Related papers: Tensor network methods for the Gross-Pitaevskii eq…
We study finite-time performance of a recently proposed distributed dual subgradient (DDSG) method for convex constrained multi-agent optimization problems. The algorithm enjoys performance guarantees on the last primal iterate, as opposed…
We review c-field methods for simulating the non-equilibrium dynamics of degenerate Bose gases beyond the mean-field Gross-Pitaevskii approximation. We describe three separate approaches that utilise similar numerical methods, but have…
The Vlasov-Poisson systems of equations (VP) describes the evolution of a distribution of collisionless particles under the effect of a collective-field potential. VP is at the basis of the study of the gravitational instability of…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
Nonlinear Schrodinger / Gross-Pitaevskii equations play a central role in the understanding of nonlinear optical and macroscopic quantum systems. The large time dynamics of such systems is governed by interactions of the nonlinear ground…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Simulating Markovian open quantum systems in the semiclassical regime poses a grand challenge for computational physics, as the highly oscillatory nature of the dynamics imposes prohibitive resolution requirements on traditional grid-based…
We study the numerical solution of the time-dependent Gross-Pitaevskii equation (GPE) describing a Bose-Einstein condensate (BEC) at zero or very low temperature. In preparation for the numerics we scale the 3d Gross-Pitaevskii equation and…
We present a review of recent developments of simulations of the Vlasov-Maxwell system of equations using a Fourier transform method in velocity space. In this method, the distribution functions for electrons and ions are Fourier…
We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer. The core setting of this anthology are lattice problems in low…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
We propose a versatile variational method to investigate the spatio-temporal dynamics of one-dimensional magnetically-trapped Bose-condensed gases. To this end we employ a \emph{q}-Gaussian trial wave-function that interpolates between the…
We present reduced-dimensional stochastic projected Gross-Pitaevskii equations describing regimes of confinement and temperature where a 1D or 2D superfluid is immersed in a 3D thermal cloud. The projection formalism provides both a…
The growing complexity of the power grid, driven by increasing share of distributed energy resources and by massive deployment of intelligent internet-connected devices, requires new modelling tools for planning and operation. Physics-based…
We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomised initial wave functions to equilibrium. We compare our numerical…
The development of algorithms for enhancing the resilience and efficiency of the power grid requires performance evaluation with real topologies of power transmission networks. However, due to security reasons, such topologies and…
Tensor network states provide an efficient class of states that faithfully capture strongly correlated quantum models and systems in classical statistical mechanics. While tensor networks can now be seen as becoming standard tools in the…
Gain-dissipative platforms consisting of lasers, optical parametric oscillators and nonequilibrium condensates operating at the condensation/coherence threshold have been recently proposed as efficient analog simulators of 2-local spin…
The dynamics of a trapped Bose-condensed gas at finite temperatures is described by a generalized Gross-Pitaevskii equation for the condensate order parameter and a semi-classical kinetic equation for the thermal cloud, solved using…
Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to…