Anomalous diffusion in disordered media and random quantum spin chains

F. Iglói, Heiko Rieger

Research output: Contribution to journalArticle

39 Citations (Scopus)

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 languageEnglish
Pages (from-to)4238-4241
Number of pages4
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number4
Publication statusPublished - 1998

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Quantum Spin Chain
Disordered Media
Fokker-Planck
Anomalous Diffusion
random walk
Random walk
Fundamental Relation
operators
Spin Chains
Random Environment
Operator
Exact Results
Critical Behavior
Ising
Persistence
Statistical property
Transverse
eigenvalues
Correspondence
Exponent

ASJC Scopus subject areas

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

Cite this

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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.

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