Spectral analysis of amplitudes and phases of elastic waves: Application to topological elasticity

The Journal of the Acoustical Society of America
M Arif HasanPierre A Deymier

Abstract

The topological characteristics of waves in elastic structures are determined by the geometric phase of waves and, more specifically, by the Berry phase, as a characterization of the global vibrational behavior of the system. A computational procedure for the numerical determination of the geometrical phase characteristics of a general elastic structure is introduced: the spectral analysis of amplitudes and phases method. Molecular dynamics simulation is employed to computationally generate the band structure, traveling modes' amplitudes and phases, and subsequently the Berry phase associated with each band of periodic superlattices. In an innovative procedure, the phase information is used to selectively excite a particular mode in the band structure. It is shown analytically and numerically, in the case of one-dimensional elastic superlattices composed of various numbers of masses and spring stiffness, how the Berry phase varies as a function of the spatial arrangement of the springs. A symmetry condition on the arrangement of springs is established, which leads to bands with Berry phase taking the values of 0 or π. Finally, it is shown how the Berry phase may vary upon application of unitary operations that mathematically de...Continue Reading

References

Jun 5, 1989·Physical Review Letters·J Zak
Sep 19, 2015·Physical Review Letters·Pai WangKatia Bertoldi
Feb 22, 2018·Science Advances·Shubo WangChe Ting Chan

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Citations

Aug 3, 2019·The Journal of the Acoustical Society of America·Romain FleuryAndrew N Norris

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