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The effects of dissipation on topological mechanical systems

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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.


The total phase Φ in  as qy is varying 2π.The angular velocity is Ω = 0.3 and the strength of dissipation is γ = 0.6.  is divided into M = 10 pieces in the calculation.
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f3: The total phase Φ in as qy is varying 2π.The angular velocity is Ω = 0.3 and the strength of dissipation is γ = 0.6. is divided into M = 10 pieces in the calculation.

Mentions: In Fig. 3, we show how the total phase in changes as qy is varying 2π. Here the angular speed is Ω = 0.3 and the dissipative strength is γ = 0.6. We see that the Wannier function centers move totally 2 unit cells as qy is varying one reciprocal vector. So we can conclude that the Chern number C is 2 for the gap between the second and the third bands.


The effects of dissipation on topological mechanical systems
The total phase Φ in  as qy is varying 2π.The angular velocity is Ω = 0.3 and the strength of dissipation is γ = 0.6.  is divided into M = 10 pieces in the calculation.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f3: The total phase Φ in as qy is varying 2π.The angular velocity is Ω = 0.3 and the strength of dissipation is γ = 0.6. is divided into M = 10 pieces in the calculation.
Mentions: In Fig. 3, we show how the total phase in changes as qy is varying 2π. Here the angular speed is Ω = 0.3 and the dissipative strength is γ = 0.6. We see that the Wannier function centers move totally 2 unit cells as qy is varying one reciprocal vector. So we can conclude that the Chern number C is 2 for the gap between the second and the third 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.