Basic properties of the infinite critical-FK random map

We investigate the critical Fortuin-Kasteleyn (cFK) random map model. For each $q\in [0,\infty]$ and integer $n\geq 1$, this model chooses a planar map of $n$ edges with a probability proportional to the partition function of critical $q$-Potts model on that map. Sheffield introduced the hamburger-cheeseburger bijection which maps the cFK random maps to a family of random words, and remarked that one can construct infinite cFK random maps using this bijection. We make this idea precise by a detailed proof of the local convergence. When $q=1$, this provides an alternative construction of the UIPQ. In addition, we show that the limit is almost surely one-ended and recurrent for the simple random walk for any $q$, and mutually singular in distribution for different values of $q$.Comment: 14 pages, 6 figures. v2: Fixed the proof of main theorem, removed old lemma 5, added results on mutually singular measures and ergodicity. Submitted to Annales de l'Institut Henri Poincar\'e

Ising Model on Random Triangulations of the Disk : Phase Transition

In Chen and Turunen (Commun Math Phys 374(3):1577-1643, 2020), we have studied the Boltzmann random triangulation of the disk coupled to an Ising model on its faces with Dobrushin boundary condition at its critical temperature. In this paper, we investigate the phase transition of this model by extending our previous results to arbitrary temperature: We compute the partition function of the model at all temperatures, and derive several critical exponents associated with the infinite perimeter limit. We show that the model has a local limit at any temperature, whose properties depend drastically on the temperature. At high temperatures, the local limit is reminiscent of the uniform infinite half-planar triangulation decorated with a subcritical percolation. At low temperatures, the local limit develops a bottleneck of finite width due to the energy cost of the main Ising interface between the two spin clusters imposed by the Dobrushin boundary condition. This change can be summarized by a novel order parameter with a nice geometric meaning. In addition to the phase transition, we also generalize our construction of the local limit from the two-step asymptotic regime used in Chen and Turunen (2020) to a more natural diagonal asymptotic regime. We obtain in this regime a scaling limit related to the length of the main Ising interface, which coincides with predictions from the continuum theory of quantum surfaces (a.k.a. Liouville quantum gravity).Peer reviewe

Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation

We investigate the mutiphoton process between different Bloch states in an amplitude modulated optical lattice. In the experiment, we perform the modulation with more than one frequency components, which includes a high degree of freedom and provides a flexible way to coherently control quantum states. Based on the study of single frequency modulation, we investigate the collaborative effect of different frequency components in two aspects. Through double frequency modulations, the spectrums of excitation rates for different lattice depths are measured. Moreover, interference between two separated excitation paths is shown, emphasizing the influence of modulation phases when two modulation frequencies are commensurate. Finally, we demonstrate the application of the double frequency modulation to design a large-momentum-transfer beam splitter. The beam splitter is easy in practice and would not introduce phase shift between two arms.Comment: 11pages, 7 figure

Asymmetric superradiant scattering and abnormal mode amplification induced by atomic density distortion

The superradiant Rayleigh scattering using a pump laser incident along the short axis of a Bose-Einstein condensate with a density distortion is studied, where the distortion is formed by shocking the condensate utilizing the residual magnetic force after the switching-off of the trapping potential. We find that very small variation of the atomic density distribution would induce remarkable asymmetrically populated scattering modes by the matter-wave superradiance with long time pulse. The optical field in the diluter region of the atomic cloud is more greatly amplified, which is not an ordinary mode amplification with the previous cognition. Our numerical simulations with the density envelop distortion are consistent with the experimental results. This supplies a useful method to reflect the geometric symmetries of the atomic density profile by the superradiance scattering.Comment: 7pages,4 figures, Optical Express 21,(2013)1437

Long-time nonlinear dynamical evolution for P-band ultracold atoms in an optical lattice

We report the long-time nonlinear dynamical evolution of ultracold atomic gases in the P-band of an optical lattice. A Bose-Einstein condensate (BEC) is fast and efficiently loaded into the Pband at zero quasi-momentum with a non-adiabatic shortcut method. For the first one and half milliseconds, these momentum states undergo oscillations due to coherent superposition of different bands, which are followed by oscillations up to 60ms of a much longer period. Our analysis shows the dephasing from the nonlinear interaction is very conducive to the long-period oscillations induced by the variable force due to the harmonic confinement.Comment: 8 pages, 7 figure

Significance of searching for ganglia in the terminal rectum/fistula of complex anorectal malformations: Related to defecation function

