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Title:

Principles of non-local field theories and their application to polymerized membranes

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0106361v1.pdf

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text

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en

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Title:

Supersymmetry Breaking in Disordered Systems and Relation to Functional Renormalization and Replica-Symmetry Breaking

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-15

Source:

http://arxiv.org/pdf/cond-mat/0411656v1.pdf

http://arxiv.org/pdf/cond-mat/0411656v1.pdf Minimize

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text

Language:

en

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own, since it allows for a distinction between single-particle and multi-particle contributions, which is not obvious in the Focker-Planck treatment. It also gives an efficient algorithm to determine S 2n numerically, by measuring the diffusion of particles in a random velocity field. In a third and final step, we generalize the Langevin treatment of a particle to polymers and membranes, or more generally to an elastic object of inner dimension D with 0 ≤ D ≤ 2. These objects can intersect each other. We also analyze what happens when self-intersections are no longer allowed. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v3.pdf

http://arxiv.org/pdf/chao-dyn/9911005v3.pdf Minimize

Document Type:

text

Language:

en

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Accepted for publication in J. Stat. Phys

Accepted for publication in J. Stat. Phys Minimize

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v1.pdf

http://arxiv.org/pdf/chao-dyn/9911005v1.pdf Minimize

Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

DISORDERED SYSTEMS AND THE FUNCTIONAL RENORMALIZATION GROUP, A PEDAGOGICAL INTRODUCTION

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0205116v1.pdf

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text

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en

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Title:

The functional renormalization group treatment of disordered systems: a review

Description:

We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is s...

We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group treatment is necessary, contrary to pure systems, where renormalization of a single coupling constant is sufficient. This leads to a disorder distribution, which after a finite renomalization becomes non-analytic, thus overcoming the predictions of the seemingly exact dimensional reduction. We discuss, how a renormalizable field theory can be constructed, even beyond 1-loop order. We then discuss an elastic manifold imbedded in N dimensions, and give the exact solution for N → ∞. This is compared to predictions of the Gaussian replica variational ansatz, using replica symmetry breaking. We finally discuss depinning, both isotropic and anisotropic, and the scaling Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0302322v1.pdf

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Document Type:

text

Language:

en

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DDC:

539 Modern physics *(computed)*

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Title:

The passive polymer problem

Description:

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity cor...

In this article, we introduce a generalization of the diffusive motion of point-particles in a turbulent convective flow with given correlations to a polymer or membrane. In analogy to the passive scalar problem we call this the passive polymer or membrane problem. We shall focus on the expansion about the marginal limit of velocity-velocity correlations which are uncorrelated in time and grow with the distance x as |x | ε, and ε small. This relation gets modified in the case of polymers and membranes (the marginal advecting flow has correlations which are shorter ranged.) The construction is done in three steps: First, we reconsider the treatment of the passive scalar problem using the most convenient treatment via field theory and renormalization group. We explicitly show why IR-divergences and thus the system-size appear in physical observables, which is rather unusual in the context of ordinary field-theories, like the φ 4-model. We also discuss, why the renormalization group can nevertheless be used to sum these divergences and leads to anomalous scaling of 2n-point correlation functions as e.g. S 2n (x): = ⟨[Θ(x,t) − Θ(0,t)] 2n ⟩. In a second step, we reformulate the problem in terms of a Langevin equation. This is interesting in its own Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-05

Source:

http://arxiv.org/pdf/chao-dyn/9911005v2.pdf

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Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

To be published in Journal of Statistical Physics 1 On the Perturbation Expansion of the KPZ- Equation

Description:

We present a simple argument to show that the β-function of the d-dimensional KPZ-equation (d ≥ 2) is to all orders in perturbation theory given by β(gR) = (d − 2)gR − 2 (8π) d/2 Γ(2 − d/2)g2 R. Neither the dynamical exponent z nor the roughness-exponent ζ have any correction in any order of perturbation theory. This shows that standard perturba...

We present a simple argument to show that the β-function of the d-dimensional KPZ-equation (d ≥ 2) is to all orders in perturbation theory given by β(gR) = (d − 2)gR − 2 (8π) d/2 Γ(2 − d/2)g2 R. Neither the dynamical exponent z nor the roughness-exponent ζ have any correction in any order of perturbation theory. This shows that standard perturbation theory cannot attain the strong-coupling regime and in addition breaks down at d = 4. We also calculate a class of correlation-functions exactly. KEY WORDS: KPZ-equation, growth processes 1 Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-15

Source:

http://arxiv.org/pdf/cond-mat/9802068v2.pdf

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text

Language:

en

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Title:

Why one needs a functional RG to survive in a disordered world

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-09-26

Source:

http://arxiv.org/pdf/cond-mat/0511529v1.pdf

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text

Language:

en

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Title:

How to measure Functional RG fixed-point functions for dynamics

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Abstract. – We show how the renormalized force correlator ∆(u), the function computed in the functional RG (FRG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. For equilibrium dynamics we recover the relation obtained recently in the statics between ∆(u) an...

Abstract. – We show how the renormalized force correlator ∆(u), the function computed in the functional RG (FRG) field theory, can be measured directly in numerics and experiments on the dynamics of elastic manifolds in presence of pinning disorder. For equilibrium dynamics we recover the relation obtained recently in the statics between ∆(u) and a physical observable. Its extension to depinning reveals interesting relations to stick-slip models of avalanches used in dry friction and earthquake dynamics. The particle limit (d = 0) is solved for illustration: ∆(u) exhibits a cusp and differs from the statics. We propose that the FRG functions be measured in wetting and magnetic interfaces experiments. Models involving elastic objects driven through random media are important for numerous physical systems and phenomena including magnets [1], superconductors [2], density waves [3], wetting [4], dry friction [5], dislocation and crack propagation [6], and earthquake dynamics [7]. There has been progress in qualitative understanding of, e.g. the existence of a depinning treshold for persistent motion at zero temperature T = 0, scale invariance at the threshold and the analogy with critical phenomena, collective pinning and roughness exponents, avalanche motion at T = 0, and ultra-slow thermally activated creep motion over diverging barriers. These phenomena are predicted by theory, i.e. phenomenological arguments [2], mean field models [8], functional renormalisation group [9–12], and Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2012-11-15

Source:

http://arxiv.org/pdf/cond-mat/0610525v1.pdf

http://arxiv.org/pdf/cond-mat/0610525v1.pdf Minimize

Document Type:

text

Language:

en

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