Abstract
It has recently been shown that interference effects in disordered systems give rise to two non-trivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions $D_1$ and $D_2$, and by the spectral form factor. We check our results using a 1D Floquet system whose states have multifractal properties controlled by a single parameter. Our predictions are fully confirmed by numerical simulations and analytic perturbation expansions on this model. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems.
Highlights
In the field of quantum transport, the coherent backscattering (CBS) effect is a well-known signature of interference effects that emerges at a time of the order of the elastic scattering time, and survives configuration average in time-reversal symmetric disordered systems [1,2,3,4]
We focus on Floquet systems, and find that the coherent forward scattering (CFS) peak shape and its peak height dynamics are generically controlled by the multifractal dimensions D1 and D2, and by the spectral form factor
We demonstrate that the height and shape of the CFS peak give direct and remarkable access to the multifractal dimensions D1 and D2
Summary
Maxime Martinez ,1 Gabriel Lemarié ,1,2,3 Bertrand Georgeot ,1 Christian Miniatura ,2,3,4,5,6 and Olivier Giraud 7 1Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France 2MajuLab, CNRS-UCA-SU-NUS-NTU International Joint Research Unit, Singapore. It has recently been shown that interference effects in disordered systems give rise to two nontrivial structures: the coherent backscattering (CBS) peak, a well-known signature of interference effects in the presence of disorder, and the coherent forward scattering (CFS) peak, which emerges when Anderson localization sets in. We study here the CFS effect in the presence of quantum multifractality, a fundamental property of several systems, such as the Anderson model at the metal-insulator transition. We focus on Floquet systems, and find that the CFS peak shape and its peak height dynamics are generically controlled by the multifractal dimensions D1 and D2, and by the spectral form factor. We check our results using a one-dimensional Floquet system whose states have multifractal properties controlled by a single parameter. Our results, which we believe to be generic, provide an original and direct way to detect and characterize multifractality in experimental systems
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