arXiv subjects

Wojtek J. Zakrzewski

Publications and source records attributed to Wojtek J. Zakrzewski.

At least 19 recordsLinked to original sources

arXiv2020

Long-range donor-acceptor electron transport mediated by alpha-helices

We study the long-range electron and energy transfer mediated by a polaron on an $α$-helix polypeptide chain coupled to donor and acceptor molecules at opposite ends of the chain. We show that for specific parameters of the system, an electron initially located on the donor can tunnel onto the $α$-helix, forming a polaron which then travels to the other extremity of the polypeptide chain where it is captured by the acceptor. We consider three families of couplings between the donor, acceptor and the chain, and show that one of them can lead to a 90\% efficiency of the electron transport from donor to acceptor. We also show that this process remains stable at physiological temperatures in the presence of thermal fluctuations in the system.

cond-mat.other↗

arXiv2018

Self-dual sectors for scalar field theories in (1 + 1) dimensions

We use ideas of generalized self-duality conditions to construct real scalar field theories in (1 + 1)-dimensions with exact self dual sectors. The approach is based on a pre-potential U that defines the topological charge and the potential energy of these theories. In our algebraic method to construct the required pre-potentials we use the representation theory of Lie groups. This approach leads naturally to an infinite set of degenerate vacua and so to topologically non-trivial self-dual solutions of these models. We present explicit examples for the groups SU(2), SU(3) and SO(5) and discuss some properties of these solutions.

hep-th↗

arXiv2016

Quasi-integrable deformations of the $SU(3)$ Affine Toda Theory

We consider deformations of the $SU(3)$ Affine Toda theory (AT) and investigate the integrability properties of the deformed theories. We find that for some special deformations all conserved quantities change to being conserved only asymptotically, {\it i.e.} in the process of the scattering of two solitons these charges do vary in time, but they return, after the scattering, to the values they had prior to the scattering. This phenomenon, which we have called quasi-integrability, is related to special properties of the two-soliton solutions under space-time parity transformations. Some properties of the AT solitons are discussed, especially those involving interesting static multi-soliton solutions. We support our analytical studies with detailed numerical ones in which the time evolution has been simulated by the 4th order Runge-Kutta method. We find that for some perturbations the solitons repel and for the others they form a quasi-bound state. When we send solitons towards each other they can repel when they come close together with or without `flipping' the fields of the model. The solitons radiate very little and appear to be stable. These results support the ideas of quasi-integrability, {\it i.e.} that many effects of integrability also approximately hold for the deformed models.

hep-th↗

arXiv2015

General solutions of the supersymmetric $\mathbb{C}P^2$ sigma model and its generalisation to $\mathbb{C}P^{N-1}$

A new approach for the construction of finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study the $\mathbb{C}P^2$ model in detail and present its solutions in an explicit form. We also show how to generalise this construction to $N>3$.

math-ph↗

arXiv2014

Geometry of surfaces associated to grassmannian sigma models

We investigate the geometric characteristics of constant gaussian curvature surfaces obtained from solutions of the $G(m,n)$ sigma model. Most of these solutions are related to the Veronese sequence. We show that we can distinguish surfaces with the same gaussian curvature using additional quantities like the topological charge and the mean curvature. The cases of $G(1,n)=\mathbb{C}P^{n-1}$ and $G(2,n)$ are used to illustrate these characteristics.

math-ph↗

arXiv2014

Constant curvature surfaces of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model

Constant curvature surfaces are constructed from the finite action solutions of the supersymmetric $\mathbb{C}P^{N-1}$ sigma model. It is shown that there is a unique holomorphic solution which leads to constant curvature surfaces: the generalized Veronese curve. We give a general criterion to construct non-holomorphic solutions of the model. We extend our analysis to general supersymmetric Grassmannian models.

math-ph↗

arXiv2014

Breather-like structures in modified sine-Gordon models

We report analytical and numerical results on breather-like field configurations in a theory which is a deformation of the integrable sine-Gordon model in (1+1) dimensions. The main motivation of our study is to test the ideas behind the recently proposed concept of quasi-integrability, which emerged from the observation that some field theories present an infinite number of quantities which are asymptotically conserved in the scattering of solitons, and periodic in time in the case of breather-like configurations. Even though the mechanism responsible for such phenomena is not well understood yet, it is clear that special properties of the solutions under a space-time parity transformation play a crucial role. The numerical results of the present paper give support for the ideas on quasi-integrability, and it is found that extremely long-lived breather configurations satisfy these parity properties. We also report on a mechanism, particular to the theory studied here, that favours the existence of long lived breathers even in cases of significant deformations of the sine-Gordon potential.

hep-th↗

arXiv2013

Numerical and analytical tests of quasi-integrability in modified Sine-Gordon models

Following our attempts to define quasi-integrability in which we related this concept to a particular symmetry of the two-soliton function we check this condition in three classes of modified Sine-Gordon models in (1+1) dimensions. We find that the numerical results seen in various scatterings of two solitons and in the time evolution of breather-like structures support our ideas about the symmetry of the field configurations and its effects on the anomalies of the conservation laws of the charges.

