### Abstract

Using exact expressions for the persistence probability and for the leading eigenvalue of the Fokker-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 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 Fokker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region.

Original language | English |
---|---|

Pages (from-to) | 4238-4241 |

Number of pages | 4 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 58 |

Issue number | 4 |

Publication status | Published - 1998 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*58*(4), 4238-4241.

**Anomalous diffusion in disordered media and random quantum spin chains.** / Iglói, F.; Rieger, Heiko.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 58, no. 4, pp. 4238-4241.

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TY - JOUR

T1 - Anomalous diffusion in disordered media and random quantum spin chains

AU - Iglói, F.

AU - Rieger, Heiko

PY - 1998

Y1 - 1998

N2 - Using exact expressions for the persistence probability and for the leading eigenvalue of the Fokker-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 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 Fokker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region.

AB - Using exact expressions for the persistence probability and for the leading eigenvalue of the Fokker-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 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 Fokker-Planck operator. In turn we derive analytically the dynamical exponent of the random transverse-field Ising spin chain in the Griffiths-McCoy region.

UR - http://www.scopus.com/inward/record.url?scp=0001340734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001340734&partnerID=8YFLogxK

M3 - Article

VL - 58

SP - 4238

EP - 4241

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

ER -