Anomalous diffusion in disordered media and random quantum spin chains

Abstract

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.

4 pages RevTeX, 1 eps-figures included

References in corpus (2)

• Random Walks, Reaction-Diffusion, and Nonequilibrium Dynamics of Spin Chains in One-dimensional Random Environments
• The Random Transverse Ising Spin Chain and Random Walks

Cited by in corpus (41)

• Persistence and First-Passage Properties in Non-equilibrium Systems
• Rare region effects at classical, quantum, and non-equilibrium phase transitions
• Strong disorder RG approach of random systems
• Effect of disorder on quantum phase transitions in anisotropic XY spin chains in a transverse field
• Entanglement entropy dynamics of disordered quantum spin chains
• Exact renormalization of the random transverse-field Ising spin chain in the strongly ordered and strongly disordered Griffiths phases
• Anomalous Diffusion in Aperiodic Environments
• Random antiferromagnetic quantum spin chains: Exact results from scaling of rare regions
• Griffiths-McCoy singularities in random quantum spin chains: Exact results through renormalization
• Partially Asymmetric Exclusion Processes with Sitewise Disorder
• Persistence of a particle in the Matheron-de Marsily velocity field
• Strong Griffiths singularities in random systems and their relation to extreme value statistics
• Exact Asymptotic Results for Persistence in the Sinai Model with Arbitrary Drift
• Random quantum magnets with long-range correlated disorder: Enhancement of critical and Griffiths-McCoy singularities
• Griffiths Singularities in the Random Quantum Ising Antiferromagnet: A Tree Tensor Network Renormalization Group Study
• Persistence of Randomly Coupled Fluctuating Interfaces
• Griffiths-McCoy Singularities in the Random Transverse-Field Ising Spin Chain
• Average persistence in random walks
• Dynamics at barriers in bidirectional two-lane exclusion processes
• Reentrant Random Quantum Ising Antiferromagnet
• Infinite randomness with continuously varying critical exponents in the random XYZ spin chain
• Transverse-field Ising spin chain with inhomogeneous disorder
• Motion of a random walker in a quenched power law correlated velocity field
• Extreme statistics of the excitations in the random transverse Ising chain
• Correlation length-exponent relation for the two-dimensional random Ising model
• Random Transverse Field Ising model on the Cayley Tree : analysis via Boundary Strong Disorder Renormalization
• Disordered contact process with asymmetric spreading
• Extended surface disorder in the quantum Ising chain
• Low-temperature dynamics of Long-Ranged Spin-Glasses : full hierarchy of relaxation times via real-space renormalization
• Random quantum Ising model with three-spin couplings
• Griffiths-McCoy singularities in random quantum spin chains: Exact results
• Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
• Scaling of local persistence in the disordered contact process
• Exact bounds on the energy gap of transverse-field Ising chains by mapping to random walks
• Random Ising chain in transverse and longitudinal fields: Strong disorder RG study
• Mean field treatment of exclusion processes with random-force disorder
• Exact bounds for dynamical critical exponents of transverse-field Ising chains with a correlated disorder
• Anomalous diffusion in a space- and time-dependent energy landscape
• Heterogeneous Mean First-Passage Time Scaling in Fractal Media
• Random transverse and longitudinal field Ising chains
• Geometry of rare regions behind Griffiths singularities in random quantum magnets