Power law behavior of the zigzag transition in Yukawa clusters

We present a mean-field description of the zig-zag phase transition of a quasi-one-dimensional system of strongly interacting particles, with interaction potential r −n e −r/λ , that are confined by a power-law potential (y α ). The parameters of the resulting one-dimensional Ginzburg-Landau theory are determined analytically for different values of α and n. Close to the transition point for the zig-zag phase transition, the scaling behavior of the order parameter is determined. For α = 2 the zig-zag transition from a single to a double chain is of second order, while for α > 2 the one chain configuration is always unstable and for α < 2 the one chain ordered state becomes unstable at a certain critical density resulting in jumps of single particles out of the chain.

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“…(6), was verified experimentally on a low dimensional dusty plasma in Ref. [25] and theoretically in Refs. [23], [15], [26] and [27].…”

Section: A Landau Theory For the Zig-zag Transitionmentioning

confidence: 81%

Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals

Galván-Moya

Peeters

2011

Phys. Rev. B

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“…The zigzag transition has been observed with ions in Paul's trap [1][2][3][4][5][6][7], with plasma dusts [8][9][10][11][12], with colloids [13], and with millimetric charged beads [14][15][16], A supercritical bifurcation has been observed in simulations of periodic systems with Coulomb interaction [17][18][19][20] and also in some periodic systems with short-range interactions [14,21], Most experiments have been done in linear traps of finite length, with repulsive boundary conditions at the edges. In these traps, the particles are not equidistant, and the simple expression (1) is not strictly valid.…”

Section: Introductionmentioning

confidence: 96%

Subcriticality of the zigzag transition: A nonlinear bifurcation analysis

Dessup

Coste²,

Jean³

2015

Phys. Rev. E

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When repelling particles are confined by a transverse potential in quasi-one-dimensional geometry, the straight line equilibrium configuration becomes unstable at small confinement, in favor of a staggered row that may be inhomogeneous or homogeneous. This conformational phase transition is a pitchfork bifurcation called the zigzag transition. We study the zigzag transition in infinite and periodic finite systems with short-range interactions. We provide numerical evidence that in this case the bifurcation is subcritical since it exhibits phase coexistence and hysteretic behavior. The physical mechanism responsible for the change in the bifurcation character is the nonlinear coupling between the transverse soft mode at the transition and the longitudinal Goldstone mode linked to the translational or rotational invariance of the zigzag pattern. An asymptotic analysis, near the bifurcation threshold and assuming an infinite system, gives an explicit expression for the normal form of the bifurcation. We establish the subcriticality, and we describe with excellent precision the inhomogeneous zigzag patterns observed in the simulations. A direct test of the physical mechanism responsible for the bifurcation character evidences a quantitative agreement.

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“…For Coulombic interactions, regardless of the boundary conditions, the bifurcation is always supercritical [3,5,6,13]. For cells with rigid extremities, regardless of the interaction range, the bifurcation is also supercritical [14,15,20,21,23]. In contrast, for short-range interactions and cyclic boundary conditions, a subcritical pitchfork bifurcation is evidenced [13,16,19,24].…”

Section: Introductionmentioning

confidence: 95%

“…For instance, laser-cooled ions in Paul traps (the socalled ions crystals or Coulomb crystals) are good candidates to create entangled states, which is a key step toward quantum information [1]; understanding the classical behavior of these systems is a necessity, which motivated several recent works on Coulomb crystals [2][3][4][5][6][7][8][9][10][11][12][13]. There are many other physical systems consisting of interacting particles confined in narrow channels, with a typical size that extends several orders of magnitude, such as optically confined paramagnetic colloidal particles [14][15][16], plasma dust in electrostatic traps [17][18][19][20][21], and electrostatically interacting macroscopic beads [13,[22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system

2016

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We study the dynamics of localized nonlinear patterns in a quasi-one-dimensional many-particle system near a subcritical pitchfork bifurcation. The normal form at the bifurcation is given and we show that these patterns can be described as solitary-wave envelopes. They are stable in a large temperature range and can diffuse along the chain of interacting particles. During their displacements the particles are continually redistributed on the envelope. This change of particle location induces a small modulation of the potential energy of the system, with an amplitude that depends on the transverse confinement. At high temperature, this modulation is irrelevant and the thermal motion of the localized patterns displays all the characteristics of a free quasiparticle diffusion with a diffusion coefficient that may be deduced from the normal form. At low temperature, significant physical effects are induced by the modulated potential. In particular, the localized pattern may be trapped at very low temperature. We also exhibit a series of confinement values for which the modulation amplitudes vanishes. For these peculiar confinements, the mean-square displacement of the localized patterns also evidences free-diffusion behavior at low temperature.

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Power law behavior of the zigzag transition in Yukawa clusters

Cited by 20 publications

References 20 publications

Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals

Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals

Subcriticality of the zigzag transition: A nonlinear bifurcation analysis

Thermal motion of a nonlinear localized pattern in a quasi-one-dimensional system

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