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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

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

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.

References

1. J. T. Edwards and D. J. Thouless, "Numerical studies of localization in disordered systems," J. Phys. C: Solid State Phys. 5, 807 (1972), doi:10.1088/0022-3719/5/8/007.
2. A. Altland, Y. Gefen, and G. Montambaux, "What is the Thouless Energy for Ballistic Systems?", Physical Review Letters 76, 1130 (1996), doi:10.1103/PhysRevLett.76.1130.

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