Dynamical localization for continuum random surface models

AbstractThe current paper is devoted to the study of existence, uniqueness and Lifshitz tails of the integrated density of surface states (IDSS) for Schrödinger operators with alloy type random surface potentials. We prove the existence and uniqueness of the IDSS for negative energies, which is defined as the thermodynamic limit of the normalized eigenvalue counting functions of localized operators on strips with sections being special cuboids. Under the additional assumption that the single-site impurity potential decays anisotropically, we also prove that the IDSS for negative energies exhibits Lifshitz tails near the bottom of the almost sure spectrum in the following three regimes: the quantum regime, the quantum-classical/classical-quantum regime and the classical regime. We point out that the quantum-classical/classical-quantum regime is new for random surface models.

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RENORMALIZATION GROUP APPROACH TO DYNAMICAL PROPERTIES OF HIERARCHICAL NETWORKS

International Journal of Modern Physics B ◽

10.1142/s0217979291000407 ◽

1991 ◽

Vol 05 (05) ◽

pp. 709-750 ◽

Cited By ~ 31

Author(s):

A. GIACOMETTI ◽

A. MARITAN ◽

A.L. STELLA

Keyword(s):

Renormalization Group ◽

Diffusion Processes ◽

Waiting Times ◽

Dynamic Scaling ◽

Ultrametric Spaces ◽

Hierarchical Networks ◽

Random Surface ◽

One Dimensional ◽

Surface Models ◽

Renormalization Group Approach

Diffusion processes in the presence of hierarchical distributions of transition rates or waiting times are investigated by Renormalization Group (RG) techniques. Diffusion on one-dimensional chains, loop-less fractals and fully ultrametric spaces are considered. RG techniques are shown to be most natural and powerful to apply when infinitely many time scales are simultaneously involved in a problem. Generalizations and extensions of existing models and results are easily accomplished in the RG context. Wherever possible, heuristic scaling arguments are also presented in order to give an easier physical interpretation of the analytical results. Two relevant applications of ultradiffusion models are reviewed in detail. One of them concerns breakdown of dynamic scaling in a one-dimensional hierarchical Glauber chain. The other one is in the context of tethered random surface models.

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Diseases of triangulated random surface models, and possible cures

Nuclear Physics B ◽

10.1016/0550-3213(85)90356-6 ◽

1985 ◽

Vol 257 ◽

pp. 433-449 ◽

Cited By ~ 505

Author(s):

J. Ambjørn ◽

B. Durhuus ◽

J. Fröhlich

Keyword(s):

Random Surface ◽

Surface Models

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Extrinsic curvature in dynamically triangulated random surface models

Physics Letters B ◽

10.1016/0370-2693(89)90038-5 ◽

1989 ◽

Vol 220 (1-2) ◽

pp. 207-214 ◽

Cited By ~ 83

Author(s):

S.M. Catterall

Keyword(s):

Extrinsic Curvature ◽

Random Surface ◽

Surface Models

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A FIELD THEORETICAL APPROACH FOR STRINGS AND INTERFACES OF ISING-LIKE MODELS AT d>1

International Journal of Modern Physics B ◽

10.1142/s0217979296001094 ◽

1996 ◽

Vol 10 (18n19) ◽

pp. 2431-2440

Author(s):

M. MARTELLINI ◽

M. SPREAFICO ◽

K. YOSHIDA

Keyword(s):

Quantum Gravity ◽

Boundary Conditions ◽

Numerical Simulations ◽

Theoretical Approach ◽

Critical Exponents ◽

Polymer Phase ◽

Random Surface ◽

Surface Models ◽

D Values ◽

Physical Boundary

Starting from a generalized version of David-Distler-Kawai treatment of 2d-induced quantum gravity, we impose a series of “physical” boundary conditions to obtain an unique field theoretical Lagrangian describing random surface models and strings at given dimensions d>1. Our theory reproduces the critical exponents obtained by numerical simulations on d-dimensional Ising-like models for lower d-values. One observes, at appropriate dimensions d, the transition to the so-called branched polymer phase.

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