Related papers: GPU-accelerated solutions of the nonlinear Schr\"o…
We sketch the major steps in a functional integral derivation of a new set of Stochastic Gross-Pitaevsky equations (GPE) for a Bose-Einstein condensate (BEC) confined to a trap at zero temperature with the averaged effects of non-condensate…
This paper investigates numerical methods for approximating the ground state of Bose--Einstein condensates (BECs) by introducing two relaxed formulations of the Gross--Pitaevskii energy functional. These formulations achieve first- and…
We demonstrate that spinor Bose-Einstein condensates (BEC) can be operated as an analog simulator of the two-dimensional vibron model. This algebraic model for the description of bending and stretching vibrations of molecules, in the case…
The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional PDEs, as Richard E. Bellman first pointed…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
We introduce CaLES, a GPU-accelerated finite-difference solver designed for large-eddy simulations (LES) of incompressible wall-bounded flows in massively parallel environments. Built upon the existing direct numerical simulation (DNS)…
The progress made in accelerating simulations of fluid flow using GPUs, and the challenges that remain, are surveyed. The review first provides an introduction to GPU computing and programming, and discusses various considerations for…
Current GPU-accelerated supercomputers promise to enable large-scale simulations of turbulent flows. Lattice Boltzmann Methods (LBM) are particularly well-suited to fulfilling this promise due to their intrinsic compatibility with highly…
Graphics processing units (GPUs) are recently being used to an increasing degree for general computational purposes. This development is motivated by their theoretical peak performance, which significantly exceeds that of broadly available…
We present an algorithm that uses a single ancilla qubit that can evolve nonlinearly, and show how to use it to efficiently solve generic nonlinear Schr\"odinger equations, including nonlocal Hartree equations and the Navier-Stokes equation…
This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct…
Quantum computers have the potential for an exponential speedup of classical molecular computations. However, existing algorithms have limitations; quantum phase estimation (QPE) algorithms are intractable on current hardware while…
We study fundamental and vortical solitons in disk-morphed Bose-Einstein condensates (BECs) subject to strong confinement along the axial direction. Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we proceed to an…
It is well known since 1960s that by exploring the tensor product structure of the discrete Laplacian on Cartesian meshes, one can develop a simple direct Poisson solver with an $\mathcal O(N^{\frac{d+1}d})$ complexity in d-dimension, where…
The year 2025 marks the 100 and 30 years anniversaries of the discovery of Bose--Einstein condensation and its successful experimental realisation. Inspired by these important research achievements, a conceptually simple approach is…
Obtaining a thermodynamically accurate phase diagram through numerical calculations is a computationally expensive problem that is crucially important to understanding the complex phenomena of solid state physics, such as superconductivity.…
We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information of the velocity distribution in localized areas of interest. This is made possible by…
We predict that exploiting spin-orbit coupling in a harmonically trapped spinor quantum gas can lead to scaling of the optimal measurement precision beyond the Heisenberg scaling. We show that quadratic scaling with the number of atoms can…
We derive a system of nonpolynomial Schroedinger equations (NPSEs) for one-dimensional wave functions of two components in a binary self-attractive Bose-Einstein condensate loaded in a cigar-shaped trap. The system is obtained by means of…
AI-driven methods have demonstrated considerable success in tackling the central challenge of accurately solving the Schr\"odinger equation for complex many-body systems. Among neural network quantum state (NNQS) approaches, the NNQS-SCI…