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Register a new userPhonon modes in the Frenkel-Kontorova chain: exponential localization and the number theory properties of frequency bands
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We study numerically phonon modes of the classical one-dimensional Frenkel-Kontorova chain, in the regime of pinned phase characterized by the phonon gap and devils staircase, as well as by a large number of states (configurational excitations), which energy splitting from the ground state is exponentially small. We demonstrate, these states behave like disorder media: their phonon modes are {it exponentially} localized, in contrast to the phonon modes in the ground state, where phonons are {it prelocalized} only. We demonstrate also, the phonon frequency spectrum of the ground state has an hierarchical structure, a direct manifestation of hierarchical spatial structure, found for the ground state of the FK chain in our recent work.
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By means of atomistic simulations, we demonstrate that a dislocation core exhibits intermittent quasistatic restructuring during incremental shear within the same Peierls valley. This can be regarded as a stick-slip transition, which is also reproduced for a one-dimensional Frenkel-Kontorova chain under rigid boundary conditions. This occurs due to a discontinuous jump in an order parameter of the system, which signifies the extent of region forbidden for the presence of particles in the chain. The stick-slip phenomenon observed in the dislocation core is also shown to be reflected after dimensionality reduction of the multidimensional atomic coordinates, which provides a basis for comparison with the simple one-dimensional chain.
The Frenkel-Kontorova chain with a free end is used to study initiation and propagation of crowdions (anti-kinks) caused by impact of a molecule consisting of K atoms. It is found that molecules with 1 < K < 10 are more efficient in initiation of crowdions as compared to single atom (K = 1) because total energy needed to initiate the crowdions by molecules is smaller. This happens because single atom can initiate in the chain only sharp, fast-moving crowdions that requires a relatively large energy. Molecule has finite length, that is why it is able to excite a wider crowdion with a smaller velocity and smaller energy. Our results can shed light on the atomistic mechanisms of mass transfer in crystals subject to atom and molecule bombardment.
We solved the Frenkel-Kontorova model with the potential $V(u)= -frac{1}{2} |lambda|(u-{rm Int}[u]-frac{1}{2})^2$ exactly. For given $|lambda|$, there exists a positive integer $q_c$ such that for almost all values of the tensile force $sigma$, the winding number $omega$ of the ground state configuration is a rational number in the $q_c$-th level Farey tree. For fixed $omega=p/q$, there is a critical $lambda_c$ when a first order phase transition occurs. This phase transition can be understood as the dissociation of a large molecule into two smaller ones in a manner dictated by the Farey tree. A kind of ``commensurate-incommensurate transition occurs at critical values of $sigma$ when two sizes of molecules co-exist. ``Soliton in the usual sense does not exist but induces a transformation of one size of molecules into the other.
A 1D model of interacting particles moving over a periodic substrate and in a position dependent temperature profile is considered. When the substrate and the temperature profile are spatially asymmetric a center-of-mass velocity develops, corresponding to a directed transport of the chain. This autonomous system can thus transform heath currents into motion. The model parameters can be tuned such that the particles exhibit a crossover from an ordered configuration on the substrate to a disordered one, the maximal motor effect being reached in such a disordered phase. In this case the manybody motor outperforms the single motor system, showing the great importance of collective effects in microscopic thermal devices. Such collective effects represent thus a free resource that can be exploited to enhance the dynamic and thermodynamic performances in microscopic machines.
In this work we include the elastic scattering of longitudinal electromagnetic waves in transport theory using a medium filled with point-like, electric dipoles. The interference between longitudinal and transverse waves creates two new channels among which one allows energy transport. This picture is worked out by extending the independent scattering framework of radiative transfer to include binary dipole-dipole interactions. We calculate the diffusion constant of light in the new transport channel and investigate the role of longitudinal waves in other aspects of light diffusion by considering the density of states, equipartition, and Lorentz local field. In the strongly scattering regime, the different transport mechanisms couple and impose a minimum conductivity of electromagnetic waves, thereby preventing Anderson localization of light in the medium. We extend the self-consistent theory of localization and compare the predictions to extensive numerical simulations.
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