arXiv subjects

Sergej Flach

Publications and source records attributed to Sergej Flach.

113 records · Page 7Linked to original sources

arXiv2004

Nonlinear Fano resonance and bistable wave transmission

We consider a discrete model that describes a linear chain of particles coupled to a single-site defect with instantaneous Kerr nonlinearity. We show that this model can be regarded as a nonlinear generalization of the familiar Fano-Anderson model, and it can generate the amplitude depended bistable resonant transmission or reflection. We identify these effects as the nonlinear Fano resonance, and study its properties for continuous waves and pulses.

cond-mat.soft↗

arXiv2004

Discrete breathers in thermal equilibrium: distributions and energy gaps

We study a discrete two-dimensional nonlinear system that allows for discrete breather solutions. We perform a spectral analysis of the lattice dynamics at thermal equilibrium and use a cooling technique to measure the amount of breathers at thermal equilibrium. Our results confirm the existence of an energy threshold for discrete breathers. The cooling method provides with a novel computational technique of measuring and analyzing discrete breather distribution properties in thermal equilibrium.

cond-mat.stat-mech↗

arXiv1997

Incremental expansions for Hubbard-Peierls systems

The ground state energies of infinite half-filled Hubbard-Peierls chains are investigated combining incremental expansion with exact diagonalization of finite chain segments. The ground state energy of equidistant infinite Hubbard (Heisenberg) chains is calculated with a relative error of less than $3 \cdot 10^{-3}$ for all values of $U$ using diagonalizations of 12-site (20-site) chain segm ents. For dimerized chains the dimerization order parameter $d$ as a function of the onsite repulsion interaction $U$ has a maximum at nonzero values of $U$, if the electron-phonon coupling $g$ is lower than a critical value $g_c$. The critical value $g_c$ is found with high accuracy to be $g_c=0.69$. For smaller values of $g$ the position of the maximum of $d(U)$ is approximately $3t$, and rapidly tends to zero as $g$ approaches $g_c$ from below. We show how our method can be applied to calculate breathers for the problem of phonon dynamics in Hubbard-Peierls systems.

cond-mat↗

arXiv1995

Tangent Bifurcation of Band Edge Plane Waves, Dynamical Symmetry Breaking and Vibrational Localization

We study tangent bifurcation of band edge plane waves in nonlinear Hamiltonian lattices. The lattice is translationally invariant. We argue for the breaking of permutational symmetry by the new bifurcated periodic orbits. The case of two coupled oscillators is considered as an example for the perturbation analysis, where the symmetry breaking can be traced using Poincare maps. Next we consider a lattice and derive the dependence of the bifurcation energy on the parameters of the Hamiltonian function in the limit of large system sizes. A necessary condition for the occurence of the bifurcation is the repelling of the band edge plane wave's frequency from the linear spectrum with increasing energy. We conclude that the bifurcated orbits will consequently exponentially localize in the configurational space.

patt-sol↗

arXiv1995

Obtaining Breathers in Nonlinear Hamiltonian Lattices

We present a numerical method for obtaining high-accuracy numerical solutions of spatially localized time-periodic excitations on a nonlinear Hamiltonian lattice. We compare these results with analytical considerations of the spatial decay. We show that nonlinear contributions have to be considered, and obtain very good agreement between the latter and the numerical results. We discuss further applications of the method and results.

patt-sol↗