Statistics of Chaotic Resonances in an Optical Microcavity

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the timescale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.Comment: 5 pages, 5 figures, and a supplemental informatio

A Study on the Vehicle Routing Problem Considering Infeasible Routing Based on the Improved Genetic Algorithm

The study aims to optimize the vehicle routing problem, considering infeasible routing, to minimize losses for the company. Firstly, a vehicle routing model with hard time windows and infeasible route constraints is established, considering both the minimization of total vehicle travel distance and the maximization of customer satisfaction. Subsequently, a Floyd-based improved genetic algorithm that incorporates local search is designed. Finally, the computational experiment demonstrates that compared with the classic genetic algorithm, the improved genetic algorithm reduced the average travel distance by 20.6% when focusing on travel distance and 18.4% when prioritizing customer satisfaction. In both scenarios, there was also a reduction of one in the average number of vehicles used. The proposed method effectively addresses the model introduced in this study, resulting in a reduction in total distance and an enhancement of customer satisfaction

4,4′-Bipyridine–2-(carb­oxy­methyl­sulfan­yl)pyridine-3-carb­oxy­lic acid (1/1)

In the title co-crystal, C10H8N2·C8H7NO4S, the formate group is coplanar with the pyridyl ring of the acid [dihedral angle = 6.2 (7)°], while the carb­oxy­methyl­sulfanyl group makes a C—S—C—C torsion angle of 70.2 (1)° with the pyridine ring. The dihedral angle between the pyridyl rings of the 4,4′-bipyridine mol­ecule is 27.4 (1)°. The acid and the 4,4′-bipyridine mol­ecules are involved in hydrogen bonding via carb­oxy­lic O and pyridyl N atoms. The structure is further consolidated by inter­molecular C—H⋯O hydrogen bonds, generating a three-dimensional network

Analogue to multiple electromagnetically induced transparency in all-optical drop-filter systems

We theoretically study a parallel optical configuration which includes N periodically coupled whispering-gallery-mode resonators. The model shows an obvious effect which has a direct analogy with the phenomenon of multiple electromagnetically induced transparency in quantum systems. The numerical simulations illuminate that the frequency transparency windows are sharp and highly transparent. We also briefly discuss the experimental feasibility of the current scheme in two practical systems, microrings and microdisks.Comment: 4 pages, 4 figure