arXiv subjects

Niurka R. Quintero

Publications and source records attributed to Niurka R. Quintero.

43 records · Page 3Linked to original sources

arXiv2000

Resonances in the dynamics of $ϕ^4$ kinks perturbed by ac forces

We study the dynamics of $ϕ^4$ kinks perturbed by an ac force, both with and without damping. We address this issue by using a collective coordinate theory, which allows us to reduce the problem to the dynamics of the kink center and width. We carry out a careful analysis of the corresponding ordinary differential equations, of Mathieu type in the undamped case, finding and characterizing the resonant frequencies and the regions of existence of resonant solutions. We verify the accuracy of our predictions by numerical simulation of the full partial differential equation, showing that the collective coordinate prediction is very accurate. Numerical simulations for the damped case establish that the strongest resonance is the one at half the frequency of the internal mode of the kink. In the conclusion we discuss on the possible relevance of our results for other systems, especially the sine-Gordon equation. We also obtain additional results regarding the equivalence between different collective coordinate methods applied to this problem.

cond-mat.stat-mech↗

arXiv2000

On the existence of internal modes of sine-Gordon kinks

We study whether or not sine-Gordon kinks exhibit internal modes or ``quasimodes.'' By considering the response of the kinks to ac forces and initial distortions, we show that neither intrinsic internal modes nor ``quasimodes'' exist in contrast to previous reports. However, we do identify a different kind of internal mode bifurcating from the bottom edge of the phonon band which arises from the discretization of the system in the numerical simulations, thus confirming recent predictions.

cond-mat.stat-mech↗

arXiv2000

Thermal diffusion of sine-Gordon solitons

We analyze the diffusive motion of kink solitons governed by the thermal sine-Gordon equation. We analytically calculate the correlation function of the position of the kink center as well as the diffusion coefficient, both up to second-order in temperature. We find that the kink behavior is very similar to that obtained in the overdamped limit: There is a quadratic dependence on temperature in the diffusion coefficient that comes from the interaction among the kink and phonons, and the average value of the wave function increases with $\sqrt{t}$ due to the variance of the centers of individual realizations and not due to kink distortions. These analytical results are fully confirmed by numerical simulations.

cond-mat.stat-mech↗

arXiv1999

Anomalous resonance phenomena of solitary waves with internal modes

We investigate the non-parametric, pure ac driven dynamics of nonlinear Klein-Gordon solitary waves having an internal mode of frequency $Ω_i$. We show that the strongest resonance arises when the driving frequency $δ=Ω_i/2$, whereas when $δ=Ω_i$ the resonance is weaker, disappearing for nonzero damping. At resonance, the dynamics of the kink center of mass becomes chaotic. As we identify the resonance mechanism as an {\em indirect} coupling to the internal mode due to its symmetry, we expect similar results for other systems.

cond-mat.stat-mech↗

arXiv1999

Overdamped sine-Gordon kink in a thermal bath

We study the sine-Gordon kink diffusion at finite temperature in the overdamped limit. By means of a general perturbative approach, we calculate the first- and second-order (in temperature) contributions to the diffusion coefficient. We compare our analytical predictions with numerical simulations. The good agreement allows us to conclude that, up to temperatures where kink-antikink nucleation processes cannot be neglected, a diffusion constant linear and quadratic in temperature gives a very accurate description of the diffusive motion of the kink. The quadratic temperature dependence is shown to stem from the interaction with the phonons. In addition, we calculate and compute the average value $<ϕ(x,t)>$ of the wave function as a function of time and show that its width grows with $\sqrt{t}$. We discuss the interpretation of this finding and show that it arises from the dispersion of the kink center positions of individual realizations which all keep their width.

cond-mat.stat-mech↗

arXiv1998

ac driven sine-Gordon solitons: dynamics and stability

The ac driven sine-Gordon equation is studied analytically and numerically, with the aim of providing a full description of how soliton solutions behave. To date, there is much controversy about when ac driven dc motion is possible. Our work shows that kink solitons exhibit dc or oscillatory motion depending on the relation between their initial velocity and the force parameters. Such motion is proven to be impossible in the presence of damping terms. For breathers, the force amplitude range for which they exist when dissipation is absent is found. All the analytical results are compared with numerical simulations, which in addition exhibit no dc motion at all for breathers, and an excellent agreement is found. In the conclusion, the generality of our results and connections to others systems for which a similar phenomenology may arise are discussed.

cond-mat↗

arXiv1997

DC motion of ac driven sine-Gordon solitons

We investigate the possibility of dc soliton motion sustained by pure ac driving in the sine-Gordon model. We show by means of the collective coordinate formalism that ac driving induces a net dc velocity whose modulus and direction depend on the driving phase. Numerical simulations of the full sine-Gordon equation confirm the correctness and accuracy of this prediction. Non trivial cases when dc soliton motion is transformed into oscillatory as well as the effects of damping are analyzed. Our results settle a long standing issue about the existence and characteristics of this phenomenon, whose possible appearance in other systems is also discussed.

cond-mat↗