Related papers: A level-set based finite difference method for the…
We systematically investigate the ground-state properties of self-bound droplets of quasi-two-dimensional binary Bose gases by using the Gaussian state theory. We find that quantum droplets consists two macroscopic squeezed phases and a…
In presence of a magnetic field, multi-component ground states appear in trapped spin-1 Bose-Einstein condensates for both ferromagnetic and anti-ferromagnetic types of spin-spin interaction. We aim to produce an accurate analytical…
We analyse the distinction between the three different ground states presented by a system of spinless bosons with short-range interactions submitted to a random potential using the disordered Bose-Hubbard model. The criteria for…
The density of bosonic states are calculated for spinless free massive bosons in generalised d dimensions. The number of bosons are calculated in the lowest energy state. The Bose Einstein condensation was found in generalised dimensions…
Motivated by the Asynchronous Finite Differences Method utilized for the calculation of the most probable distributions of finite particle number systems, this study employs numerical variation and central difference techniques to provide…
We study the anomalous density in an ultra-cold trapped bose gas in a variational framework, for both zero and finite temperature. We show that it is finite in 1D, while it is logarithmically and linearly divergent in 2D and 3D. The…
This paper investigates the numerical approximation of ground states of rotating Bose-Einstein condensates. This problem requires the minimization of the Gross-Pitaevskii energy $E$ on a Hilbert manifold $\mathbb{S}$. To find a…
We propose a method of measuring diffusion of the relative phase between two Bose-Einstein condensates occupying different nuclear or spin hyperfine states coupled by a two-photon transition via an intermediate level. Due to the macroscopic…
A disordered version of the one dimensional asymmetric exclusion model where the particle hopping rates are quenched random variables is studied. The steady state is solved exactly by use of a matrix product. It is shown how the phenomenon…
We review how the local particle number cutoff introduced in [11] is used to build trial states for the dilute Bose gas that capture the substantial correlation structure of the ground state in the thermodynamic limit. In particular, we…
The diffuse domain method for partial differential equations on complicated geometries recently received strong attention in particular from practitioners, but many fundamental issues in the analysis are still widely open. In this paper we…
A fourth-order finite volume embedded boundary (EB) method is presented for the unsteady Stokes equations. The algorithm represents complex geometries on a Cartesian grid using EB, employing a technique to mitigate the "small cut-cell"…
We study the properties of coupled linear and nonlinear resonances. The fundamental phenomena and the level crossing scenarios are introduced for a nonlinear two-level system with one decaying state, describing the dynamics of a…
We develop time-splitting finite difference methods, using implicit Backward-Euler and semi-implicit Crank-Nicolson discretization schemes, to study the spin-orbit coupled spinor Bose Einstein condensates with coherent coupling in quasi-one…
We study analytically and asymptotically as well as numerically ground states and dynamics of two-component spin-orbit-coupled Bose-Einstein condensates (BECs) modeled by the coupled Gross-Pitaevskii equations (CGPEs). In fact, due to the…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
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…
Convergence results for the immersed boundary method applied to a model Stokes problem with the homogeneous Dirichlet boundary condition are presented. As a discretization method, we deal with the finite element method. First, the immersed…
Modern quantum engineering techniques allow for synthesizing quantum systems in exotic lattice geometries, from self-similar fractal networks to negatively curved hyperbolic graphs. We demonstrate that these structures profoundly reshape…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…