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Equation 4 · Part 2 · From Origins to Frontier: A History of Quantum and Condensed-Matter Systems

Symbol T_c

kBTc≈1.13 ℏωD e−1/N(0)Vk_B T_c \approx 1.13\, \hbar\omega_D \, e^{-1/N(0)V}
TcT_c

What this part means

TcT_c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

TcT_c is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…one of its few genuinely load-bearing equations, and it is worth writing down because it exposes a real, falsifiable assumption rather than decorating the prose. In the weak-coupling limit, the transition temperature TcT_c is related to the strength of the electron-phonon coupling N(0)V (density of states at the Fermi level times the pairing interaction) and the characteristic phonon energy ℏ\hbarωD\omega_D (the Debye frequency) by: kBTc≈1.13 ℏωD e−1/N(0)Vk_B T_c \approx 1.13\, \hbar\omega_D \, e^{-1/N(0)V}. The exponential is the important feature, not decoration: it…

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