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By inverting the time-dependent Kohn-Sham equation for a numerically exact dynamics of the helium atom, we show that the dynamical step and peak features of the exact correlation potential found previously in one-dimensional models persist…
A challenging problem in decentralized optimization is to develop algorithms with fast convergence on random and time varying topologies under unreliable and bandwidth-constrained communication network. This paper studies a stochastic…
We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current-…
Attention-based Transformers have revolutionized natural language processing (NLP) and shown strong performance in computer vision (CV) tasks. However, as the input sequence varies, the computational bottlenecks in Transformer models…
An exactly solvable model is introduced, which is equivalent to the exact shell-model treatment of protons and neutrons in a single j-shell for Fermi-type excitations. Exact energies, quasiparticle numbers and double beta decay Fermi…
Here we describe the form of the Asymmetric Superfluid Local Density Approximation (ASLDA), a Density Functional Theory (DFT) used to model the two-component unitary Fermi gas. We give the rational behind the functional, and describe…
Junctions of multiple one-dimensional quantum wires of interacting electrons have received considerable theoretical attention as a basic constituent of quantum circuits. While results have been obtained on these models using bosonization…
In the previous work, Zhang et al. proposed a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interactions (FSI) with achieving an optimized computational efficiency meanwhile maintaining good numerical…
We develop a self-consistent first-principle method based on the density functional theory. Physical quantities, such as the density of states, Fermi energy and electron density are obtained using a time-dependent random state method…
We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
The mean spherical approximation (MSA) can be solved semi-analytically for the Gaussian core model (GCM) and yields - rather surprisingly - exactly the same expressions for the energy and the virial equations. Taking advantage of this…
Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…
A relativistic mean field description of collective excitations of atomic nuclei is studied in the framework of a fully self-consistent relativistic random phase approximation (RRPA). In particular, results of RRPA calculations of multipole…
We present a theoretical study of the compressibility, $\kappa$, in a Fermi gas with attractive contact interactions, providing predictions for the strongly-attractive regime and the superfluid phase. Our work emphasizes the compressibility…
Physical field reconstruction (PFR) aims to predict the state distribution of physical quantities (e.g., velocity, pressure, and temperature) based on limited sensor measurements. It plays a critical role in domains such as fluid dynamics…
In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a…
Relativistic dynamics of a charged particle in time-dependent electromagnetic fields has theoretical significance and a wide range of applications. It is often multi-scale and requires accurate long-term numerical simulations using…
We present a concise account of our development of the first genuine Local Density Approximation (LDA) to the Energy Density Functional (EDF) for fermionic systems with superfluid correlations, with a particular emphasis to nuclear systems.
We explore the non-equilibrium dynamics of a one-dimensional Fermi-Hubbard system as a sensitive testbed for the capabilities of the time-dependent two-particle reduced density matrix (TD2RDM) theory to accurately describe time-dependent…