# Thouless energy

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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, [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]

David James Thouless is a British condensed-matter physicist. He is a winner of the 1990 Wolf Prize and laureate of the 2016 Nobel Prize for physics along with F. Duncan M. Haldane and J. Michael Kosterlitz for theoretical discoveries of topological phase transitions and topological phases of matter. In 2016, Thouless was reported to be suffering from dementia.

In condensed matter physics, Anderson localization is the absence of diffusion of waves in a disordered medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first to suggest that electron localization is possible in a lattice potential, provided that the degree of randomness (disorder) in the lattice is sufficiently large, as can be realized for example in a semiconductor with impurities or defects.

It is defined by

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

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.

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## 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 Letters76, 1130 (1996), doi : 10.1103/PhysRevLett.76.1130.