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The effects of dissipation on topological mechanical systems

View Article: PubMed Central - PubMed

ABSTRACT

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.

No MeSH data available.


(left) and the strength of berry curvature  perpendicular to the BZ plane (right) are shown for the first three bands, a = 1, 2, 3 from up to down.
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f7: (left) and the strength of berry curvature perpendicular to the BZ plane (right) are shown for the first three bands, a = 1, 2, 3 from up to down.

Mentions: In Fig. 7, we plot the gradient of κ, in the BZ with small arrows in the left panels and the strength of Berry curvature with the contour in the right panels. The Berry curvature is calculated by discretizing the BZ into small grids and counting the accumulated phase by the eigenstates along the edges of each grid24. Of course, the new definition of inner product must be taken in the calculation. Here only those for the first three phonon bands are plotted and the forth band is ignored because, as shown in Fig. 6, κ is not varying rapidly for this band. It is shown that for the 2nd and the 3rd bands, there is a cirque in the BZ, in which both and are relatively large. According to the equations of motion, , the free wave packet composed by the eigenstates of the these bands suffers a tendency towards the transverse direction caused by the combination of Berry curvature and the extra force in the last term. As this term is also varying with , as well as with the time, the trace of the wave packet is a curved line, similar to the trace of electron in 2D hall bar with longitudinal electric field. We suggest that such effect may be observed by preparing the proper wave packet composited by the states for which both and are large in the 2nd band or in the 3rd bands.


The effects of dissipation on topological mechanical systems
(left) and the strength of berry curvature  perpendicular to the BZ plane (right) are shown for the first three bands, a = 1, 2, 3 from up to down.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015026&req=5

f7: (left) and the strength of berry curvature perpendicular to the BZ plane (right) are shown for the first three bands, a = 1, 2, 3 from up to down.
Mentions: In Fig. 7, we plot the gradient of κ, in the BZ with small arrows in the left panels and the strength of Berry curvature with the contour in the right panels. The Berry curvature is calculated by discretizing the BZ into small grids and counting the accumulated phase by the eigenstates along the edges of each grid24. Of course, the new definition of inner product must be taken in the calculation. Here only those for the first three phonon bands are plotted and the forth band is ignored because, as shown in Fig. 6, κ is not varying rapidly for this band. It is shown that for the 2nd and the 3rd bands, there is a cirque in the BZ, in which both and are relatively large. According to the equations of motion, , the free wave packet composed by the eigenstates of the these bands suffers a tendency towards the transverse direction caused by the combination of Berry curvature and the extra force in the last term. As this term is also varying with , as well as with the time, the trace of the wave packet is a curved line, similar to the trace of electron in 2D hall bar with longitudinal electric field. We suggest that such effect may be observed by preparing the proper wave packet composited by the states for which both and are large in the 2nd band or in the 3rd bands.

View Article: PubMed Central - PubMed

ABSTRACT

We theoretically study the effects of isotropic dissipation in a topological mechanical system which is an analogue of Chern insulator in mechanical vibrational lattice. The global gauge invariance is still conserved in this system albeit it is destroyed by the dissipation in the quantum counterpart. The chiral edge states in this system are therefore robust against strong dissipation. The dissipation also causes a dispersion of damping for the eigenstates. It will modify the equation of motion of a wave packet by an extra effective force. After taking into account the Berry curvature in the wave vector space, the trace of a free wave packet in the real space should be curved, feinting to break the Newton’s first law.

No MeSH data available.