arXiv subjects

Christian von Ferber

Publications and source records attributed to Christian von Ferber.

25 records · Page 2Linked to original sources

arXiv1998

Multifractality of Brownian motion near absorbing polymers

We characterize the multifractal behavior of Brownian motion in the vicinity of an absorbing star polymer. We map the problem to an O(M)-symmetric phi^4-field theory relating higher moments of the Laplacian field of Brownian motion to corresponding composite operators. The resulting spectra of scaling dimensions of these operators display the convexity properties which are necessarily found for multifractal scaling but unusual for power of field operators in field theory. Using a field-theoretic renormalization group approach we obtain the multifractal spectrum for absorbtion at the core of a polymer star as an asymptotic series. We evaluate these series using resummation techniques.

cond-mat↗

arXiv1998

Multifractal dimension spectra in polymer physics

We study the multifractal properties of diffusion in the presence of an absorbing polymer and report the numerical values of the multifractal dimension spectra for the case of an absorbing self avoiding walk or random walk.

cond-mat↗

arXiv1997

Copolymer Networks and Stars: Scaling Exponents

We explore and calculate the rich scaling behavior of copolymer networks in solution by renormalization group methods. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of scaling dimensions brings about remarkable features: The special convexity properties of the spectra allow for a multifractal interpretation while preserving stability of the theory. This behavior could not be found for power of field operators of usual $ϕ^4$ field theory. The 2D limit of the mutually avoiding walk star apparently corresponds to results of a conformal Kac series. Such a classification seems not possible for the 2D limit of other copolymer stars. We furthermore provide a consistency check of two complementary renormalization schemes: epsilon expansion and renormalization at fixed dimension, calculating a large collection of independent exponents in both approaches.

cond-mat.soft↗

arXiv1997

Field theoretic operators for multifractal moments

While multifractal spectra are convex, general field theoretic arguments show that power of field operators $ϕ^f$ yield a concave spectrum of exponents as function of $f$. This is resolved by appropriate choice of operators to describe multifractal moments. In a Lagrangian field theory of two mutually interacting species of fields $ϕ,ψ$, operators $O_{f'f}=ψ^{f'}ϕ^f$ with traceless symmetry give rise to multifractal spectra of harmonic diffusion near absorbing fractals when evaluated for zero component fields.

cond-mat↗

arXiv1997

Polymer stars in three dimensions. Three loop results

We study scaling properties of self avoiding polymer stars and networks of arbitrary given but fixed topology. We use massive field theoretical renormalization group framework to calculate critical exponents governing their universal properties (star exponents). Calculations are performed directly in three dimensions, renormalization group functions are obtained in three loop approximation. Resulting asymptotic series for star exponents are resummed with the help of Pade-Borel and conformal mapping transformation.

cond-mat↗

arXiv1997

Operator Product Expansion on a Fractal: The Short Chain Expansion for Polymer Networks

We prove to all orders of renormalized perturbative polymer field theory the existence of a short chain expansion applying to polymer solutions of long and short chains. For a general polymer network with long and short chains we show factorization of its partition sum by a short chain factor and a long chain factor in the short chain limit. This corresponds to an expansion for short distance along the fractal perimeter of the polymer chains connecting the vertices and is related to a large mass expansion of field theory. The scaling of the second virial coefficient for bimodal solutions is explained. Our method also applies to the correlations of the multifractal measure of harmonic diffusion onto an absorbing polymer. We give a result for expanding these correlations for short distance along the fractal carrier of the measure.

cond-mat↗

arXiv1997

Copolymer Networks: Multifractal dimension spectra in polymer field theory

We explore the rich scaling behavior of copolymer networks in solution. We establish a field theoretic description in terms of composite operators. Our 3rd order resummation of the spectrum of scaling dimensions brings about remarkable features: Convexity of the spectra allows for a multifractal interpretation. This has not been conceived for power of field operators of $ϕ^4$ field theory before. The 2D limit of the mutually avoiding walk star apparently corresponds to results of a conformal Kac series. Such a classification seems not possible for the 2D limit of other copolymer stars. The 3rd order calculation of a large collection of exponents furthermore allows for a consistency check of two complementary schemes: epsilon expansion and renormalization at fixed dimension.

cond-mat↗