### Abstract

We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long-range Coulomb interactions. In its lower energy regime, we first detect macroscopically the transition from a "crystallinelike" to a "liquidlike" behavior, which we call the "melting transition." We then proceed to study this transition using a microscopic chaos indicator called the smaller alignment index (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasiperiodic) orbits, while it decays exponentially to zero for chaotic orbits as exp [- (λ1 - λ2) t], where λ1 > λ2 >0 are the two largest Lyapunov exponents. During the melting phase, SALI exhibits a peculiar stairlike decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the Δλ= λ1 - λ2 variations in that regime and helps us identify the energy range over which "melting" occurs as a multistage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the GALIk indices, which generalize SALI (= GALI2) to the case of k>2 deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

Original language | English |
---|---|

Article number | 016211 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 81 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 21 2010 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*81*(1), [016211]. https://doi.org/10.1103/PhysRevE.81.016211

**Weak chaos and the "melting transition" in a confined microplasma system.** / Antonopoulos, Chris; Basios, Vasileios; Bountis, Tassos.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 81, no. 1, 016211. https://doi.org/10.1103/PhysRevE.81.016211

}

TY - JOUR

T1 - Weak chaos and the "melting transition" in a confined microplasma system

AU - Antonopoulos, Chris

AU - Basios, Vasileios

AU - Bountis, Tassos

PY - 2010/1/21

Y1 - 2010/1/21

N2 - We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long-range Coulomb interactions. In its lower energy regime, we first detect macroscopically the transition from a "crystallinelike" to a "liquidlike" behavior, which we call the "melting transition." We then proceed to study this transition using a microscopic chaos indicator called the smaller alignment index (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasiperiodic) orbits, while it decays exponentially to zero for chaotic orbits as exp [- (λ1 - λ2) t], where λ1 > λ2 >0 are the two largest Lyapunov exponents. During the melting phase, SALI exhibits a peculiar stairlike decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the Δλ= λ1 - λ2 variations in that regime and helps us identify the energy range over which "melting" occurs as a multistage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the GALIk indices, which generalize SALI (= GALI2) to the case of k>2 deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

AB - We present results demonstrating the occurrence of changes in the collective dynamics of a Hamiltonian system which describes a confined microplasma characterized by long-range Coulomb interactions. In its lower energy regime, we first detect macroscopically the transition from a "crystallinelike" to a "liquidlike" behavior, which we call the "melting transition." We then proceed to study this transition using a microscopic chaos indicator called the smaller alignment index (SALI), which utilizes two deviation vectors in the tangent dynamics of the flow and is nearly constant for ordered (quasiperiodic) orbits, while it decays exponentially to zero for chaotic orbits as exp [- (λ1 - λ2) t], where λ1 > λ2 >0 are the two largest Lyapunov exponents. During the melting phase, SALI exhibits a peculiar stairlike decay to zero, reminiscent of "sticky" orbits of Hamiltonian systems near the boundaries of resonance islands. This alerts us to the importance of the Δλ= λ1 - λ2 variations in that regime and helps us identify the energy range over which "melting" occurs as a multistage diffusion process through weakly chaotic layers in the phase space of the microplasma. Additional evidence supporting further the above findings is given by examining the GALIk indices, which generalize SALI (= GALI2) to the case of k>2 deviation vectors and depend on the complete spectrum of Lyapunov exponents of the tangent flow about the reference orbit.

UR - http://www.scopus.com/inward/record.url?scp=76149084811&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevE.81.016211

DO - 10.1103/PhysRevE.81.016211

M3 - Article

VL - 81

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 1

M1 - 016211

ER -