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Register a new userNonlinear conductance and noise in boundary sine-Gordon and related models
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We study a conjecture by Fendley, Ludwig and Saleur for the nonlinear conductance in the boundary sine-Gordon model. They have calculated the perturbative series of twisted partition functions, which require particular (unphysical) imaginary values of the bias, by applying the tools of Jack symmetric functions to the log-sine Coulomb gas on a circle. We have analyzed the conjectured relation between the analytically continued free energy and the nonlinear conductance in various limits. We confirm the conjecture for weak and strong tunneling, in the classical regime, and in the zero temperature limit. We also shed light on this special variant of the ${rm Im} F$-method and compare it with the real-time Keldysh approach. In addition, we address the issue of quantum statistical fluctuations.
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Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system.
In this work, we study the localization of the vector gauge field in two five-dimensional braneworlds generated by scalar fields coupled to gravity. The sine-Gordon like potentials are employed to produce different thick brane setups. A zero mode localized is obtained, and we show the existence of reverberations with the wave solutions indicating a quasi-localized massive mode. More interesting results are achieved when we propose a double sine-Gordon potential to the scalar field. The resulting thick brane shows a more detailed topology with the presence of an internal structure composed by two kinks. The massive spectrum of the gauge field is revalued on this scenario revealing the existence of various resonant modes. Furthermore, we compute the corrections to Coulomb law coming from these massive KK vector modes in these thick scenarios, where is concluded that the dilaton parameter regulates these corrections.
We discuss the nature of criticality in the $beta^2 = 2 pi N$ self-dual extention of the sine-Gordon model. This field theory is related to the two-dimensional classical XY model with a N-fold degenerate symmetry-breaking field. We briefly overview the already studied cases $N=2,4$ and analyze in detail the case N=3 where a single phase transition in the three-state Potts universality class is expected to occur. The Z$_3$ infrared critical properties of the $beta^2 = 6 pi$ self-dual sine-Gordon model are derived using two non-perturbative approaches. On one hand, we map the model onto an integrable deformation of the Z$_4$ parafermion theory. The latter is known to flow to a massless Z$_3$ infrared fixed point. Another route is based on the connection with a chirally asymmetric, su(2)$_4$ $otimes$ su(2)$_1$ Wess-Zumino-Novikov-Witten model with anisotropic current-current interaction, where we explore the existence of a decoupling (Toulouse) point.
We present a comparative numerical study of the ordered and the random two-dimensional sine-Gordon models on a lattice. We analytically compute the main features of the expected high temperature phase of both models, described by the Edwards-Wilkinson equation. We then use those results to locate the transition temperatures of both models in our Langevin dynamics simulations. We show that our results reconcile previous contradictory numerical works concerning the superroughening transition in the random sine-Gordon model. We also find evidence supporting the existence of two different low temperature phases for the disordered model. We discuss our results in view of the different analytical predictions available and comment on the nature of these two putative phases.
Nonlinear space-time dynamics, defined in terms of celebrated solitonic equations, brings indispensable tools for understanding, prediction and control of complex behaviors in both physical and life sciences. In this paper, we review sine-Gordon solitons, kinks and breathers as models of nonlinear excitations in complex systems in physics and in living cellular structures, both intra-cellular (DNA, protein folding and microtubules) and inter-cellular (neural impulses and muscular contractions). Key words: Sine-Gordon solitons, kinks and breathers, DNA, Protein folding, Microtubules, Neural conduction, Muscular contraction
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