Linear instability of a zigzag pattern

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Tommy DessupMichel Saint Jean

Abstract

Interacting particles confined in a quasi-one-dimensional channel are physical systems which display various equilibrium patterns according to the interparticle interaction and the transverse confinement potential. Depending on the confinement, the particles may be distributed along a straight line, in a staggered row (zigzag), or in a configuration in which the linear and zigzag phases coexist (distorted zigzag). In order to clarify the conditions of existence of each configuration, we have studied the linear stability of the zigzag pattern. We find an acoustic transverse mode that destabilizes the zigzag configuration for short-range interaction potentials, and we calculate the interaction range above which this instability disappears. In particular, we recover the unconditional stability of zigzag patterns for Coulomb interactions. We show that the domain of existence for the distorted zigzag patterns is accurately described by our linear stability analysis. We also emphasize the complexity of finite size effects. Last, we provide a criterion for the onset of instability in the thermodynamic limit and propose a biphasic model that explains some characteristics of the distorted zigzag patterns.

References

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May 21, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bin Liu, J Goree
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Oct 15, 2013·The Journal of Chemical Physics·Arthur V StraubeArd A Louis

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Citations

Apr 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tommy DessupMichel Saint Jean
Aug 31, 2016·Physical Review. E·Tommy DessupMichel Saint Jean
Jul 15, 2016·Physical Review. E·D McDermottC Reichhardt
Mar 20, 2018·Physical Review. E·Tommy DessupMichel Saint Jean
Nov 21, 2020·Physical Review. E·A V ZampetakiA V Ivlev

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