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 Non‐aqueous Redox Flow Batteries: Achieving High Chemical Stability through Bicyclic Substitution

1,4‐Dimethoxybenzene derivatives are materials of choice for use as catholytes in non‐aqueous redox flow batteries, as they exhibit high open‐circuit 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 ring‐addition reactions. By incorporating bicyclic substitutions and ether chains into the dialkoxybenzenes, a novel catholyte molecule, 9,10‐bis(2‐methoxyethoxy)‐1,2,3,4,5,6,7,8‐octahydro‐1,4:5,8‐dimethanenoanthracene (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 charge–discharge cycles with a minimal loss of capacity.A novel bicyclical substituted dialkoxy‐benzene molecule, 9,10‐bis(2‐methoxy‐ethoxy)‐1,2,3,4,5,6,7,8‐octahydro‐1,4:5,8‐dimethanenoanthracene (BODMA), is developed for use as catholyte materials in non‐aqueous 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