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One source of dephasing (pointed out to us by P.G. Silvestrov) is the finite energy range (Formula presented) of the entangled edge channels. Referring to Fig.� 1, consider the area (Formula presented) between the two equipotentials starting at (Formula presented), through (Formula presented), and ending at (Formula presented). This enclosed area varies by (Formula presented) when the energy of the equipotentials varies by (Formula presented). Dephasing results if (Formula presented). The ratio (Formula presented) depends on the gradient of the electric field (Formula presented) near the edge. For (Formula presented), (Formula presented), one would need (Formula presented) to avoid dephasing by energy averaging
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One source of dephasing (pointed out to us by P.G. Silvestrov) is the finite energy range (Formula presented) of the entangled edge channels. Referring to Fig.� 1, consider the area (Formula presented) between the two equipotentials starting at (Formula presented), through (Formula presented), and ending at (Formula presented). This enclosed area varies by (Formula presented) when the energy of the equipotentials varies by (Formula presented). Dephasing results if (Formula presented). The ratio (Formula presented) depends on the gradient of the electric field (Formula presented) near the edge. For (Formula presented), (Formula presented), one would need (Formula presented) to avoid dephasing by energy averaging.
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