Related papers: Tensor network methods for the Gross-Pitaevskii eq…
The microscopic mechanism of thermal dissipation in quantum turbulence has been numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the…
We review some recent results on the long time dynamics of solutions to the Gross-Pitaevskii equation governing non-trapped dipolar Quantum Gases. We describe the asymptotic behaviours of solutions for different initial configurations of…
Unitary integrable models typically relax to a stationary Generalized Gibbs Ensemble (GGE), but in experimental realizations dissipation often breaks integrability. In this work, we use the recently introduced time-dependent GGE (t-GGE)…
A method based on orthogonal function series interpolation of the square root probability density to analyze higher dimensional scattered data is presented. The method is targeted for the use-case when the model and/or data are available…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable source for the coherent matter waves in these devices are Bose-Einstein condensates. A…
We introduce 1D and 2D models of a degenerate bosonic gas composed of ions with positive and negative charges (cations and anions). The system may exist in the mean-field condensate state, enabling the competition of the Coulomb coupling,…
We present a quantum-inspired solver for the one-dimensional Gross-Pitaevskii equation in the Quantics Tensor-Train (QTT) representation. By evolving the system entirely within a low-rank tensor manifold, the method sidesteps the memory and…
An increasing amount of gas-fired power plants are currently being installed in modern power grids worldwide. This is due to their low cost and the inherent flexibility offered to the electrical network, particularly in the face of…
A plethora of next-generation all-optical devices based on exciton-polaritons have been proposed in latest years, including prototypes of transistors, switches, analogue quantum simulators and others. However, for such systems consisting of…
New efficient and accurate numerical methods are proposed to compute ground states and dynamics of dipolar Bose-Einstein condensates (BECs) described by a three-dimensional (3D) Gross-Pitaevskii equation (GPE) with a dipolar interaction…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
In Newtonian gravity, a self-gravitating collisionless gas around a massive object such as a star or a planet is modeled via the Vlasov--Poisson system with an external Kepler potential. The presence of this attractive potential allows for…
The large size of multiscale, distribution and transmission, power grids hinder fast system-wide estimation and real-time control and optimization of operations. This paper studies graph reduction methods of power grids that are favorable…
This paper presents a practical and scalable grid-based state estimation method for high-dimensional models with invertible linear dynamics and with highly non-linear measurements, such as the nearly constant velocity model with…
Solving partial differential equations of highly featured problems represents a formidable challenge, where reaching high precision across multiple length scales can require a prohibitive amount of computer memory or computing time.…
We devise a deterministic algorithm to efficiently sample high-quality solutions of certain spin-glass systems that encode hard optimization problems. We employ tensor networks to represent the Gibbs distribution of all possible…
The increasing integration of renewable energy sources (RESs) and distributed energy resources (DERs) has significantly heightened operational complexity and uncertainty in modern power systems. Concurrently, the widespread deployment of…
We describe a method for evolving the projected Gross-Pitaevskii equation (PGPE) for an interacting Bose gas in a harmonic oscillator potential, with the inclusion of a long-range dipolar interaction. The central difficulty in solving this…
This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…