chaotic orbits; using Aubry-Mather theory and…

Analysis of PDEs · Mathematics 2016-12-20 Ugo Bessi

In this paper, we show that two-dimensional billiards with point interactions inside exhibit a chaotic nature in the microscopic world, although their classical counterpart is non-chaotic. After deriving the transition matrix of the system…

Quantum Physics · Physics 2007-05-23 Takaomi Shigehara , Hiroshi Mizoguchi , Taketoshi Mishima , Taksu Cheon

We study the chaotic dynamics of spinless extended bodies in a wide class of spherically symmetric spacetimes, which encompasses black-hole scenarios in many modified theories of gravity. We show that a spherically symmetric pulsating ball…

General Relativity and Quantum Cosmology · Physics 2024-10-01 Fernanda de F. Rodrigues , Ricardo A. Mosna , Ronaldo S. S. Vieira

We consider the Rydberg electron in a circularly polarized microwave field, whose dynamics is described by a 2 d.o.f. Hamiltonian, which is a perturbation of size $K>0$ of the standard rotating Kepler problem. In a rotating frame, the…

Dynamical Systems · Mathematics 2024-11-18 Amadeu Delshams , Mercè Ollé , Juan Ramon Pacha , Óscar Rodríguez

We analyze, by means of Melnikov method, the possibility of modifying the threshold of homoclinic chaos in general 1-dimensional problems, by introducing small periodic resonant modulations. We indicate in particular a prescription in order…

chao-dyn · Physics 2009-10-22 G. Cicogna , L. Fronzoni

Results of direct numerical simulations and laboratory experiments have been used in order to show that the buoyancy driven bubbly flows at high gas volume fraction are mixed by deterministic chaos with typical exponential spectrum of the…

Fluid Dynamics · Physics 2022-04-29 A. Bershadskii

The interaction of a quantized electromagnetic field in a cavity with a set of two-level atoms inside can be described with algebraic Hamiltonians of increasing complexity, from the Rabi to the Dicke models. Their algebraic character…

We consider linear and time-dependent perturbations of periodic transport equations on the two-dimensional torus. For generic perturbations, we prove the existence of a large class of initial data whose Sobolev norms diverge exponentially…

Analysis of PDEs · Mathematics 2025-10-21 Gabriel Rivière , Maria Teresa Rotolo

Although granular materials are the second most processed in industry after water, the theoretical study of granules-structure interactions is not as advanced as that of fluid-structure interactions due to the lack of a unified view of the…

Chaotic Dynamics · Physics 2024-10-10 Hang Li , Jian Li , Hongzhu Fei , Guangyang Hong , Jinlu Dong , Aibing Yu

It is shown that a relevant control of Hamiltonian chaos is possible through suitable small perturbations whose form can be explicitly computed. In particular, it is possible to control (reduce) the chaotic diffusion in the phase space of a…

As demonstrated by observations, every stellar-mass object rotates around some axis; some objects spin faster than others due to different mechanisms. Furthermore, these spinning objects are slightly deformed and are no longer perfect…

General Relativity and Quantum Cosmology · Physics 2026-02-03 Adrián Eduarte-Rojas , Francisco Frutos-Alfaro , Rodrigo Carboni

It is argued that, if a regular Hamiltonian is perturbed by a term that produces chaos, the onset of chaos is shifted towards larger values of the perturbation parameter if the unperturbed spectrum is degenerate and the lifting of the…

Nuclear Theory · Physics 2009-10-28 W. Dieter Heiss , Stefanel Radu

This paper summarises a numerical investigation which aimed to identify and characterise regular and chaotic behaviour in time-dependent Hamiltonians H(r,p,t) = p^2/2 + U(r,t), with U=R(t)V(r) or U=V[R(t)r], where V(r) is a polynomial in x,…

Astrophysics · Physics 2009-10-31 Henry E. Kandrup , John Drury

Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain…

Chaotic Dynamics · Physics 2009-11-10 L. Chotorlishvili , Z. Toklikishvili , V. Bochorishvili , A. Sagaradze

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

Chaotic Dynamics · Physics 2023-06-14 Arkady Pikovsky , Alexander Nepomnyashchy

We present a technique to control chaos in Hamiltonian systems which are close to integrable. By adding a small and simple control term to the perturbation, the system becomes more regular than the original one. We apply this technique to a…

Chaotic Dynamics · Physics 2007-05-23 G. Ciraolo , C. Chandre , R. Lima , M. Vittot , M. Pettini

We consider perturbations of the non-unitary minimal model solutions of two-dimensional conformal turbulence proposed by Polyakov. Demanding the absence of non-integrable singularities in the resulting theories leads to constraints on the…

High Energy Physics - Theory · Physics 2015-06-26 Omduth Coceal , Steven Thomas

We consider the Kirchhoff equation on tori of any dimension and we construct solutions whose Sobolev norms oscillates in a chaotic way on certain long time scales. The chaoticity is encoded in the time between oscillations of the norm,…

Analysis of PDEs · Mathematics 2023-03-02 Pietro Baldi , Filippo Giuliani , Marcel Guardia , Emanuele Haus