Anomalous diffusion in disordered media and random quantum spin chains

Details Anomalous diffusion in disordered media and random quantum spin chains Anomalous diffusion in disordered media and random quantum spin chains

1998-04-29

arxiv.org/abs/cond-mat/9804316v1

Phys. Rev. E 58, 4238 (1998)

Physics

Condensed Matter

Statistical Mechanics

4 pages RevTeX, 1 eps-figures included

Scientific paper

10.1103/PhysRevE.58.4238

Using exact expressions for the persistence probability and for the leading eigenvalue of the Focker-Planck operator of a random walk in a random environment we establish a fundamental relation between the statistical properties of anomalous diffusion and the critical and off-critical behavior of random quantum spin chains. Many new exact results are obtained from this correspondence including the space and time correlations of surviving random walks and the distribution of the gaps of the corresponding Focker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region.

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