Mode absorption and non-Hermiticity. In a region of space (grey circle), we count the number of in-and out-flowing modes (black arrows) and apply the pigeonhole principle. Insets in (a-d) show different bulk (green) and interface (red) dispersion relations. (a) Ungapped time-reversal-symmetric system. Every in-flowing mode is paired with a mode flowing out by time-reversal symmetry (TRS). The net mode flux Φ is zero. (b-d) Gapped systems, for which Φ = ΦL + ΦR, where Φ L/R counts modes at the two points where the interface (dotted/solid lines) crosses the region's boundary. (b) Gapped system with TRS. ΦL = ΦR = 0, even if BCs change the number of interface modes. (c) System for which TRS is broken, but bulk-interface correspondence holds. Topological protection guarantees one out-flowing mode for each inflowing mode, even along complex interfaces, ΦL + ΦR = 0. (d) When both TRS and bulk-interface correspondence are broken, the in-flowing modes can outnumber the out-flowing modes, so that Φ > 0 and non-Hermiticity is guaranteed.

Contexts in source publication

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... and (ii) violate bulk-interface correspondence. (i) Time-reversal symmetry (in this case equivalent to reciprocity) implies that for every rightmoving wave at wavevector q and frequency ω(q) there exists a left-moving wave with equal frequency ω(−q). Then, through every boundary there is an equal number of modes flowing in each direction, Fig. 2(a-b). Therefore, the net number of modes going into any region is zero. (ii) In non-reciprocal systems which satisfy bulkinterface correspondence, the net flux of modes into a region is still zero. This is because topological protection guarantees that for each incoming wave, there exists an outgoing wave along the same boundary at the ...

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... Therefore, the net number of modes going into any region is zero. (ii) In non-reciprocal systems which satisfy bulkinterface correspondence, the net flux of modes into a region is still zero. This is because topological protection guarantees that for each incoming wave, there exists an outgoing wave along the same boundary at the opposite end, Fig. ...

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... active fluids satisfy both of these conditions and can have the interface mode structure depicted in Fig. 2(d). As a consequence, more modes enter a region than can leave. The net flux of modes Φ into a region can be evaluated using the ...

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... elements. In analogy with typical expressions for a flux, the quantity sgn(q · ˆ n) acts as a vector field dotted into a surface normal. However, this quantity can only be an integer because it corresponds to a mode count for flow either into (contributing flux 1) or out of (contributing flux −1) the region. The mode flux Φ for the geometry in Fig. 2(d) is positive and can be evaluated as the sum of fluxes at the two points L/R where the interface crosses the boundary of the ...

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... of motion are linear and have wave-like solutions.) (i) Time-reversal symmetry (in this case equivalent to reciprocity) implies that for every right-moving wave at wavevector q and frequency ω(q) there exists a leftmoving wave with equal frequency ω(−q). Then, through every boundary there is an equal number of modes flowing in each direction, Fig. 2(a-b). Therefore, the net number of modes going into any region is zero. (ii) In non-reciprocal systems which satisfy bulk-interface correspondence, the net flux of modes into a region is still zero. This is because topological protection guarantees that for each incoming wave, there exists an outgoing wave along the same boundary at the ...

Context 6

... Therefore, the net number of modes going into any region is zero. (ii) In non-reciprocal systems which satisfy bulk-interface correspondence, the net flux of modes into a region is still zero. This is because topological protection guarantees that for each incoming wave, there exists an outgoing wave along the same boundary at the opposite end, Fig. ...

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... active fluids satisfy both of these conditions and can have the interface mode structure depicted in Fig. 2(d). As a consequence, more modes enter a region than can leave. The net flux of modes Φ into a region can be evaluated using the ...

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... elements. In analogy with typical expressions for a flux, the quantity sgn(q · ˆ n) acts as a vector field dotted into a surface normal. However, this quantity can only be an integer because it corresponds to a mode count for flow either into (contributing flux 1) or out of (contributing flux −1) the region. The mode flux Φ for the geometry in Fig. 2(d) is positive and can be evaluated as the sum of fluxes at the two points L/R where the interface crosses the boundary of the ...