Critical Fidelity

Ng, Gim Seng; Bodyfelt, Joshua; Kottos, Tsampikos

Critical Fidelity

Authors

Ng, Gim Seng

Bodyfelt, Joshua

Kottos, Tsampikos

Description

Using a Wigner Lorentzian Random Matrix ensemble, we study the fidelity, $F(t)$, of systems at the Anderson metal-insulator transition, subject to small perturbations that preserve the criticality. We find that there are three decay regimes as perturbation strength increases: the first two are associated with a gaussian and an exponential decay respectively and can be described using Linear Response Theory. For stronger perturbations $F(t)$ decays algebraically as $F(t)\sim t^{-D_2}$, where $D_2$ is the correlation dimension of the critical eigenstates.
4 pages, 3 figures. Revised and published in Phys. Rev. Lett