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B. Piette

Publications and source records attributed to B. Piette.

At least 19 recordsLinked to original sources
arXiv2012

Bio-Polymer Hairpin Loops Sustained by Polarons

We show that polarons can sustain loop-like configurations in flexible bio-polymers and that the size of the loops depend on both the flexural rigidity of the polymer and the electron-phonon coupling constant. In particular we show that for single stranded DNA (ssDNA) such loops can have as little as 10 base pairs. For polyacetylene the shortest loop must have at least 12 nodes. We also show that these configurations are very stable under thermal fluctuations and can facilitate the formation of hairpin-loops of ssDNA.

physics.bio-ph↗
arXiv2008

Skyrmion Vibration Modes within the Rational Map Ansatz

We study the vibration modes of the Skyrme model within the rational map ansatz. We show that the vibrations of the radial profiles and the rational maps are decoupled and we consider explicitly the case B=1, B=2 and B=4. We then compare our results with the vibration modes obtained numerically by Barnes et al. and show that qualitatively the rational map reproduces the vibration modes obtained numerically but that the vibration frequencies of these modes do not match very well.

hep-th↗
arXiv2007

Scattering of sine-Gordon Breathers on Potential Wells

We analyse the scattering of sine-Gordon breathers on a square potential well. We show that the scattering process depends not only on the vibration frequency of the breather and its incoming speed but also on its phase as well as the depth and width of the well. We show that the breather can pass through the well and exit with a speed different, sometime larger, from the initial one. It can also be trapped and very slowly decay inside the well or bounce out of the well and go back to where it came from. We also show that the breather can split into a kink and an anti-kink pair when it hits the well.

cond-mat.other↗
arXiv2006

Scattering of Sine-Gordon kinks on potential wells

We study the scattering properties of Sine Gordon kinks on obstructions in the form of finite size potential `wells'. We model this by making the coefficient of the $\cos(ϕ)-1$ term in the Lagrangian position dependent. We show that when the kinks find themselves in the well they radiate and then interact with this radiation. As a result of this energy loss the kinks become trapped for small velocities while at higher velocities they are transmitted with a loss of energy. However, the interaction with the radiation can produce `unexpected' reflections by the well. We present two simple models which capture the gross features of this behaviour. Both involve standing waves either at the edges of the well or in the well itself.

hep-th↗
arXiv2006

Dynamical properties of a Soliton in a Potential Well

We analyse the scattering of a two-dimensional soliton on a potential well. We show that this soliton can pass through the well, bounce back or become trapped and we study the dependence of the critical velocity on the width and the depth of the well. We also present a model based on a pseudo-geodesic approximation to the full system which shows that the vibrational modes of the soliton play a crucial role in the dynamical properties of its interactions with potential wells.

hep-th↗
arXiv2005

Adiabatic self-trapped states in carbon nanotubes

We study here polaron (soliton) states of electrons or holes in a model describing carbon-type nanotubes. In the Hamiltonian of the system we take into account the electron-phonon interaction that arises from the deformation dependencies of both the on-site and the hopping interaction energies. Using an adiabatic approximation, we derive the equations for self-trapped electron states in zigzag nanotubes. We find the ground states of an electron in such a system and show that the polaron states can have different symmetries depending on the strength of the electron-phonon coupling. Namely, at relatively weak coupling the polarons possess quasi-one-dimensional (quasi-1D) properties and have an azimuthal symmetry. When the coupling constant exceeds some critical value, the azimuthal symmetry breaks down and the polaron spreads out in more than one dimension. We also study polarons that are formed by the electrons in the conducting band (or by holes in the valence band) in semiconducting carbon nanotubes. We show that their properties are more complex than those of quasi-1D ground state polarons. In particular, polarons in semiconducting carbon nanotubes possess an inner structure: being self-trapped along the nanotube axis they exhibit some modulations around the nanotube.

cond-mat.other↗
arXiv2005

Self-trapped electron states in nanotubes

We study numerically self-trapped (polaron) states of quasiparticles (electrons, holes or excitons) in a deformable nanotube formed by a hexagonal lattice, wrapped into a cylinder (carbon- and boron nitride-type nanotube structures). We present a Hamiltonian for such a system taking into account an electron-phonon interaction, and determine conditions under which the lowest energy states are polarons.We compute a large class of numerical solutions of this model for a wide range of the parameters. We show that at not too strong electron-phonon coupling, the system admits ring-like localized solutions wrapped around the nanotube (the charge carrier is localized along the nanotube axis and uniformly distributed with respect to the azimuthal coordinate). At stronger coupling, solutions are localized on very few lattice sites in both directions of the nanotube. The transition from one type solution to the other one depends on the diameter of the nanotube. We show that for the values of the carbon nanotube parameters, the polarons have a ring-like structure wrapped around the nanotube with a profile resembling that of the nonlinear Schrodinger soliton.

