Thouless energy

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,^[1] 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.^[2]

It is defined by

${\displaystyle E_{\rm {T}}={\frac {\hbar D}{L^{2}}}}$,

where D is the diffusion constant and L the size of the system, and thereby inversely proportional to the diffusion time

${\displaystyle t_{D}={\frac {L^{2}}{D}}}$

through the system.