Related papers: Tensor network methods for the Gross-Pitaevskii eq…
We resume the recent successes of the grid-based tensor numerical methods and discuss their prospects in real-space electronic structure calculations. These methods, based on the low-rank representation of the multidimensional functions and…
We propose a numerical method for kinetic plasma simulation in which the phase-space distribution function is represented by a low-rank tensor network with an adaptive level of compression. The Vlasov-Poisson system is advanced using Strang…
Energy distribution networks are crucial for human societies and since they often cover large geographical areas, their physical analysis is challenging. Modeling and simulation can be used to analyze such complex energy networks. In this…
The stable operation of gas networks is an important optimization target. While for this task commonly finite volume methods are used, we introduce a new finite difference approach. With a summation by part formulation for the spatial…
We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation…
We develop an approximate formalism suitable for performing simulations of the thermal dynamics of interacting Bose gases. The method is based on the observation that when the lowest energy modes of the Bose field operator are highly…
Intending to describe the dark matter of dwarf galaxies, we concentrate on one model of the slowly rotating and gravitating Bose-Einstein condensate. For a deeper understanding of its properties, we calculate the partition function and…
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…
Holographic duality provides a description of strongly coupled quantum systems in terms of weakly coupled gravitational theories in a higher-dimensional space. It is a challenge, however, to quantitatively determine the physical parameters…
We present a thermodynamic description of ultracold gases with dipolar interactions which properly accounts for the long-range nature and broken rotation invariance of the interactions. It involves an additional thermodynamic field…
Developing non-perturbative methods to reveal exotic properties of strongly correlated fermionic systems remains one of the most essential tasks of theoretical physics. Tensor network methods with Grassmann algebra offer powerful numerical…
We introduce a tool for simulation and optimization of gas pipeline networks coupled to power grids by gas-to-power plants. The model under consideration consists of the isentropic Euler equations to describe the gas flow coupled to the AC…
Tensor network methods are a class of numerical tools and algorithms to study many-body quantum systems in and out of equilibrium, based on tailored variational wave functions. They have found significant applications in simulating lattice…
A simple derivation of the static Gross-Pitaevskii (GP) equation is given from an energy variational principle. The result is then generalized heuristically to the time-dependent GP form. With this as background, a number of different…
Deep neural networks are powerful tools for approximating functions, and they are applied to successfully solve various problems in many fields. In this paper, we propose a neural network-based numerical method to solve partial differential…
We present previously unknown solutions to the 3D Gross--Pitaevskii equation describing atomic Bose-Einstein condensates. This model supports elaborate patterns, including excited states bearing vorticity. The discovered coherent structures…
The stochastic Gross-Pitaevskii equation is used as a model to describe Bose-Einstein condensation at positive temperature. The equation is a complex Ginzburg Landau equation with a trapping potential and an additive space-time white noise.…
We present two accelerated numerical algorithms for single-component and binary Gross-Pitaevskii (GP) equations coupled with microwaves (electromagnetic fields) in steady state. One is based on a normalized gradient flow formulation, called…
We study the evolution of 3d weakly interacting bosons at finite chemical potential with the stochastic Gross-Pitaevskii equation. We fully characterise the vortex network in an out of equilibrium. At high temperature the filament…
Given observations of a physical system, identifying the underlying non-linear governing equation is a fundamental task, necessary both for gaining understanding and generating deterministic future predictions. Of most practical relevance…