The Thouless energy is a characteristic energy scale of diffusive disordered conductors. It was first introduced by the Scottish-American physicist David J. Thouless when studying Anderson localization, as a measure of the sensitivity of energy levels to a change in the boundary conditions of the system. Though being a classical quantity, it has been shown to play an important role in the quantum-mechanical treatment of disordered systems. It is defined by
E T = ℏ D L 2 {\displaystyle E_{\rm {T}}={\frac {\hbar D}{L^{2}}}} , where D is the diffusion constant and L the size of the system, and thereby inversely proportional to the diffusion time
t D = L 2 D {\displaystyle t_{D}={\frac {L^{2}}{D}}}
through the system.
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