Anderson localisation is a state of matter where there is no diffusion of particles because of randonmness in the potential landscape.
The wavefunction is localised, i.e. exponentially dropping to zero, because of the interference of all the reflected waves from the random potential.

Some experimental groups, i.e. Aspect in Paris as the first one, showed that, by varying the disorder potential $\Delta$, one can induce a "phase transition" from an extended (not localised) state to an Anderson localised state.

Can this be called a "phase transition"? What is the broken symmetry between the two regimes?


Anderson localization, like other metal-insulator transitions (Mott, band insulator) is not a thermodynamic phase transition (thermodynamic functions are not singular), and there is no local order parameter (and no symmetry associated with a local order parameter). There is a non-local order parameter, the diffusion constant, which can be defined in terms of the Kubo limit of a current-current correlation function.

  • $\begingroup$ So what kind of phase transition is it? How do you call it? $\endgroup$
    – SuperCiocia
    Sep 23 '18 at 9:47
  • $\begingroup$ @SuperCiocia Does it need a name? I guess ordinary metal-insulator transitions are called "transitions" rather than "phase transitions". $\endgroup$
    – Thomas
    Sep 26 '18 at 1:29

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