BackgroundThe need to search for ganglia in the terminal rectum/fistula of complex anorectal malformations (ARMs) remains controversial. This study aims to evaluate the relationship between ganglia absence in the terminal rectum/fistula and defecation function after anoplasty.MethodsA retrospective review of patients who received anoplasty for treating male imperforate anus with rectobulbar (RB)/rectoprostatic (RP) fistulas at a tertiary pediatric hospital was conducted with registered demographic data, imaging study results, and information on the terminal rectum/fistula specimen (excision extension and pathological findings). According to the pathological findings, patients were divided into Groups 1 (ganglia absence) and 2 (ganglia presence). Furthermore, the postoperative defecation function was evaluated using various rating scale questionnaires. Statistical analysis was performed using SPSS 22.0.ResultsOf the 62 patients, 18 (29.0%) showed ganglia absence in the terminal rectum/fistula. By analyzing the imaging data, spinal anomalies and spinal cord anomalies were found in 30.6% (19/62) and 56.5% (35/62) of patients, respectively. Baseline information was comparable between Groups 1 and 2 (P > 0.05). For defecation function, there were no significant differences in Kelly scores between the two groups (4.0 ± 0.8 vs. 4.4 ± 1.1, P = 0.177), while Krickenbeck (3.7 ± 1.8 vs. 5.2 ± 1.4) and Rintala (13.7 ± 3.6 vs. 16.0 ± 2.7) scores in Group 1 were significantly lower than those in Group 2 (both P < 0.05). The overall incidence of constipation was 50% (31/62), being higher for Group 1 than Group 2 (77.5% vs. 38.6%, P = 0.002). The area under the curve of ganglia absence for predicting constipation was 0.696, with 77.8% sensitivity and 61.4% specificity.ConclusionGanglia absence in the terminal rectum/fistula of male imperforate anus with RB/RP fistulas is associated with constipation after anoplasty, but it has limited predictive value for postoperative constipation. It is necessary to search for ganglia in the terminal rectum/fistula, both intraoperatively and postoperatively

Roadmap on optical energy conversion

For decades, progress in the field of optical (including solar) energy conversion was dominated by advances in the conventional concentrating optics and materials design. In recent years, however, conceptual and technological breakthroughs in the fields of nanophotonics and plasmonics combined with a better understanding of the thermodynamics of the photon energy-conversion processes reshaped the landscape of energy-conversion schemes and devices. Nanostructured devices and materials that make use of size quantization effects to manipulate photon density of states offer a way to overcome the conventional light absorption limits. Novel optical spectrum splitting and photon-recycling schemes reduce the entropy production in the optical energy-conversion platforms and boost their efficiencies. Optical design concepts are rapidly expanding into the infrared energy band, offering new approaches to harvest waste heat, to reduce the thermal emission losses, and to achieve noncontact radiative cooling of solar cells as well as of optical and electronic circuitries. Light–matter interaction enabled by nanophotonics and plasmonics underlie the performance of the third- and fourth-generation energy-conversion devices, including up- and down-conversion of photon energy, near-field radiative energy transfer, and hot electron generation and harvesting. Finally, the increased market penetration of alternative solar energy-conversion technologies amplifies the role of cost-driven and environmental considerations. This roadmap on optical energy conversion provides a snapshot of the state of the art in optical energy conversion, remaining challenges, and most promising approaches to address these challenges. Leading experts authored 19 focused short sections of the roadmap where they share their vision on a specific aspect of this burgeoning research field. The roadmap opens up with a tutorial section, which introduces major concepts and terminology. It is our hope that the roadmap will serve as an important resource for the scientific community, new generations of researchers, funding agencies, industry experts, and investors.United States. Department of Energy (DE-AC36-086038308

Critical Ising model on random triangulations of the disk : enumeration and local limits

We consider Boltzmann random triangulations coupled to the Ising model on their faces, under Dobrushin boundary conditions and at the critical point of the model. The first part of this paper computes explicitly the partition function of this model by solving its Tutte's equation, extending a previous result by Bernardi and Bousquet-Melou (J Combin Theory Ser B 101(5):315-377, 2011) to the model with Dobrushin boundary conditions. We show that the perimeter exponent of the model is 7/3 in contrast to the exponent 5/2 for uniform triangulations. In the second part, we show that the model has a local limit in distribution when the two components of the Dobrushin boundary tend to infinity one after the other. The local limit is constructed explicitly using the peeling process along an Ising interface. Moreover, we show that the main interface in the local limit touches the (infinite) boundary almost surely only finitely many times, a behavior opposite to that of the Bernoulli percolation on uniform maps. Some scaling limits closely related to the perimeters of finite clusters are also obtained.Peer reviewe