Geometric phase invariance in spatiotemporal modulated elastic system

摘要: Abstract We study the topological characteristics of elastic waves in a one-dimensional mass and spring superlattice that exhibits non-reciprocal wave propagation due to extrinsic application single sinusoidal spatiotemporal modulation its stiffness. employ computational procedure generate band structure, traveling modes' amplitudes phases, subsequently geometric phases characterize global vibrational behavior system character. The demonstrates notion non-conventional where hybridization gaps arise as bands appear cross for certain wavenumber values. estimate these points using multiple time scale perturbation theory low velocity. At points, both theoretical numerical analyses display discontinuity modes’ amplitudes. Consequently, we find π , sometimes zero, phase value modulated system, if unit cell has inversion symmetry imposed by values constant at initial time. temporal modulation, which creates gaps, changes nature from closed loop when is only spatial, an open phase. This invariant modulation.