Anderson Localization Transition: Introductory Training Course

When a single-particle quantum Hamiltonian system is subjected to a disorder potential, it is expected on physical grounds that a transition from localised to extended energy eigenstates takes place as a function of the disorder strength. Such a transi...

When a single-particle quantum Hamiltonian system is subjected to a disorder potential, it is expected on physical grounds that a transition from localised to extended energy eigenstates takes place as a function of the disorder strength. Such a transition should be accompanied by a characteristic change in the energy spectrum: if the disorder is large enough for Anderson localisation to occur, the random Schrödinger operator is known to have dense point spectrum; on the other hand, if the disorder is weak and the space dimension larger than d = 2, then one expects the existence of absolutely continuous spectrum.

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