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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.


The real parts (left) and the imaginary parts (right) of the eigen-frequencies for a ribbon with width W = 30.The two chiral edge modes with finite life time are confirmed.
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f4: The real parts (left) and the imaginary parts (right) of the eigen-frequencies for a ribbon with width W = 30.The two chiral edge modes with finite life time are confirmed.

Mentions: We confirm the above conclusion by a calculation of spectrum of a ribbon with two geometric boundaries. In the left panel of Fig. 4, we show the real parts of the eigenvalues of the ribbon with width W = 30. All parameters are the same as those in Fig. 3. An open boundary condition is taken in the transverse direction and the wave vector qx along the longitudinal direction is a good quantum number. We can see two chiral edge modes whose eigen-frequencies are within the gap between the second and the third phonon bands. Interestingly, this gap is more pronounced in the dissipative case than that in the dissipativeless case. The dissipation induced damping, which corresponds to the imaginary parts of the eigenvalues, are shown in the right panel of Fig. 4. It can be seen that all eigenstates are damped, but the damping rate is not uniform for different eigenstates at different qx. This is the origin of the dissipation induced force that is discussed in the next section.


The effects of dissipation on topological mechanical systems
The real parts (left) and the imaginary parts (right) of the eigen-frequencies for a ribbon with width W = 30.The two chiral edge modes with finite life time are confirmed.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: The real parts (left) and the imaginary parts (right) of the eigen-frequencies for a ribbon with width W = 30.The two chiral edge modes with finite life time are confirmed.
Mentions: We confirm the above conclusion by a calculation of spectrum of a ribbon with two geometric boundaries. In the left panel of Fig. 4, we show the real parts of the eigenvalues of the ribbon with width W = 30. All parameters are the same as those in Fig. 3. An open boundary condition is taken in the transverse direction and the wave vector qx along the longitudinal direction is a good quantum number. We can see two chiral edge modes whose eigen-frequencies are within the gap between the second and the third phonon bands. Interestingly, this gap is more pronounced in the dissipative case than that in the dissipativeless case. The dissipation induced damping, which corresponds to the imaginary parts of the eigenvalues, are shown in the right panel of Fig. 4. It can be seen that all eigenstates are damped, but the damping rate is not uniform for different eigenstates at different qx. This is the origin of the dissipation induced force that is discussed in the next section.

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.