1,375 research outputs found
Resonances and Twist in Volume-Preserving Mappings
The phase space of an integrable, volume-preserving map with one action and
angles is foliated by a one-parameter family of -dimensional invariant
tori. Perturbations of such a system may lead to chaotic dynamics and
transport. We show that near a rank-one, resonant torus these mappings can be
reduced to volume-preserving "standard maps." These have twist only when the
image of the frequency map crosses the resonance curve transversely. We show
that these maps can be approximated---using averaging theory---by the usual
area-preserving twist or nontwist standard maps. The twist condition
appropriate for the volume-preserving setting is shown to be distinct from the
nondegeneracy condition used in (volume-preserving) KAM theory.Comment: Many typos fixed and notation simplified. New order
averaging theorem and volume-preserving variant. Numerical comparison with
averaging adde
Heisenberg exchange enhancement by orbital relaxation in cuprate compounds
We calculate the Heisenberg exchange J in the quasi-2D antiferromagnetic
cuprates La2CuO4, YBa2Cu3O6, Nd2CuO4 and Sr2CuO2Cl2. We apply all-electron
(MC)SCF and non-orthogonal CI calculations to [Cu2O11]18-, [Cu2O9]14-,
[Cu2O7]10- and [Cu2O7Cl4]14- clusters in a model charge embedding. The (MC)SCF
triplet and singlet ground states are well characterized by Cu2+ (dx2-y2) and
O2-. The antiferromagnetic exchange is strongly enhanced by admixing relaxed
(MC)SCF triplet and singlet excited states, in which a single electron is
transferred from the central O ion to Cu. We ascribe this effect to orbital
relaxation in the charge transfer component of the wave function. Close
agreement with experiment is obtained.Comment: publishe
A Cantor set of tori with monodromy near a focus-focus singularity
We write down an asymptotic expression for action coordinates in an
integrable Hamiltonian system with a focus-focus equilibrium. From the
singularity in the actions we deduce that the Arnol'd determinant grows
infinitely large near the pinched torus. Moreover, we prove that it is possible
to globally parametrise the Liouville tori by their frequencies. If one
perturbs this integrable system, then the KAM tori form a Whitney smooth
family: they can be smoothly interpolated by a torus bundle that is
diffeomorphic to the bundle of Liouville tori of the unperturbed integrable
system. As is well-known, this bundle of Liouville tori is not trivial. Our
result implies that the KAM tori have monodromy. In semi-classical quantum
mechanics, quantisation rules select sequences of KAM tori that correspond to
quantum levels. Hence a global labeling of quantum levels by two quantum
numbers is not possible.Comment: 11 pages, 2 figure
Resonances in a spring-pendulum: algorithms for equivariant singularity theory
A spring-pendulum in resonance is a time-independent Hamiltonian model system for formal reduction to one degree of freedom, where some symmetry (reversibility) is maintained. The reduction is handled by equivariant singularity theory with a distinguished parameter, yielding an integrable approximation of the Poincaré map. This makes a concise description of certain bifurcations possible. The computation of reparametrizations from normal form to the actual system is performed by Gröbner basis techniques.
On the relation between local and charge-transfer exciton binding energies in organic photovoltaic materials
In organic photovoltaic devices two types of excitons can be generated for which different binding energies can be defined: the binding energy of the local exciton generated immediately after light absorption on the polymer and the binding energy of the charge-transfer exciton generated through the electron transfer from polymer to PCBM. Lowering these two binding energies is expected to improve the efficiency of the devices. Using (time-dependent) density functional theory, we studied whether a relation exists between the two different binding energies. For a series of related co-monomers, we found that the local exciton binding energy on a monomer is not directly related to that of the charge-transfer exciton on a monomer-PCBM complex because the variation in exciton binding energy depends mainly on the variation in electron affinity, which does not affect in a direct way the charge-transfer exciton binding energy. Furthermore, for the studied co-monomers and their corresponding trimers, we provide detailed information on the amount of charge transfer upon excitation and on the charge transfer excitation length. This detailed study of the excitation process reveals that the thiophene unit that links the donor and acceptor fragments of the co-monomer actively participates in the charge transfer process
A Predator-Prey Model with Non-Monotonic Response Function
We study the dynamics of a family of planar vector fields that models certain populations of predators and their prey. This model is adapted from the standard Volterra-Lotka system by taking into account group defense, competition between prey and competition between predators. Also we initiate computer-assisted research on time-periodic perturbations, which model seasonal dependence. We are interested in persistent features. For the planar autonomous model this amounts to structurally stable phase portraits. We focus on the attractors, where it turns out that multi-stability occurs. Further, we study the bifurcations between the various domains of structural stability. It is possible to fix the values of two of the parameters and study the bifurcations in terms of the remaining three. We find several codimension 3 bifurcations that form organizing centers for the global bifurcation set. Studying the time-periodic system, our main interest is the chaotic dynamics. We plot several numerical examples of strange attractors
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