arXiv subjects

Rossen Dandoloff

Publications and source records attributed to Rossen Dandoloff.

24 records · Page 2Linked to original sources

arXiv2005

Quantum effective potential, electron transport and conformons in biopolymers

In the Kirchhoff model of a biopolymer, conformation dynamics can be described in terms of solitary waves, for certain special cross-section asymmetries. Applying this to the problem of electron transport, we show that the quantum effective potential arising due to the bends and twists of the polymer enables us to formalize and quantify the concept of a {\it conformon} that has been hypothesized in biology. Its connection to the soliton solution of the cubic nonlinear Schrödinger equation emerges in a natural fashion.

math-ph↗

arXiv2003

Nonlinear elastodynamics and energy transport in biopolymers

We present an exact analysis of the intrinsic dynamics of two types of biopolymers, described by the wormlike chain (WLC) and the wormlike rod chain (WLRC) models, respectively. We map each model to a classical field theory for an appropriate unit vector field defined on the space curve formed by the axis of the biopolymer. Conformation dynamics and energy transport are shown to be described, respectively, by the soliton-bearing Landau-Lifshitz equation and the nonlinear Schrödinger equation. This enables us to identify the soliton representing the ``conformon'' hypothesized in biopolymers.

nlin.PS↗

arXiv2001

A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.

math-ph↗

arXiv2001

Heisenberg Spins on a Cylinder Section

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic cylinder section with homogeneous boundary conditions. The latter may serve as a physical realization of magnetically coated microtubules and cylindrical membranes. The corresponding rigid cylinder model exhibits topological soliton configurations with geometrical frustration due to the finite length of the cylinder section. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking of the cylinder section with swellings.

cond-mat↗

arXiv2001

Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: the sigma model sector and the kink sector

We identify two distinct low-energy sectors in the classical isotropic antiferromagnetic Heisenberg spin-S chain. In the continuum limit, we show that two types of rotation generators arise for the field in each sector. Using these, the Lagrangian for sector I is shown to be that of the nonlinear sigma model. Sector II has a null Lagrangian; Its Hamiltonian density is just the Pontryagin term. Exact solutions are found in the form of magnons and precessing pulses in I and moving kinks in II. The kink has `spin' S. Sector I has a higher minimum energy than II.

cond-mat↗

arXiv1998

Heisenberg Spins on an Elastic Torus Section

Classical Heisenberg spins in the continuum limit (i.e. the nonlinear sigma-model) are studied on an elastic torus section with homogeneous boundary conditions. The corresponding rigid model exhibits topological soliton configurations with geometrical frustration due to the torus eccentricity. Assuming small and smooth deformations allows to find shapes of the elastic support by relaxing the rigidity constraint: an inhomogeneous Lamé equation arises. Finally, this leads to a novel geometric effect: a global shrinking with swellings.

cond-mat↗