Observation of ordered structures of laser-cooled ions in a quadrupole storage ring, Physical Review Letters, vol.68, issue.13, p.2007, 1992. ,
DOI : 10.1103/PhysRevLett.68.2007
Theory of structural phase transitions in a trapped Coulomb crystal, Physical Review Letters, vol.71, issue.17, p.2753, 1993. ,
DOI : 10.1103/PhysRevLett.71.2753
Phase transitions in anisotropically confined ionic crystals, Physical Review Letters, vol.70, issue.6, p.818, 1993. ,
DOI : 10.1103/PhysRevLett.70.818
Observation of Power-Law Scaling for Phase Transitions in Linear Trapped Ion Crystals, Physical Review Letters, vol.85, issue.12, p.2466, 2000. ,
DOI : 10.1103/PhysRevLett.85.2466
Microfabricated surface-electrode ion trap for scalable quantum information processing, Phys. Rev. Lett, vol.96, p.253003, 2006. ,
Normal modes of trapped ions in the presence of anharmonic trap potentials, New Journal of Physics, vol.13, issue.7, p.73026, 2011. ,
DOI : 10.1088/1367-2630/13/7/073026
Trapping of Topological-Structural Defects in Coulomb Crystals, Physical Review Letters, vol.110, issue.13, p.133004, 2013. ,
DOI : 10.1103/PhysRevLett.110.133004
Phonons in a one-dimensional Yukawa chain: Dusty plasma experiment and model, Physical Review E, vol.71, issue.4, p.46410, 2005. ,
DOI : 10.1103/PhysRevE.71.046410
Zigzag transition of finite dust clusters, Physical Review E, vol.73, issue.5, p.56404, 2006. ,
DOI : 10.1103/PhysRevE.73.056404
Dusty plasma ring model, Physica Scripta, vol.80, issue.6, p.65502, 2009. ,
DOI : 10.1088/0031-8949/80/06/065502
Dimensional phase transition in small Yukawa clusters, Physical Review E, vol.81, issue.1, p.16404, 2010. ,
DOI : 10.1103/PhysRevE.81.016404
Power law behavior of the zigzag transition in Yukawa clusters, Physics of Plasmas, vol.17, issue.11, p.113703, 2010. ,
DOI : 10.1063/1.3511442
Zigzag transitions and nonequilibrium pattern formation in colloidal chains, The Journal of Chemical Physics, vol.139, issue.13, p.134908, 2013. ,
DOI : 10.1063/1.4823501
Transverse single-file diffusion near the zigzag transition, Physical Review E, vol.87, issue.3, p.32163, 2013. ,
DOI : 10.1103/PhysRevE.87.032163
URL : https://hal.archives-ouvertes.fr/hal-01404826
Noisy zigzag transition, fluctuations, and thermal bifurcation threshold, Physical Review E, vol.87, issue.6, p.62135, 2013. ,
DOI : 10.1103/PhysRevE.87.062135
URL : https://hal.archives-ouvertes.fr/hal-01404829
Linear instability of a zigzag pattern, Physical Review E, vol.91, issue.2, p.22908, 2015. ,
DOI : 10.1103/PhysRevE.91.022908
Structural phase transitions in low-dimensional ion crystals, Physical Review B, vol.77, issue.6, p.64111, 2008. ,
DOI : 10.1103/PhysRevB.77.064111
Spontaneous nucleation of structural defects in inhomogeneous ion chains, New Journal of Physics, vol.12, issue.11, p.115003, 2010. ,
DOI : 10.1088/1367-2630/12/11/115003
Continuous structural transitions in quasi-one-dimensional classical Wigner crystals, Physical Review B, vol.81, issue.2, p.24108, 2010. ,
DOI : 10.1103/PhysRevB.81.024108
URL : http://hdl.handle.net/10067/812430151162165141
Quantum Zigzag Transition in Ion Chains, Physical Review Letters, vol.106, issue.1, p.10401, 2011. ,
DOI : 10.1103/PhysRevLett.106.010401
Ginzburg-Landau theory of the zigzag transition in quasi-one-dimensional classical Wigner crystals, Physical Review B, vol.84, issue.13, p.134106, 2011. ,
