Asymptotic analysis of combined breather–kink modes in a Fermi–Pasta–Ulam chain

Butt, Imran A; Wattis, Jonathan A. D.

doi:10.1016/j.physd.2007.05.003

Cited by 7 publications

(7 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The FPU potential can be derived as a fourth-order Taylor expansion of a generic nearest-neighbor interaction potential with respect to the equilibrium positions of the chain. For the sake of simplicity we will neglect cubic terms, which are known to give rise to specific topological (kink) excitations in the system, where also the equilibrium position of atoms are shifted and also to more complex combined breather-kink modes [73].…”

Section: Exciton-lattice Coupled Dynamicsmentioning

confidence: 99%

Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

et al. 2015

View full text Add to dashboard Cite

The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system. ( ) ( ) and J J u u . 5

show abstract

Section: Exciton-lattice Coupled Dynamicsmentioning

confidence: 99%

Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

et al. 2015

View full text Add to dashboard Cite

show abstract

“…To investigate the asymptotic moving breather-kink mode found in [6] we perform a multiple-scales expansion for the onedimensional FPU form…”

Section: Formulationmentioning

confidence: 99%

“…The work of Butt and Wattis [6] uses a simpler asymptotic ansatz to show how breather-kink modes might arise in the Wang [4] finds that the cubic anharmonicity of lattices causes high-frequency modes to suffer a long wavelength modulation. Simulations confirming this effect exhibit breathing-kink modes.…”

Section: Introductionmentioning

confidence: 99%

Combined breathing–kink modes in the FPU lattice

Wattis

Pickering

Gordoa

2011

Physica D: Nonlinear Phenomena

Self Cite

View full text Add to dashboard Cite

“…The kink-breather solution is a breather with a kink wave background. The asymptotic form of the combined kink-breather mode in Fermi-Pasta-Ulam (FPU) chains is analyzed, and it is shown that the amplitude of the breather in the kinkbreather wave can be arbitrarily small [24]. Several interesting transition phenomena of a loop-like kinkbreather in the Vakhnenko equation (VE) are helpful to understand the compressed mechanism to pulses in ultra fast optics [25].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interactions of two-kink-breather solution in Yu-Toda-Sasa-Fukuyama equation by modulated phase shift

Chen

Wang

2023

Phys. Scr.

View full text Add to dashboard Cite

The waveforms and nonlinear interactions of a two-kink-breather solution of the (2 + 1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) equation are studied by modulated phase shift. First, we obtain the parameter relationsthat respective affect the amplitudes of the kink and the breather solutions in kink-breather solution. Then, itis proved that the solutions in the regions near the singular boundaries of the phase shift can be divided intothree kinds of solutions with repulsive or attractive interactions, in addition to the two-kink-breather solution.Interestingly, a breather soliton acts as a messenger to transfer energy during the repulsive interaction between thetwo kink-breather solutions with small amplitudes.

show abstract

Asymptotic analysis of combined breather–kink modes in a Fermi–Pasta–Ulam chain

Cited by 7 publications

References 27 publications

Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

Transport of quantum excitations coupled to spatially extended nonlinear many-body systems

Combined breathing–kink modes in the FPU lattice

Nonlinear interactions of two-kink-breather solution in Yu-Toda-Sasa-Fukuyama equation by modulated phase shift

Contact Info

Product

Resources

About