Untitled

Arévalo, E.; Gaididei, Yuri; Mertens, Franz G.

doi:10.1007/s10051-002-9004-2

Cited by 35 publications

(20 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Moreover, we have interpreted Eqs. (27) and (28) in the Stratonovich sense, because it assumes ξ(s, τ ) is a real noise with finite correlation time, which is then allowed to become infinitesimally small after calculating measurable quantities [33]. Notice that white noise means taking the limit of zero correlation time.…”

Section: Collective Coordinate Approachmentioning

confidence: 99%

“…Both forces couple the discrete system with a thermal bath. Here, we use the inner or hydrodynamical damping, which reads [24,28]…”

Section: The Continuum Limitmentioning

confidence: 99%

“…To analyze our problem we assume that the soliton profile, u 0 (s, τ ), is not disturbed by the noise and damping terms and that only the width and amplitude are modified. This assumption is well satisfied for low-energy solitons, whose velocity is close to the sound velocity, because tails induced by the perturbations are small in this velocity regime [28,29]. So we introduce a generalized traveling wave ansatz of the form…”

Section: Collective Coordinate Approachmentioning

confidence: 99%

See 2 more Smart Citations

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

et al. 2003

View full text Add to dashboard Cite

We study the nonequilibrium 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 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 solitons with very low energy, where the noise-induced phonons also make a significant contribution to the soliton diffusion.

show abstract

Section: Collective Coordinate Approachmentioning

confidence: 99%

“…Both forces couple the discrete system with a thermal bath. Here, we use the inner or hydrodynamical damping, which reads [24,28]…”

Section: The Continuum Limitmentioning

confidence: 99%

Section: Collective Coordinate Approachmentioning

confidence: 99%

See 1 more Smart Citation

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

et al. 2003

View full text Add to dashboard Cite

show abstract

“…(3), where m i is the mass of the oscillator, k M is the spring constant, a M is the anharmonicity parameter, and γ M is a material specific damping constant. 31,32 At the interface of LSMO and STO the differential equation is asymmetric, since k M , a M , and γ M cannot be factored out as in Eq. (3).…”

mentioning

confidence: 99%

Calibrated real-time detection of nonlinearly propagating strain waves

et al. 2012

View full text Add to dashboard Cite

Epitaxially grown metallic oxide transducers support the generation of ultrashort strain pulses in SrTiO 3 (STO) with high amplitudes up to 0.5%. The strain amplitudes are calibrated by real-time measurements of the lattice deformation using ultrafast x-ray diffraction. We determine the speed at which the strain fronts propagate by broadband picosecond ultrasonics and conclude that, above a strain level of approx. 0.2%, the compressive and tensile strain components travel at considerably different sound velocities, indicating nonlinear wave behavior. Simulations based on an anharmonic linear-chain model are in excellent accord with the experimental findings and show how the spectrum of coherent phonon modes changes with time.

show abstract

“…As in [20,21], we proceed to find a statistically equivalent Langevin system (yielding the same Fokker-Planck equation as (23) in the Stratonovich interpretation [44]), which is more convenient for further numerical and analytical studies. The Langevin-system with two independent Gaussian white noise processes reads:…”

Section: Langevin Equationsmentioning

confidence: 99%

Thermal diffusion of solitons on anharmonic chains with long-range coupling

2007

View full text Add to dashboard Cite

We extend our studies of thermal diffusion of nontopological solitons to anharmonic Fermi-Pasta-Ulam-type chains with additional long-range couplings. The observed superdiffusive behavior in the case of nearest-neighbor interaction turns out to be the dominating mechanism for the soliton diffusion on chains with long-range interactions. Using a collective variable technique in the framework of a variational analysis for the continuum approximation of the chain, we derive a set of stochastic integrodifferential equations for the collective variables (CVs) soliton position and the inverse soliton width. This set can be reduced to a statistically equivalent set of Langevin-type equations for the CV, which shares the same Fokker-Planck equation. The solution of the Langevin set and the Langevin dynamics simulations of the discrete system agree well and demonstrate that the variance of the soliton increases stronger than linearly with time (superdiffusion). This result for the soliton diffusion on anharmonic chains with long-range interactions reinforces the conjecture that superdiffusion is a generic feature of nontopological solitons.

show abstract

Untitled

Cited by 35 publications

References 0 publications

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

Thermal diffusion of supersonic solitons in an anharmonic chain of atoms

Calibrated real-time detection of nonlinearly propagating strain waves

Thermal diffusion of solitons on anharmonic chains with long-range coupling

Contact Info

Product

Resources

About