O(N) Generalized nonlinear sigma model and its applications

Ferrari, Franco; Paturej, Jarosław; Vilgis, Thomas A.

doi:10.1134/s1063778810020158

Cited by 3 publications

(7 citation statements)

References 9 publications

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“…(64) consists of a statistical sum over all particle trajectories that satisfy the Langevin equations (32) together with the inextensibility constraints (33) as it is expected. In [30] it has been verified that in the continuous case the statistical sum in the GNLσM contains only the chain conformations for which Ṙ(t, s) = ν(t, s) and |∂R(t, s)/∂s| = 1. These equations are respectively the continuous counterparts of Eqs.…”

Section: Discussionmentioning

confidence: 99%

“…(65). So far, the partition function and the so-called dynamic structure factor have been derived in the semiclassical approximation [29,30]. One could simplify the theory even further if it would be possible to extend the well known approximation of the Dirac delta function with a gaussian function also to the functional Dirac delta function imposing the inextensible constraints in the GNLσM.…”

Section: Discussionmentioning

confidence: 99%

“…For this reason it has been called the generalized nonlinear sigma model or simply GNLσM. Within the GNLσM it is possible to perform analytical calculations of physical quantities that can be applied to study the dynamics of cold chains or of chains moving in a very viscous environment [29,30,31]. One drawback of the GNLσM is that it regards the FHC as a gas of fluctuating particles with the inextensibility constraints being implemented by means of a product of delta functions.…”

Section: Introductionmentioning

confidence: 99%

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Dynamical Aspects of Inextensible Chains

Ferrari

Pyrka

2012

Int. J. Mod. Phys. B

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In the present work the dynamics of a continuous inextensible chain is studied. The chain is regarded as a system of small particles subjected to constraints on their reciprocal distances. It is proposed a treatment of systems of this kind based on a set Langevin equations in which the noise is characterized by a non-gaussian probability distribution. The method is explained in the case of a freely hinged chain. In particular, the generating functional of the correlation functions of the relevant degrees of freedom which describe the conformations of this chain is derived. It is shown that in the continuous limit this generating functional coincides with a model of an inextensible chain previously discussed by one of the authors of this work. Next, the approach developed here is applied to a inextensible chain, called the freely jointed bar chain, in which the basic units are small extended objects. The generating functional of the freely jointed bar chain is constructed. It is shown that it differs profoundly from that of the freely hinged chain. Despite the differences, it is verified that in the continuous limit both generating functionals coincide as it is expected.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical Aspects of Inextensible Chains

Ferrari

Pyrka

2012

Int. J. Mod. Phys. B

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“…[31], which allows the computation of several measurable quantities. For example, the dynamical form factor of the chain has been evaluated in [44]. Always in [44] it has been estimated how the fluctuations of the distance between two arbitrary points on the chain are influenced by physical parameters like the length of the chain and the relaxation time τ .…”

Section: Discussionmentioning

confidence: 99%

“…For example, the dynamical form factor of the chain has been evaluated in [44]. Always in [44] it has been estimated how the fluctuations of the distance between two arbitrary points on the chain are influenced by physical parameters like the length of the chain and the relaxation time τ . The novelty of the present approach with respect to [31] is the possibility to add also the external forces f i .…”

Section: Discussionmentioning

confidence: 99%

From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited

Ferrari

2012

Nuclear Physics B

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A gaussian model of the dynamics of an inextensible chain

Ferrari,

Pyrka

2010

Preprint

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In this work an approximated path integral model describing the dynamics of a inextensible chain is presented. To this purpose, the nonlinear constraints which enforce the property of inextensibility of the chain are relaxed and are just imposed in an average sense. This strategy, which has been originally proposed for semiflexible polymers in statistical mechanics, is complicated in the case of dynamics by the extra dependence on the time variable and by the presence of nontrivial boundary conditions. Despite these complications, the probability function of the chain, which measures the probability to pass to a given initial conformation to a final one, is computed exactly. The Lagrange multiplier imposing the relaxed condition satisfies a complicated nonlinear equation, which has been solved assuming that the chain is very long.

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O(N) Generalized nonlinear sigma model and its applications

Cited by 3 publications

References 9 publications

Dynamical Aspects of Inextensible Chains

Dynamical Aspects of Inextensible Chains

From constrained stochastic processes to the nonlinear sigma model. Two old problems revisited

A gaussian model of the dynamics of an inextensible chain

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