DOI : 10.1103/PhysRevB.84.134106
Thermal and quantum fluctuations in chains of ultracold polar molecules, Journal of Physics B: Atomic, Molecular and Optical Physics, vol.42, issue.15, p.154026, 2009. ,
DOI : 10.1088/0953-4075/42/15/154026
Traveling-wave convection in an annulus, Physical Review Letters, vol.60, issue.17, p.1723, 1988. ,
DOI : 10.1103/PhysRevLett.60.1723
Nonadiabatic effects in convection, Physical Review A, vol.38, issue.10, p.5461, 1988. ,
DOI : 10.1103/PhysRevA.38.5461
Localized traveling-wave states in binary-fluid convection, Physical Review Letters, vol.64, issue.12, p.1365, 1990. ,
DOI : 10.1103/PhysRevLett.64.1365
Wave-number selection and parity-breaking bifurcation in directional viscous fingering, Physical Review E, vol.58, issue.1, p.565, 1998. ,
DOI : 10.1103/PhysRevE.58.565
Oscillatory Phase Modulation of Parametrically Forced Surface Waves, Europhysics Letters (EPL), vol.10, issue.4, p.309, 1989. ,
DOI : 10.1209/0295-5075/10/4/005
Solitary Modes and the Eckhaus Instability in Directional Solidification, Physical Review Letters, vol.61, issue.22, p.2574, 1988. ,
DOI : 10.1103/PhysRevLett.61.2574
Solitary Tilt Waves in Thin Lamellar Eutectics, Europhysics Letters (EPL), vol.9, issue.8, p.779, 1989. ,
DOI : 10.1209/0295-5075/9/8/007
Dynamical regimes of directional viscous fingering: Spatiotemporal chaos and wave propagation, Physical Review Letters, vol.64, issue.2, p.184, 1990. ,
DOI : 10.1103/PhysRevLett.64.184
Comment on ??????Parity-breaking transitions of modulated patterns in hydrodynamic systems??????, Physical Review Letters, vol.65, issue.3, p.385, 1990. ,
DOI : 10.1103/PhysRevLett.65.385
On the phenomenology of tilted domains in lamellar eutectic growth, Journal de Physique I, vol.2, issue.3, p.281, 1992. ,
DOI : 10.1051/jp1:1992143
URL : https://hal.archives-ouvertes.fr/jpa-00246483
Nonlinear Dynamics of Coupled Oscillators, Annales de Physique, vol.19, issue.6, p.691, 1994. ,
DOI : 10.1051/anphys:01994001906069100
Parity-breaking transitions of modulated patterns in hydrodynamic systems, Physical Review Letters, vol.63, issue.18, p.1954, 1989. ,
DOI : 10.1103/PhysRevLett.63.1954
Instabilities of one-dimensional cellular patterns, Physical Review Letters, vol.64, issue.8, p.866, 1990. ,
DOI : 10.1103/PhysRevLett.64.866
we see that odd powers of 1/2 appear in the power expansion of the distances as even derivatives of and odd derivatives of H . In the expansion of the energy, the odd powers of 1/2 necessarily include odd powers of such terms, and thus they change sign in a parity transformation. Since the resulting equations should be invariant under parity, odd powers of 1/2 in the Lagrangian density should necessarily be in a factor of exact X derivatives, as shown for the 3 ,
Single-file diffusion of particles with long-range interactions: Damping and finite-size effects, Physical Review E, vol.84, issue.1, p.11101, 2011. ,
DOI : 10.1103/PhysRevE.84.011101
URL : https://hal.archives-ouvertes.fr/hal-01404847
Single-file diffusion of interacting particles in a finite-sized channel, Physical Review E, vol.82, issue.3, p.31201, 2010. ,
DOI : 10.1103/PhysRevE.82.031201
URL : https://hal.archives-ouvertes.fr/hal-01404851
A Course of Modern Analysis, 1920. ,