Final published version, 1.31 MB, PDF document
Available under license: CC BY: Creative Commons Attribution 4.0 International License
Final published version
Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Nonreciprocal response theory of non-Hermitian mechanical metamaterials
T2 - response phase transition from the skin effect of zero modes
AU - Schomerus, Henning
PY - 2020/1/17
Y1 - 2020/1/17
N2 - Nonreciprocal non-Hermitian systems provide an unconventional localization mechanism of topological zero modes via the non-Hermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I show that such nonreciprocal mechanical metamaterials reveal their underlying biorthogonality in the directly observable response of the system to external excitation. Applied to the experiment, this nonreciprocal response theory predicts that the zero-mode skin effect coincides with an extended phase where the system is highly sensitive to physical perturbations, leading to a diverging response in the limit of a large system.
AB - Nonreciprocal non-Hermitian systems provide an unconventional localization mechanism of topological zero modes via the non-Hermitian skin effect. While fundamental theoretical characterizations of this effect involve the biorthogonal system of right and left eigenmodes, the recent demonstration of this effect for a zero mode in a robotic metamaterial (Ghatak et al., arXiv:1907.11619) is based on the direct experimental observation of the conventional right eigenvectors. Here I show that such nonreciprocal mechanical metamaterials reveal their underlying biorthogonality in the directly observable response of the system to external excitation. Applied to the experiment, this nonreciprocal response theory predicts that the zero-mode skin effect coincides with an extended phase where the system is highly sensitive to physical perturbations, leading to a diverging response in the limit of a large system.
U2 - 10.1103/PhysRevResearch.2.013058
DO - 10.1103/PhysRevResearch.2.013058
M3 - Journal article
VL - 2
JO - Physical Review Research
JF - Physical Review Research
SN - 2643-1564
IS - 1
M1 - 013058
ER -