Related papers: Tensor network methods for the Gross-Pitaevskii eq…
In high-temperature plasma physics, a strong magnetic field is usually used to confine charged particles. Therefore, for studying the classical mathematical models of the physical problems it needs to consider the effect of external…
We introduce an algorithmic framework based on tensor networks for computing fluid flows around immersed objects in curvilinear coordinates. We show that the tensor network simulations can be carried out solely using highly compressed…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
We show that the knowledge of the time dependent response of a trapped gas, subject to a sudden rotation of a confining harmonic potential, allows for the determination of the moment of inertia of dipolar supersolid configurations. While in…
In two dimensions the Gross-Pitaevskii equation for a cold, dilute gas of bosons has an energy dependent coupling parameter describing particle interactions. We present numerical solutions of this equation for bosons in harmonic traps and…
In the present work, the Tensor-Train decomposition algorithm is applied to reduce the memory footprint of a stochastic discrete velocity solver for rarefied gas dynamics simulation. An energy-conserving modification to the algorithm is…
We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational…
Many methods for modelling spatial processes assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modelling spatial processes that display heterogeneity or contain discontinuities.…
Quantum vortex dynamics in Bose-Einstein condensates or superfluid helium can be informatively described by the Gross-Pitaevskii (GP) equation. Various approximate analytical formulae for a single stationary vortex are recalled and their…
A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…
In many power systems, particularly those isolated from larger intercontinental grids, operational dependence on natural gas becomes pivotal, especially during fluctuations or unavailability of renewables coupled with uncertain consumption…
We investigate the behavior of solutions of the complex Gross-Pitaevskii equation, a model that describes the dynamics of pumped decaying Bose-Einstein condensates. The stationary radially symmetric solutions of the equation are studied and…
We introduce a unified framework to compute the solution space properties of a broad class of combinatorial optimization problems. These properties include finding one of the optimum solutions, counting the number of solutions of a given…
Tensor networks are powerful techniques that widely used in condensed matter physics. In this language, the wave function of a quantum manybody system is described by a network of tensors with specific entanglement structures. Recently, it…
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical…
The transition away from carbon-based energy sources poses several challenges for the operation of electricity distribution systems. Increasing shares of distributed energy resources (e.g. renewable energy generators, electric vehicles) and…
An overview of the Bose-Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the…
We derive the time-dependent dipolar Gross-Pitaevskii (GP) equation from the N-body Schr{\"o}dinger equation. More precisely we show a norm approximation for the solution of the many body equation as well as the convergence of its one-body…
The application of deep learning methods to speed up the resolution of challenging power flow problems has recently shown very encouraging results. However, power system dynamics are not snap-shot, steady-state operations. These dynamics…
Coexistence of different dynamical phases is a hallmark of glassy dynamics. This is well-studied in classical systems where the underlying theoretical framework is that of large deviation theory. The presence of a similar phase coexistence…