Anderson localisation and the equation-of-motion method

Alain Aspect

Hideo Aoki

L. A. Toikka, Alexei Andreanov

The quantum motion of $N$ coupled kicked rotors is mapped to an interacting $N$-particle Anderson-Aubry-Andr$é$ tight-binding problem supporting many-body localised (MBL) phases. Interactions in configuration space are known to be insufficient for destroying Anderson localisation in a system in the MBL phase. The mapping we establish here predicts that a similar effect takes place in momentum space and determines the quantum dynamics of the coupled kicked rotors. Due to the boundedness of the Floquet quasi-energy spectrum there exists limitations on the interacting lattice models that can be mapped to quantum kicked rotors; in particular, no extensive observable can be mapped in the thermodynamic limit.

R. Orbach

Peter Bowcock, Ruth Gregory

An approach for calculating tunneling amplitudes from a nonlocalized initial state is presented. Generalizing the matching conditions and equations of motion to allow for complex momentum permits a description of tunneling in the presence of so-called classical motion. Possible applications of the method are presented.

B. Kramer, A. MacKinnon, Tomi Ohtsuki +1 more

This chapter describes the progress made during the past three decades in the finite size scaling analysis of the critical phenomena of the Anderson transition.The scaling theory of localisation and the Anderson model of localisation are briefly sketched.The finite size scaling method is described.Recent results for the critical exponents of the different symmetry classes are summarised.The importance of corrections to scaling are emphasised.A comparison with experiment is made, and a direction for future work is suggested.