Marc Thilo Figge

New Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations

For the recently introduced algorithms to solve the time-dependent Maxwell equations [J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001)], we construct a variable grid implementation and an improved spatial discretization implementation that preserve the exceptional property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.

Solving the Maxwell equations by the Chebyshev method: a one-step finite-difference time-domain algorithm

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.

Higher-order unconditionally stable algorithms to solve the time-dependent Maxwell equations

For the recently introduced algorithms to solve the time-dependent Maxwell equations [J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001)], we construct a variable grid implementation and an improved spatial discretization implementation that preserve the exceptional property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.

Disorder-induced solitons in conjugated polymers

We show that weak off-diagonal disorder in degenerate ground-state conjugated polymers results in a finite density of randomly positioned kinks (solitons and antisolitons) in the lattice dimerization. For realistic values of the disorder, these kinks should clearly show up in the optical and magnetic properties.

Density of Neutral Solitons in Weakly Disordered Peierls Chains

We study the effects of weak off-diagonal disorder on Peierls systems with a doubly degenerate ground state. We show that for these systems disorder in the electron hopping amplitudes induces a finite density of solitons in the minimal-energy lattice configuration of a single chain. These disorder-induced dimerization kinks are neutral and have spin 1 . Using a continuum model for the Peierls chain and treating the lattice classically, we analytically calculate the average free energy and density of kinks. We compare these results to numerical calculations for a discrete model and discuss the implications of the kinks for the optical and magnetic properties of the conjugated polymer trans-polyacetylene.

Disorder-induced neutral solitons in degenerate ground state polymers

We study the effects of weak off-diagonal disorder on π-conjugated polymers with a doubly degenerate ground-state. We find that disorder induces a finite density of neutral solitons in the lattice dimerization of a polymer chain. Interchain interactions result in a linear potential between the solitons and, if sufficiently strong, bind them into pairs resulting in an exponential suppression of the soliton density. As neutral solitons carry spin 1/2, they contribute to the polymers magnetic properties. We calculate the magnetic susceptibility and suggest measurements of the magnetic susceptibility in trans-polyacetylene at low temperatures.

Magnetic susceptibility due to disorder-induced neutral solitons in interacting polymer chains

We study the magnetic response due to neutral solitons induced by disorder in polymer materials. We account for interchain interactions, which, if sufficiently strong, result in a bond-ordered phase, in which the neutral solitons are bound into pairs. We analytically calculate the corresponding pair-size distribution. As the spins of the solitons have a distance-dependent antiferromagnetic coupling, this allows us to calculate the magnetic susceptibility in the ordered phase. At low temperatures, the result deviates from the usual Curie behavior in a way that depends on the relative strength of the disorder and the interchain interactions. We compare our results to the observed magnetic susceptibility of transpolyacetylene and we suggest experiments extending towards lower temperatures. [S0163-1829(99)02721-6].