Engineering Photon Delocalization in a Rabi Dimer with a Dissipative Bath

A Rabi dimer is used to model a recently reported circuit quantum electrodynamics system composed of two coupled transmission-line resonators with each coupled to one qubit. In this study, a phonon bath is adopted to mimic the multimode micromechanical resonators and is coupled to the qubits in the Rabi dimer. The dynamical behavior of the composite system is studied by the Dirac-Frenkel time-dependent variational principle combined with the multiple Davydov D$_{2}$ ans\"{a}tze. Initially all the photons are pumped into the left resonator, and the two qubits are in the down state coupled with the phonon vacuum. In the strong qubit-photon coupling regime, the photon dynamics can be engineered by tuning the qubit-bath coupling strength $\alpha$ and photon delocalization is achieved by increasing $\alpha$. In the absence of dissipation, photons are localized in the initial resonator. Nevertheless, with moderate qubit-bath coupling, photons are delocalized with quasiequilibration of the photon population in two resonators at long times. In this case, high frequency bath modes are activated by interacting with depolarized qubits. For strong dissipation, photon delocalization is achieved via frequent photon-hopping within two resonators and the qubits are suppressed in their initial down state.Comment: 11 pages, 11 figure

Extraction of Impervious Surface Areas from High Spatial Resolution Imagery by Multiple Agent Segmentation and Classification

In recent years impervious surface areas (ISA) have emerged as a key paradigm to explain and predict ecosystem health in relationship to watershed development. The ISA data are essential for environmental monitoring and management in coastal State of Rhode Island. However, there is lack of information on high spatial resolution ISA. In this study, we developed an algorithm of multiple agent segmentation and classification (MASC) that includes submodels of segmentation, shadow-effect, MANOVA-based classification, and post-classification. The segmentation sub-model replaced the spectral difference with heterogeneity change for regions merging. Shape information was introduced to enhance the performance of ISA extraction. The shadow-effect sub-model used a split-and-merge process to separate shadows and the objects that cause the shadows. The MANOVA-based classification sub-model took into account the relationship between spectral bands and the variability in the training objects and the objects to be classified. Existing GIS data were used in the classification and post-classification process. The MASC successfully extracted ISA from high spatial resolution airborne true-color digital orthophoto and space-borne QuickBird-2 imagery in the testing areas, and then was extended for extraction of high spatial resolution ISA in the State of Rhode Island

Elliptic genera of level NN for complete intersections

We study the elliptic genera of level $N$ at the cusps of $\Gamma_1(N)$ for any complete intersection. These genera are described as the summations of generalized binomial coefficients, where each generalized binomial coefficient is related to the dimension and multi-degree of complete intersection. For complete intersection $X_n(\underline{d})$, write $c_1(X_n(\underline{d}))=c_1x$, where $x\in H^2(X_n(\underline{d});\mathbb{Z})\cong\mathbb{Z}$ is a generator. We mainly discuss the values of the elliptic genera of level $N$ for $X_n(\underline{d})$ in the case of $c_1>0, =0$ or $<0$. In particular, the values about the Todd genus, $\hat{A}$-genus and $A_k$-genus of $X_n(\underline{d})$ can be derived from the elliptic genera of level $N$.Comment: 18 pages, 1 tabl

Examples of diffeomorphic complete intersections with different Hodge numbers

In this paper, we give three pairs of complex 3-dim complete intersections and a pair of complex 5-dim complete intersections, and every pair of them is diffeomorphic but with different Hodge numbers. Moreover, the diffeomorphic complex 3-dim complete intersections have different Chern mumbers $c_1^3, c_1c_2$.Comment: 7 pages, 2 table

Risk exchange under infinite-mean Pareto models

We study the optimal decisions of agents who aim to minimize their risks by allocating their positions over extremely heavy-tailed (i.e., infinite-mean) and possibly dependent losses. The loss distributions of our focus are super-Pareto distributions which include the class of extremely heavy-tailed Pareto distributions. For a portfolio of super-Pareto losses, non-diversification is preferred by decision makers equipped with well-defined and monotone risk measures. The phenomenon that diversification is not beneficial in the presence of super-Pareto losses is further illustrated by an equilibrium analysis in a risk exchange market. First, agents with super-Pareto losses will not share risks in a market equilibrium. Second, transferring losses from agents bearing super-Pareto losses to external parties without any losses may arrive at an equilibrium which benefits every party involved. The empirical studies show that extremely heavy tails exist in real datasets.Comment: arXiv admin note: substantial text overlap with arXiv:2208.0847