Displacement Transformations as a Tool to Study Many-Body Localization

We obtain eigenstates of interacting disorder Hamiltonians using unitary displacement transformations that rotate the state of the system. The method generates excited states if the strength of these transformations is chosen to optimize the energy, while decreasing the energy variance. We apply the method to analyse the localization properties of one-dimensional spinless fermions with short range interactions, reaching relatively large system sizes. We quantify the degree of localization through the size and disorder dependence of the inverse participation ratio.

Indicators of wavefunction (de)localisation for avoided crossing in a quadrupole quantum billiard

The relationship between wavefunction (de)localisation and avoided crossing in a quadrupole billiard is analysed. The following three-types of measures are employed for wavefunction (de)localisation: inverse participation ratio, inverse of Rényi entropy, and root-mean-square (RMS) image contrast. All these measures exhibit minimal values at the centre of the avoided crossing, where the wavefunction is maximally delocalised. Our results indicate that these quantities can be sufficient for the indication of wavefunction (de)localisation.

The temporal fluctuation of the inverse participation ratio for localized field modes in three-dimensional percolation system

We investigate the structure of the optical field radiated by the disordered optical nano-emitters randomly incorporated in three-dimensional cluster of a percolation material. Our numerical studies shown that the temporal variations of the inverse participation ratio (IPR) allow analyzing the extended and localized field structures over a long time range. The properties of IPR and the dynamics of the lasing emitters allow to find the characteristic time scales when the localization of the field in a general three-dimensional disordered system occurs. The studied effect opens new perspectives to control the optical fields localization in modern optical nano-technologies.