Critical Fidelity

Gim Seng Ng; Joshua Bodyfelt; Tsampikos Kottos

doi:10.1103/physrevlett.97.256404

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Critical Fidelity

Gim Seng Ng·Joshua Bodyfelt·Tsampikos Kottos

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Abstract

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.

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Gim Seng Ng, Joshua Bodyfelt, Tsampikos Kottos. 2006-12-31. Critical Fidelity. https://doi.org/10.1103/physrevlett.97.256404

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