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Franz G. Mertens

Publications and source records attributed to Franz G. Mertens.

At least 55 records · Page 3Linked to original sources
arXiv2003

Internal mode mechanism for collective energy transport in extended systems

We study directed energy transport in homogeneous nonlinear extended systems in the presence of homogeneous ac forces and dissipation. We show that the mechanism responsible for unidirectional motion of topological excitations is the coupling of their internal and translation degrees of freedom. Our results lead to a selection rule for the existence of such motion based on resonances that explains earlier symmetry analysis of this phenomenon. The direction of motion is found to depend both on the initial and the relative phases of the two harmonic drivings, even in the presence of noise.

cond-mat.stat-mech↗
arXiv2003

Amplitudes for magnon scattering by vortices in two-dimensional weakly easy-plane ferromagnets

We study magnon modes in the presence of a vortex in a circular easy-plane ferromagnet. The problem of vortex-magnon scattering is investigated for partial modes with different values of the azimuthal quantum number m over a wide range of wave numbers. The analysis was done by combining analytical and numerical calculations in the continuum limit with numerical diagonalization of adequately large discrete systems. The general laws governing vortex-magnon interactions are established. We give simple physical explanations of the scattering results: the splitting of doublets for the modes with opposite signs of $m$, which takes place for the long wavelength limit, is an analogue of the Zeeman splitting in the effective magnetic field of the vortex. A singular behavior for the scattering amplitude, $σ_m\propto k$, takes place as $k$ diverges; it corresponds to the generalized Levinson theorem and can be explained by the singular behavior of the effective magnetic field at the origin.

cond-mat.str-el↗
arXiv2003

Soliton ratchets out of point-like inhomogeneities

We introduce and study a novel design for a ratchet potential for soliton excitations. The potential is implemented by means of an array of point-like (delta) inhomogeneities in an otherwise homogeneous potential. We develop a collective coordinate theory that predicts that the effective potential acting on the soliton is periodic but asymmetric and gives rise to the ratchet effect. Numerical simulations fully confirm this prediction; quantitative agreement is reached by an improved version of the theory. Although we specifically show that it is most interesting for building Josephson junction ratchets capable to rectify time-symmetric ac forces, the proposed mechanism is very general and can appear in many contexts, including biological systems.

cond-mat.mes-hall↗
arXiv2002

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

We study the non-equilibrium diffusion dynamics of supersonic lattice solitons in a classical chain of atoms with nearest-neighbor interactions coupled to a heat bath. As a specific example we choose an interaction with cubic anharmonicity. The coupling between the system and a thermal bath with a given temperature is made by adding noise, delta-correlated in time and space, and damping to the set of discrete equations of motion. Working in the continuum limit and changing to the sound velocity frame we derive a Korteweg-de Vries equation with noise and damping. We apply a collective coordinate approach which yields two stochastic ODEs which are solved approximately by a perturbation analysis. This finally yields analytical expressions for the variances of the soliton position and velocity. We perform Langevin dynamics simulations for the original discrete system which fully confirm the predictions of our analytical calculations, namely noise-induced superdiffusive behavior which scales with the temperature and depends strongly on the initial soliton velocity. A normal diffusion behavior is observed for very low-energy solitons where the noise-induced phonons also make a significant contribution to the soliton diffusion.

cond-mat.soft↗
arXiv2001

Anomalies of ac driven solitary waves with internal modes: Nonparametric resonances induced by parametric forces

We study the dynamics of kinks in the $ϕ^4$ model subjected to a parametric ac force, both with and without damping, as a paradigm of solitary waves with internal modes. By using a collective coordinate approach, we find that the parametric force has a non-parametric effect on the kink motion. Specifically, we find that the internal mode leads to a resonance for frequencies of the parametric driving close to its own frequency, in which case the energy of the system grows as well as the width of the kink. These predictions of the collective coordinate theory are verified by numerical simulations of the full partial differential equation. We finally compare this kind of resonance with that obtained for non-parametric ac forces and conclude that the effect of ac drivings on solitary waves with internal modes is exactly the opposite of their character in the partial differential equation.

cond-mat.stat-mech↗
arXiv2001

Internal Modes and Magnon Scattering on Topological Solitons in 2d Easy-Axis Ferromagnets

We study the magnon modes in the presence of a topological soliton in a 2d Heisenberg easy-axis ferromagnet. The problem of magnon scattering on the soliton with arbitrary relation between the soliton radius R and the "magnetic length" Delta_0 is investigated for partial modes with different values of the azimuthal quantum numbers m. Truly local modes are shown to be present for all values of m, when the soliton radius is enough large. The eigenfrequencies of such internal modes are calculated analytically on limiting case of a large soliton radius and numerically for arbitrary soliton radius. It is demonstrated that the model of an isotropic magnet, which admits an exact analytical investigation, is not adequate even for the limit of small radius solitons, R<<Delta_0: there exists a local mode with nonzero frequency. We use the data about local modes to derive the effective equation of soliton motion; this equation has the usual Newtonian form in contrast to the case of the easy-plane ferromagnet. The effective mass of the soliton is found.

cond-mat.str-el↗
arXiv2000

Multi-component structure of nonlinear excitations in systems with length-scale competition

We investigate the properties of nonlinear excitations in different types of soliton bearing systems with long-range dispersive interaction. We show that length-scale competition in such systems universally results in a multi-component structure of nonlinear excitations and can lead to a new type of multistability: coexistence of different nonlinear excitations at the same value of the spectral parameter (i.e., velocity in the case of anharmonic lattices or frequency in nonlinear Schroedinger models).

cond-mat.soft↗
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

Solitons in anharmonic chains with ultra-long-range interatomic interactions

We study the influence of long-range interatomic interactions on the properties of supersonic pulse solitons in anharmonic chains. We show that in the case of ultra-long-range (e.g., screened Coulomb) interactions three different types of pulse solitons coexist in a certain velocity interval: one type is unstable but the two others are stable. The high-energy stable soliton is broad and can be described in the quasicontinuum approximation. But the low-energy stable soliton consists of two components, short-range and long-range ones, and can be considered as a bound state of these components.

patt-sol↗
arXiv1999

On the semiclassical treatment of anharmonic quantum oscillators via coherent states - The Toda chain revisited

We use coherent states as a time-dependent variational ansatz for a semiclassical treatment of the dynamics of anharmonic quantum oscillators. In this approach the square variance of the Hamiltonian within coherent states is of particular interest. This quantity turns out to have natural interpretation with respect to time-dependent solutions of the semiclassical equations of motion. Moreover, our approach allows for an estimate of the decoherence time of a classical object due to quantum fluctuations. We illustrate our findings at the example of the Toda chain.

cond-mat↗
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↗
arXiv1999

Stochastic vortex dynamics in two-dimensional easy-plane ferromagnets: Multiplicative versus additive noise

We study how thermal fluctuations affect the dynamics of vortices in the two-dimensional classical, ferromagnetic, anisotropic Heisenberg model depending on their additive or multiplicative character. Using a collective coordinate theory, we analytically show that multiplicative noise, arising from fluctuations in the local field term of the Landau-Lifshitz equations, and Langevin-like additive noise both have the same effect on vortex dynamics (within a very plausible assumption consistent with the collective coordinate approach). This is a non-trivial result, as multiplicative and additive noises usually modify the dynamics quite differently. We also carry out numerical simulations of both versions of the model finding that they indeed give rise to very similar vortex dynamics.

cond-mat↗
arXiv1998

Vortices in Quantum Spin Systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices.

cond-mat↗