Critical Fidelity

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.

4 pages, 3 figures. Revised and published in Phys. Rev. Lett

References in corpus (2)

• Coherence properties and quantum state transportation in an optical conveyor belt
• Anomalous power law of quantum reversibility for classically regular dynamics

Cited by in corpus (2)

• Decoherence, Entanglement and Irreversibility in Quantum Dynamical Systems with Few Degrees of Freedom
• Short-Time Loschmidt Gap in Dynamical Systems with Critical Chaos