Multifractality corresponds to scale-invariant fluctuations which cannot be described by a single fractal dimension. This property can be found in many problems of classical physics, for example turbulence, the stock market, cloud images... It has also been recently theoretically predicted to occur in quantum mechanics in specific systems. However, the experimental observation remains very difficult. It is therefore of great interest to understand how this multifractality can survive experimental conditions. In a paper recently published in Physical Review Letters, we have studied theoretically the effect of imperfections unavoidably present in experimental realizations on the multifractality of quantum wave functions. We have observed that a sufficiently large perturbation eventually destroys multifractality, but in two sharply different ways. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In this case, one can compensate a finite perturbation by using high resolution to resolve very small scales. In the second scenario, the multifractality is destroyed at all scales in a similar way. In this case, one definitely needs to control the perturbation below a critical value. These results should provide guidance towards the observation of quantum multifractality in a real experimental setting.
Reference : Remy Dubertrand, Ignacio Garcia-Mata, Bertrand Georgeot, Olivier Giraud, Gabriel Lemarie and John Martin "Two scenarios for quantum multifractality breakdown", Phys. Rev. Lett. 112, 234101 (2014)