hep-th↗

arXiv2013

The concept of quasi-integrability

We show that certain field theory models, although non-integrable according to the usual definition of integrability, share some of the features of integrable theories for certain configurations. Here we discuss our attempt to define a "quasi-integrable theory", through a concrete example: a deformation of the (integrable) sine-Gordon potential. The techniques used to describe and define this concept are both analytical and numerical. The zero-curvature representation and the abelianisation procedure commonly used in integrable field theories are adapted to this new case and we show that they produce asymptotically conserved charges that can then be observed in the simulations of scattering of solitons.

hep-th↗

arXiv2013

A Skyrme-like model with an exact BPS bound

We propose a new Skyrme-like model with fields taking values on the sphere S^3 or, equivalently, on the group SU(2). The action of the model contains a quadratic kinetic term plus a quartic term which is the same as that of the Skyrme-Faddeev model. The novelty of the model is that it possess a first order Bogomolny type equation whose solutions automatically satisfy the second order Euler-Lagrange equations. It also possesses a lower bound on the static energy which is saturated by the Bogomolny solutions. Such Bogomolny equation is equivalent to the so-called force free equation used in plasma and solar Physics, and which possesses large classes of solutions. An old result due to Chandrasekhar prevents the existence of finite energy solutions for the force free equation on the entire tridimensional space R^3. We construct new exact finite energy solutions to the Bogomolny equations for the case where the space is the three-sphere S^3, using toroidal like coordinates.

hep-th↗

arXiv2013

Constant curvature solutions of Grassmannian sigma models: (2) Non-holomorphic solutions

We generalize here our general procedure for constructing constant curvature maps of 2-spheres into Grassmannian manifolds G(m,n) this time concentrating our attention on maps which are non-holomorphic. We present some expressions describing these solutions in the general case and discuss how to use these results to construct solutions of constant curvature. We also discuss possible values of this constant curvature.

math-ph↗

arXiv2012

The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an infinite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V = |psi|^(2(2+epsilon)), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

hep-th↗

arXiv2012

Constant curvature solutions of Grassmannian sigma models: (1) Holomorphic solutions

We present a general formula for the Gaussian curvature of curved holomorphic 2-spheres in Grassmannian manifolds G(m, n). We then show how to construct such solutions with constant curvature. We also make some relevant conjectures for the admissible constant curvatures in G(m, n) and give some explicit expressions, in particular, for G(2, 4) and G(2, 5).

math-ph↗

arXiv2012

Darkon fluid - a model for the dark sector of the Universe?

We introduce darkons as fluid particles of a Galilean massless self-gravitating fluid. This fluid exhibits anisotropic scaling with $z=5/3$. The minimal gravitational coupling dynamically generates a gravitational mass density of either sign. Hence such fluid may serve as a model for the dark sector of the Universe. Its cosmological solutions give a deceleration phase for the early Universe and an acceleration phase for the late Universe. Will the steady flow solutions lead to a confining potential and so a possible model for halos?

hep-th↗

arXiv2010

The concept of quasi-integrability: a concrete example

We use the deformed sine-Gordon models recently presented by Bazeia et al to discuss possible definitions of quasi-integrability. We present one such definition and use it to calculate an infinite number of quasi-conserved quantities through a modification of the usual techniques of integrable field theories. Performing an expansion around the sine-Gordon theory we are able to evaluate the charges and the anomalies of their conservation laws in a perturbative power series in a small parameter which describes the "closeness" to the integrable sine-Gordon model. Our results indicate that in the case of the two-soliton scattering the charges are conserved asymptotically, i.e. their values are the same in the distant past and future, when the solitons are well separated. We back up our results with numerical simulations which also demonstrate the existence of long lived breather-like and wobble-like states in these models.

hep-th↗

arXiv2009

Q-ball Scattering on Barriers and Holes in 1 and 2 Spatial Dimensions

We discuss various scattering properties of non-topological solitons, Q-balls, on potential obstructions in (1+1) and (2+1) dimensions. These obstructions, barriers and holes, are inserted into the potential of the theory via the coupling parameter, ie \tildeλ, that is effective only in a certain region of space. When \tildeλ> 1 the obstruction is a barrier and when 0 < \tildeλ< 1 the obstruction is a hole. The dynamics of Q-balls on such obstructions in (1+1) dimensions is shown to be very similar to that of topological solitons provided that the Q-balls are stable. In (2+1) dimensions, numerical simulations have shown some differences from the dynamics of topological solitons. We discuss these differences in some detail.

math-ph↗

arXiv2008

Scattering of Topological Solitons on Barriers and Holes of Deformed Sine-Gordon Models

We study scattering properties of topological solitons in two classes of models, which are generalizations of the Sine-Gordon model and which have recently been proposed by Bazeia et al. These two classes of models depend on an integer parameter n which, when n=2(for the first class) and n=1 (for the second class), reduce to the Sine-Gordon model. We take the soliton solutions of these models (generalizations of the 'kink' solution of the Sine-Gordon model) and consider their scattering on potential holes and barriers. We present our results for n=1,...6. We find that, like in the Sine Gordon models, the scattering on the barrier is very elastic while the scattering on the hole is inelastic and can at times, lead to a reflection. We discuss the dependence of our results on n and find that the critical velocity for the transmission through the hole is lowest for n=3.

hep-th↗

arXiv2008

Skyrme Model with Different Mass Terms

We consider a one parameter family of mass terms for the Skyrme model that disfavours shell-like configurations for multi-baryon classical solutions. We argue that a model with such mass terms can provide a better description of nuclei as shell like configurations are now less stable than in the traditional massive Skyrme model

hep-th↗