Related papers: Riemannian optimisation methods for ground states …
We study the ground-state properties of a quasi-two-dimensional Bose-Einstein condensate of indirect excitons, which are confined in an anisotropic harmonic potential. Incorporating the interactions, we calculate the order parameter…
In this article we introduce a multi-modal variational method to analytically estimate the full number- and corresponding energy-density profile of a spin-1 Bose-Einstein condensate (BEC) for a number of particles as low as 500 under…
Many machine learning applications are naturally formulated as optimization problems on Riemannian manifolds. The main idea behind Riemannian optimization is to maintain the feasibility of the variables while moving along a descent…
We investigate the phenomenon of Bose-Einstein condensation on manifolds constructed as a product of a three-dimensional Euclidian space and a general smooth, compact $d$-dimensional manifold possibly with boundary. By using spectral…
Two independently prepared condensates can be combined into a single larger condensate by detection of their relative phase in an intereference measurement.
Determining the ultimate limits of quantum communication, such as the quantum capacity of a channel and the distillable entanglement of a shared state, remains a central challenge in quantum information theory, primarily due to the…
Motivated by energy based analyses for descent methods in the Euclidean setting, we investigate a generalisation of such analyses for descent methods over Riemannian manifolds. In doing so, we find that it is possible to derive…
By improving the Bose-Einstein condensate model of dark matter through the repulsive three-particle interaction to better reproduce observables such as rotation curves, both different thermodynamic phases and few-particle correlations are…
Repulsive Bose-Einstein condensates immersed into a double-well trap potential are studied within the framework of the recently introduced mean-field approach which allows for bosons to reside in several different orthonormal orbitals. In…
We study the perfect Bose gas in random external potentials and show that there is generalized Bose-Einstein condensation in the random eigenstates if and only if the same occurs in the one-particle kinetic-energy eigenstates, which…
Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting…
We discuss theoretically the ground state of a Bose-Einstein condensate with attractive atom-atom interactions in a double-well trap as a starting point of Heisenberg-limited atom interferometry. The dimensionless parameter governing the…
The structure and degeneracy of ground states of the Gross-Pitaevskii energy functional play a central role in both analysis and computation, yet a precise characterization of the ground-state manifold in the presence of symmetries remains…
The ground state energy of a binary mixture of Bose-Einstein condensates can be estimated for large atomic samples by making use of suitably regularized Thomas-Fermi density profiles. By exploiting a variational method on the trial…
We study theoretically and experimentally the emergence of supersolid properties in a dipolar Bose-Einstein condensate. The theory reveals a ground state phase diagram with three distinct regimes - a regular Bose-Einstein condensate,…
We consider a two-dimensional nonlinear Schr{\"o}dinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both…
We report the computational discovery of complex, topologically charged, and spectrally stable states in three-dimensional multi-component nonlinear wave systems of nonlinear Schr{\"o}dinger type. While our computations relate to…
In this paper, we study Riemannian zeroth-order optimization in settings where the underlying Riemannian metric $g$ is geodesically incomplete, and the goal is to approximate stationary points with respect to this incomplete metric. To…
We consider the Gross-Pitaevskii equation describing a dipolar Bose-Einstein condensate without external confinement. We first consider the unstable regime, where the nonlocal nonlinearity is neither positive nor radially symmetric and…
We consider the 3d cubic nonlinear Schr\"odinger equation (NLS) with a strong 2d harmonic potential. The model is physically relevant to observe the lower-dimensional dynamics of the Bose-Einstein condensate, but its ground state cannot be…