cond-mat.other↗
arXiv2005

Mass terms in the Skyrme Model

We consider various forms of the mass term that can be used in the Skyrme model and their implications on the properties of baryonic states. We show that, with an appropriate choice for the mass term, without changing the asymptotic behaviour of the profile functions at large $r$, we can considerably reduce or increase the mass term's contribution to the classical mass of the solitons. We find that multibaryon configurations can be classically bound at large baryon numbers for some choices of this mass term.

hep-th↗
arXiv2004

Solitons in alpha-helical proteins

We investigate some aspects of the soliton dynamics in an alpha-helical protein macromolecule within the steric Davydov-Scott model. Our main objective is to elucidate the important role of the helical symmetry in the formation, stability and dynamical properties of Davydov's solitons in an alpha-helix. We show, analytically and numerically, that the corresponding system of nonlinear equations admits several types of stationary soliton solutions and that solitons which preserve helical symmetry are dynamically unstable: once formed, they decay rapidly when they propagate. On the other hand, the soliton which spontaneously breaks the local translational and helical symmetries possess the lowest energy and is a robust localized entity. We also demonstrate that this soliton is the result of an hybridization of the quasiparticle states from the two lowest degenerate bands and has an inner structure which can be described as a modulated multi-hump amplitude distribution of excitations on individual spines. The complex and composite structure of the soliton manifests itself distinctly when the soliton is moving and some interspine oscillations take place. Such a soliton structure and the interspine oscillations have previosly been observed numerically in [A.C. Scott, Phys.Rev. A 26 578 (1982)]. Here we argue that the solitons studied by A. Scott, are hybrid solitons and that the oscillations arise due to the helical symmetry of the system and result from the motion of the soliton along the $α$-helix. The frequency of the interspine oscillations is shown to be proportional to the soliton velocity.

cond-mat.other↗
arXiv2001

Multi-Skyrmion Solutions for the 6th order Skyrme Model

Following Marleau, we study an extended version of the Skyrme model to which a sixth order term has been added to the Lagrangian and we analyse some of its classical properties. We compute the multi-Skyrmion solutions numerically for up to B=5 and show that they have the same symmetries as the usual Skyrmion solutions. We use the rational map ansatz introduced by Houghton et al. to evaluate the energy and the radius for multi-skyrmion solutions of up to B=6 for both the SU(2) and SU(3) models and compare these results to the ones obtained numerically. We show that the rational map ansatz works as well for the generalised model as for the pure Skyrme model.

hep-th↗
arXiv2000

Static solutions in the U(1) gauged Skyrme model

We use a prescription to gauge the su(2) Skyrme model with a U(1) field, characterised by a conserved Baryonic current. This model reverts to the usual Skyrme model in the limit of the gauge coupling constant vanishing. We show that there exist axially symmetric static solutions with zero magnetic charge, which can be electrically either charged or uncharged. The energies of the (uncharged) gauged Skyrmions are less than the energy of the (usual) ungauged Skyrmion. For physical values of the parameters the impact of the U(1) field is very small, so that it can be treated as a perturbation to the (ungauged) spherically symmetric Hedgehog. This allows the perturbative calculation of the magnetic moment.

hep-th↗
arXiv1999

Spherically Symmetric Solutions of the SU(N) Skyrme Models

Recently we have presented in hep-th/9811071 an ansatz which allows us to construct skyrmion fields from the harmonic maps of $S\sp2$ to $CP\sp{N-1}$. In this paper we examine this construction in detail and use it to construct, in an explicit form, new static spherically symmetric solutions of the SU(N) Skyrme models. We also discuss some properties of these solutions.

hep-th↗
arXiv1998

Low Energy States in the SU(N) Skyrme Models

We show that any solution of the SU(2) Skyrme model can be used to give a topologically trivial solution of the SU(4) one. In addition, we extend the method introduced by Houghton et al. and use harmonic maps from S2 to CP(N-1) to construct low energy configurations of the SU(N) Skyrme models. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only marginally higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon (and energy) densities of the SU(3) configurations with baryon number B=2-4 are more symmetrical than their SU(2) analogues. We also present the baryon densities for the B=5 and B=6 configurations and discuss their symmetries.

hep-th↗
arXiv1997

Skyrmions and domain walls

We study the 3+1 dimensional Skyrme model with a mass term different from the usual one. We show that this new model possesses domain walls solutions. We describe how, in the equivalent 2+1 dimensional model, the Skyrmion is absorbed by the wall.

hep-th↗
arXiv1997

Nontopological structures in the baby-Skyrme model

We report our observations that the baby-Skyrme model in (2+1) dimensions possesses non-topological stationary solutions which we call pseudo-breathers. We discuss their properties and present our results on their interaction with the topological skyrmions.

hep-th↗