Chaoticity in vibrating nuclear billiards

Burgio, G. F.; Baldo, M.; Rapisarda, Andrea; Schuck, Peter

doi:10.1103/physrevc.52.2475

Cited by 20 publications

(51 citation statements)

References 15 publications

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“…[2][3][4][5]. It can be noticed the increase of the chaotic bearing once the oscillation frequency of the potential well is varied from the adiabatic to the resonance regime, for all degrees of multipole.…”

Section: Autocorrelation Functionmentioning

confidence: 99%

“…In addition to [4,5], we introduced a physical constraint and continued the study of the dynamical system. Thus, we first considered a physical situation [8] and we take instead a static vibrating nuclear billiard, a projectile nucleus having the same proprieties and we impinge it on a giving target nucleus.…”

Section: Numerical Studymentioning

confidence: 99%

“…The ensemble of nucleons is considered as a Hamiltonian system therefore the total energy is conserved and this means that the walls can give energy to nucleons. The Hamiltonian of this kind of interaction in polar coordinates is [4,5]:…”

Section: The Toy Modelmentioning

confidence: 99%

“…In both cases the dynamical evolution showed a regular undamped collective motion which coexist with a weakly chaotic single-particle dynamics. Then Burgio et al [4,5] considered a number of nucleons without spin and charge and with no internal structure which are moving in a 2D deep WoodsSaxon potential well and hitting the oscillating surface with a certain frequency. They discuss the dissipative behavior of the wall motion and its relation with the order to chaos transition in the dynamics of the microscopic degree of freedom.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Chaotic dynamics in classical nuclear billiards

Bordeianu

Felea

Beşliu

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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Section: Autocorrelation Functionmentioning

confidence: 99%

Section: Numerical Studymentioning

confidence: 99%

Section: The Toy Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Chaotic dynamics in classical nuclear billiards

Bordeianu

Felea

Beşliu

et al. 2011

Communications in Nonlinear Science and Numerical Simulation

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“…While most of the theoretical treatments of oscillations rely on the linear response method or RPA methods, large amplitude oscillations require methods beyond. Especially the question of the appearance of chaos is recently investigated [1][2][3]. The hypothesis was established that the octupole mode is overdamped due to negative curved surface and consequently additional chaotic damping [4][5][6].…”

mentioning

confidence: 99%

Giant octupole resonance simulation

Walke

Morawetz

1999

Phys. Rev. C

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Using a pseudo-particle technique we simulate large-amplitude isoscalar giant octupole excitations in a finite nuclear system. Dependent on the initial conditions we observe either clear octupole modes or over-damped octupole modes which decay immediately into quadrupole ones. This shows clearly a behavior beyond linear response. We propose that octupole modes might be observed in central collisions of heavy ions.Giant resonances regain much attention presently for the investigation of many particle effects in finite quantum systems. While most of the theoretical treatments of oscillations rely on the linear response method or RPA methods, large amplitude oscillations require methods beyond. Especially the question of the appearance of chaos is recently investigated [1][2][3]. The hypothesis was established that the octupole mode is overdamped due to negative curved surface and consequently additional chaotic damping [4][5][6]. Here we want to discuss at which conditions one might observe octupole modes at least in Vlasov -simulation of giant resonances.We will consider different initial conditions of isoscalar giant resonances using a pseudo-particle simulation of Vlasov kinetic equation [7]. With a local potential U (r) the quasi-classical Vlasov equation readsWe represent the distribution function f (p, r, t) by a sum of pseudo-particle distributionsand use Gaussian pseudo-particlesat r 1 with momentum p 1 [8]. These pseudo-particles follow classical Hamilton equationsWe assume for the interacting nucleons a phenomenological density dependent Skyrme interaction [9] which results into the mean fieldwith a = −356MeV, b = 303MeV and s = 7/6. The compression modulus is K = 200 MeV. The evolution given by (1) is deterministic, fluctuations appear only due to numerical noise [10]. We are using 75 pseudo-particles per nucleon and a pseudo-particle width, σ r = 0.53 fm, is adjusted so that the isovector giant dipole energy is reproduced at a single mass number. The experimental behavior of centroid energy with mass number is than reproduced. We have checked different numbers of test particles. The dependence of observables on the width is discussed in [11]. Numerically the ground state of nucleons is realized by Wood-Saxon shapes of density and Fermi spheres in momentum. The distribution n a (p) = dra i f (p, r) of mass distribution, a i = 1, isospin, a i = τ i , kinetic energy, a i = p 2 i 2m , and kinetic isospin energy, a i =

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Chaotic Motion in the Breathing Circle Billiard

Bonanno

Marò

2021

Ann. Henri Poincaré

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We consider the free motion of a point particle inside a circular billiard with periodically moving boundary, with the assumption that the collisions of the particle with the boundary are elastic so that the energy of the particle is not preserved. It is known that if the motion of the boundary is regular enough then the energy is bounded due to the existence of invariant curves in the phase space. We show that it is nevertheless possible that the motion of the particle is chaotic, also under regularity assumptions for the moving boundary. More precisely, we show that there exists a class of functions describing the motion of the boundary for which the billiard map has positive topological entropy. The proof relies on variational techniques based on the Aubry–Mather theory.

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Chaoticity in vibrating nuclear billiards

Cited by 20 publications

References 15 publications

Chaotic dynamics in classical nuclear billiards

Chaotic dynamics in classical nuclear billiards

Giant octupole resonance simulation

Chaotic Motion in the Breathing Circle Billiard

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