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Atomic Fermi gases have been an ideal platform for simulating conventional and engineering exotic physical systems owing to their multiple tunable control parameters. Here we investigate the effects of mixed dimensionality on the superfluid…
Recently I proposed a new method for solving the pairing Hamiltonian with the pair-condensate wavefunction ansatz based on the Heisenberg equations of motion for the density matrix operators. In this work an improved version is given by…
We develop a formalism for mapping the exact dynamics of an ensemble of disordered quantum systems onto the dynamics of a single particle propagating along a semi-infinite lattice, with parameters determined by the probability distribution…
Using loop equation technics, we compute all mixed traces correlation functions of the 2-matrix model to large N leading order. The solution turns out to be a sort of Bethe Ansatz, i.e. all correlation functions can be decomposed on…
Statistical matching is an effective method for estimating causal effects in which treated units are paired with control units with ``similar'' values of confounding covariates prior to performing estimation. In this way, matching helps…
We investigate the quantum phases of mixed-dimensional cold atom mixtures. In particular, we consider a mixture of a Fermi gas in a two-dimensional lattice, interacting with a bulk Fermi gas or a Bose-Einstein condensate in a…
We study a system of functional relations among a commuting family of row-to-row transfer matrices in solvable lattice models. The role of exact sequences of the finite dimensional quantum group modules is clarified. We find a curious…
In this paper, we propose a learning-based image fragment pair-searching and -matching approach to solve the challenging restoration problem. Existing works use rule-based methods to match similar contour shapes or textures, which are…
In real life situations often paired comparisons involving alternatives of either full or partial profiles to mitigate cognitive burden are presented. For this situation the problem of finding optimal designs is considered in the presence…
Based on the Lippmann-Schwinger equation approach, a generalized L\"uscher's formula in 1+1 dimensions for two particles scattering in both the elastic and coupled-channel cases in moving frames is derived. A 2D coupled-channel scattering…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
A series of robust and optimal mixed methods based on two mixed formulations of the fourth-order elliptic singular perturbation problem are developed in this paper. First, a mixed method based on a second-order system is proposed without…
All-pairs compute problems apply a user-defined function to each combination of two items of a given data set. Although these problems present an abundance of parallelism, data reuse must be exploited to achieve good performance. Several…
The bipartite matching problem is widely applied in the field of transportation; e.g., to find optimal matches between supply and demand over time and space. Recent efforts have been made on developing analytical formulas to estimate the…
We propose a matching method that recovers direct treatment effects from randomized experiments where units are connected in an observed network, and units that share edges can potentially influence each others' outcomes. Traditional…
We present the first numerical implementation of a non-perturbative renormalization method for lattice operators, based on the study of correlation functions in coordinate space at short Euclidean distance. The method is applied to compute…
This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…
In paired comparison experiments respondents usually evaluate pairs of competing options. For this situation we introduce an appropriate model and derive optimal designs in the presence of second-order interactions when all attributes are…
In this paper we develop an algorithm for obtaining some new linear relations among the Lauricella $F_D$ functions. Relations we obtain, generalize those hinted in the work of B. C. Carlson. The coefficients of these relations are contained…
In this paper we construct energy based numerical methods free of ghost forces in three dimensional lattices arising in crystalline materials. The analysis hinges on establishing a connection of the coupled system to conforming finite…