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σ
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42
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14944373702
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note
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One can easily check that the derivation of Eq. (9) is valid not only for a Wigner crystal, but for any translation-invariant model of interacting electrons.
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14944370808
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note
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The asymptotics at x→±∞ in Eq. (26) are chosen to correspond to outgoing plasmon wave.
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52
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85088491215
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note
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2/h, but this value is still independent of the electron density. The reduction of the quantized value was attributed to the imperfect coupling of the wire to the leads (Ref. 50).
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14944379226
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note
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It is worth mentioning that the violation of the spin-charge separation in Eq. (30) is due to the inhomogeneity of the system. In the homogeneous case J = const, and the spin-charge separation is restored.
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14944351875
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The standard solution (Ref. 60) applies the WKB approximation to the ground states of the oscillatory potentials near the minima of U(x). As a result it underestimates the level splitting (A4) by a factor (Ref. 62) of √π/e ≈ 1.075.
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