



01867nas a2200157   4500008004100000245008200041210006900123260001500192300001100207490000600218520138400224100001701608700002201625700002501647856003701672       2018                        eng d00aEnergy-level statistics in strongly disordered systems with power-law hopping0 aEnergylevel statistics in strongly disordered systems with power  c2018/07/16  a0142010 vB3 a<p>Motivated by neutral excitations in disordered electronic materials and systems of trapped ultracold particles with long-range interactions, we study energy-level statistics of quasiparticles with the power-law hopping Hamiltonian &prop;1/rα in a strong random potential. In solid-state systems such quasiparticles, which are exemplified by neutral dipolar excitations, lead to long-range correlations of local observables and may dominate energy transport. Focussing on the excitations in disordered electronic systems, we compute the energy-level correlation function R2(ω) in a finite system in the limit of sufficiently strong disorder. At small energy differences the correlations exhibit Wigner-Dyson statistics. In particular, in the limit of very strong disorder the energy-level correlation function is given by R2(ω,V)=A3ωωV for small frequencies ω≪ωV and R2(ω,V)=1&minus;(α&minus;d)A1(ωVω)dα&minus;A2(ωVω)2 for large frequencies ω≫ωV, where ωV&prop;V&minus;αd is the characteristic matrix element of excitation hopping in a system of volume V, and A1, A2 and A3 are coefficient of order unity which depend on the shape of the system. The energy-level correlation function, which we study, allows for a direct experimental observation, for example, by measuring the correlations of the ac conductance of the system at different frequencies.</p>1 aTitum, Paraj1 aQuito, Victor, L.1 aSyzranov, Sergey, V.  uhttps://arxiv.org/abs/1803.11178