77 research outputs found
Quantum correlations and classical resonances in an open chaotic system
We show that the autocorrelation of quantum spectra of an open chaotic system
is well described by the classical Ruelle-Pollicott resonances of the
associated chaotic strange repeller. This correspondence is demonstrated
utilizing microwave experiments on 2-D n-disk billiard geometries, by
determination of the wave-vector autocorrelation C(\kappa) from the
experimental quantum spectra S_{21}(k). The correspondence is also established
via "numerical experiments" that simulate S_{21}(k) and C(\kappa) using
periodic orbit calculations of the quantum and classical resonances.
Semiclassical arguments that relate quantum and classical correlation functions
in terms of fluctuations of the density of states and correlations of particle
density are also examined and support the experimental results. The results
establish a correspondence between quantum spectral correlations and classical
decay modes in an open systems.Comment: 10 pages, 5 eps figures, "Quantum chaos Y2K" Nobel symposium, to
appear in Physica Script
Close-packed dimers on nonorientable surfaces
The problem of enumerating dimers on an M x N net embedded on non-orientable
surfaces is considered. We solve both the Moebius strip and Klein bottle
problems for all M and N with the aid of imaginary dimer weights. The use of
imaginary weights simplifies the analysis, and as a result we obtain new
compact solutions in the form of double products. The compact expressions also
permit us to establish a general reciprocity theorem.Comment: 13 pages, 1 figure, typo corrected to the version published in Phys.
Lett. A 293, 235 (2002
Ising model on nonorientable surfaces: Exact solution for the Moebius strip and the Klein bottle
Closed-form expressions are obtained for the partition function of the Ising
model on an M x N simple-quartic lattice embedded on a Moebius strip and a
Klein bottle for finite M and N. The finite-size effects at criticality are
analyzed and compared with those under cylindrical and toroidal boundary
conditions. Our analysis confirms that the central charge is c=1/2.Comment: 8 pages, 3 eps figure
Microwave study of quantum n-disk scattering
We describe a wave-mechanical implementation of classically chaotic n-disk
scattering based on thin 2-D microwave cavities. Two, three, and four-disk
scattering are investigated in detail. The experiments, which are able to probe
the stationary Green's function of the system, yield both frequencies and
widths of the low-lying quantum resonances. The observed spectra are found to
be in good agreement with calculations based on semiclassical periodic orbit
theory. Wave-vector autocorrelation functions are analyzed for various
scattering geometries, the small wave-vector behavior allowing one to extract
the escape rate from the quantum repeller. Quantitative agreement is found with
the value predicted from classical scattering theory. For intermediate
energies, non-universal oscillations are detected in the autocorrelation
function, reflecting the presence of periodic orbits.Comment: 13 pages, 8 eps figures include
Annulated Dialkoxybenzenes as Catholyte Materials for Nonâaqueous Redox Flow Batteries: Achieving High Chemical Stability through Bicyclic Substitution
1,4âDimethoxybenzene derivatives are materials of choice for use as catholytes in nonâaqueous redox flow batteries, as they exhibit high openâcircuit potentials and excellent electrochemical reversibility. However, chemical stability of these materials in their oxidized form needs to be improved. Disubstitution in the arene ring is used to suppress parasitic reactions of their radical cations, but this does not fully prevent ringâaddition reactions. By incorporating bicyclic substitutions and ether chains into the dialkoxybenzenes, a novel catholyte molecule, 9,10âbis(2âmethoxyethoxy)â1,2,3,4,5,6,7,8âoctahydroâ1,4:5,8âdimethanenoanthracene (BODMA), is obtained and exhibits greater solubility and superior chemical stability in the charged state. A hybrid flow cell containing BODMA is operated for 150 chargeâdischarge cycles with a minimal loss of capacity.A novel bicyclical substituted dialkoxyâbenzene molecule, 9,10âbis(2âmethoxyâethoxy)â1,2,3,4,5,6,7,8âoctahydroâ1,4:5,8âdimethanenoanthracene (BODMA), is developed for use as catholyte materials in nonâaqueous redox flow batteries with greater solubility (in their neutral state) and improved chemical stability (in their charged state). A hybrid flow cell using BODMA demonstrates stable efficiencies and capacity over 150 cycles. The molecular design approach of BODMA can be inspirational for future development of redox active molecules.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/139992/1/aenm201701272.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139992/2/aenm201701272-sup-0001-S1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/139992/3/aenm201701272_am.pd
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