102 research outputs found
Comparison of averages of flows and maps
It is shown that in transient chaos there is no direct relation between
averages in a continuos time dynamical system (flow) and averages using the
analogous discrete system defined by the corresponding Poincare map. In
contrast to permanent chaos, results obtained from the Poincare map can even be
qualitatively incorrect. The reason is that the return time between
intersections on the Poincare surface becomes relevant. However, after
introducing a true-time Poincare map, quantities known from the usual Poincare
map, such as conditionally invariant measure and natural measure, can be
generalized to this case. Escape rates and averages, e.g. Liapunov exponents
and drifts can be determined correctly using these novel measures. Significant
differences become evident when we compare with results obtained from the usual
Poincare map.Comment: 4 pages in Revtex with 2 included postscript figures, submitted to
Phys. Rev.
The resonance spectrum of the cusp map in the space of analytic functions
We prove that the Frobenius--Perron operator of the cusp map
, (which is an approximation of the
Poincar\'e section of the Lorenz attractor) has no analytic eigenfunctions
corresponding to eigenvalues different from 0 and 1. We also prove that for any
the spectrum of in the Hardy space in the disk
\{z\in\C:|z-q|<1+q\} is the union of the segment and some finite or
countably infinite set of isolated eigenvalues of finite multiplicity.Comment: Submitted to JMP; The description of the spectrum in some Hardy
spaces is adde
Diffusion in normal and critical transient chaos
In this paper we investigate deterministic diffusion in systems which are
spatially extended in certain directions but are restricted in size and open in
other directions, consequently particles can escape. We introduce besides the
diffusion coefficient D on the chaotic repeller a coefficient which
measures the broadening of the distribution of trajectories during the
transient chaotic motion. Both coefficients are explicitly computed for
one-dimensional models, and they are found to be different in most cases. We
show furthermore that a jump develops in both of the coefficients for most of
the initial distributions when we approach the critical borderline where the
escape rate equals the Liapunov exponent of a periodic orbit.Comment: 4 pages Revtex file in twocolumn format with 2 included postscript
figure
Superconducing Alloys with Weak and Strong Scattering: Anderson's Theorem and a Superconductor-Insulator Transition
We have studied the effects of strong impurity scattering on disordered
superconductors beyond the low impurity concentration limit. By applying the
full CPA to a superconductiong A-B binary alloy, we calculated the fluctuations
of the local order parameters and charge densities,
for weak and strong on site disorder. We find that for narrow
band alloy s-wav e superconductors the conditions for Anderson's theorem are
satisfied in general only for the case of particle-hole symmetry. In this case
it is satisfied regardless whether we are in the weak or strong scattering
regimes. Interestingly, we find that strong scattering leads to band splitting
and in this regime for any band filling we have a critical concentration where
a superconductor-insulator quantum phase transition occurs at T=0.Comment: 28 pages, 13 figure
Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems
A Coherent Potential Approximation is developed for s-wave and d-wave
superconductivity in disordered systems. We show that the CPA formalism
reproduces the standard pair-breaking formula, the self-consistent Born
Approximation and the self-consistent T-matrix approximation in the appropriate
limits. We implement the theory and compute T_c for s-wave and d-wave pairing
using an attractive nearest neighbor Hubbard model featuring both binary alloy
disorder and a uniform distribution of scattering site potentials. We determine
the density of states and examine its consequences for low temperature heat
capacity. We find that our results are in qualitative agreement with
measurements on Zn doped YBCO superconductors.Comment: 35 pages, 23 figures, submitted to Phys Rev.
First-principles study and modeling of strain-dependent ionic migration in ZrO(2)
Electrolytes with high ionic conductivity at lower temperatures are the prerequisite for the success of Solid Oxide Fuel Cells (SOFC). One promising candidate is doped zirconia. In the past its ionic conductivity has mainly been increased by decreasing its thickness. However, the influence of the thickness is only linear, whereas the impact of migration barriers is exponential. Therefore understanding the oxygen transport in doped zirconia is of fundamental importance. In this work we pursue the approach of the strain dependent ionic migration in zirconia. We investigate how the migration barriers for oxygen ions respond to a change of the atomic strain. We employ the method of Density Functional Theory (DFT) calculations to relax the atomic configurations to the ground state. In connection with the Nudged Elastic Band (NEB) method we obtain the migration barrier of the oxygen ion jumps in zirconia for a given lattice constant. Similar to other publications we observe a decrease in the migration barrier for expansive strain, but in addition we also find a migration barrier decrease for high compressive strains beyond a maximal height of the migration barrier at an intermediate compressive strain. We present a simple analytic model which, by using interactions of the Lennard-Jones type, gives an explanation for this behavior
Enhanced anisotropic ionic diffusion in layered electrolyte structures from density functional theory
Electrolytes with high ionic diffusivity at temperatures distinctively lower than the presently used ones are the prerequisite for the success of, e.g., solid oxide fuel cells. We have found a promising structure having an asymmetric but superior ionic mobility in the direction of the oxygen-ion current. Using a layering of zirconium and yttrium in the fluorite structure of zirconia, a high vacancy concentration and a low migration barrier in two dimensions are obtained, while the mobility in the third direction is basically sacrificed. According to our density functional theory calculations an electrolyte made of this structure could operate at a temperature reduced by ≈200∘C. Thus a window to a different class of electrolytes has been flung open. In our structure the price paid is a more complicated manufacturing metho
Finding stable minima using a nudged-elastic-band-based optimization scheme
Optimization is essential in many scientific and economical areas, but it is often too complex to be tackled by simple straightforward calculations or by trial and error. Two well-known methods to find low-lying minima in such complex systems are simulated annealing and the genetic algorithm. In these methods artificial fluctuations control the probability of the system to overcome a local minimum having a certain depth. Here we present a complementary scheme that is based on the nudged-elastic-band method ordinarily used to find saddle points and we apply the scheme to find the most stable isomers of the phosphorus P-4, P-8 molecules and the corresponding molecules of As-n, Sb-n, and Bi-n (n = 4,8) in the framework of the density functional theory. In the case of n = 8 we have found stable and metastable configurations, some of which are new and have similar energies. As a by-product we obtained an upper bound for the energy barriers between these configurations
- …