Related papers: Two-Level discretization techniques for ground sta…
The ground state solutions of a dilute Bose condensate with contact and magnetic dipole-dipole interactions are examined. By lowering the value of the scattering length, Goral et al. [cond-mat/9907308 and Phys. Rev. A {\bf 61}, 051601…
In the present report we analyze the eventual modifications caused by the polymer quantization upon the ground state of a homogeneous one-dimensional Bose-Einstein condensate. We obtain the ground state energy of the corresponding N-body…
In this work, we analyze the corrections obtained on a homogeneous one-dimensional Bose gas within the high densities limit by means of the polymer quantization scheme. Thus, starting from the Bogoliubov formalism, we analyze the ground…
We study ground-state properties of interacting two-component boson gases in a one-dimensional harmonic trap by using the exact numerical diagonalization method. Based on numerical solutions of many-body Hamiltonians, we calculate the…
The gradient flow with semi-implicit discretization (GFSI) is the most widely used algorithm for computing the ground state of Gross-Pitaevskii energy functional. Numerous numerical experiments have shown that the energy dissipation holds…
We present an improved many-body T-matrix theory for partially Bose-Einstein condensed atomic gases by treating the phase fluctuations exactly. The resulting mean-field theory is valid in arbitrary dimensions and able to describe the…
The possibility of creating a Bose condensate of trapped atoms in a non-ground state is suggested. Such a nonequilibrium Bose condensate can be formed if one, first, obtains the conventional Bose condensate in the ground state and then…
The full Stokes equations are solved by a finite element method for simulation of large ice sheets and glaciers. The simulation is particularly sensitive to the discretization of the grounding line which separates the ice resting on the…
We consider a mixture of two distinct species of atoms of pseudospin-1/2 with both intraspecies and Interspecies spin-exchange interactions, and find all the ground stats in a general case of the parameters in the effective Hamiltonian. In…
In the studies of the Bose-Einstein condensation of ideal gases in finite systems, the divergence problem usually arises in the equation of state. In this paper, we present a technique based on the heat kernel expansion and the…
We analyze a system of coupled Bose-Einstein condensates in the domain of a unitary ball in $\mathbb{R}^3$. The coupling is due to atom-to-atom interactions that occur between different gas components. The multi-component Bose-Einstein…
We consider the Landau-Zener problem for a Bose-Einstein condensate in a linearly varying two-level system, for the full many-particle system as well and in the mean-field approximation. The many-particle problem can be solved approximately…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
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 provide a priori error estimates for variational approximations of the ground state eigenvalue and eigenvector of nonlinear elliptic eigenvalue problems of the form $-{div} (A\nabla u) + Vu + f(u^2) u = \lambda u$, $\|u\|_{L^2}=1$. We…
It is shown using the Gross-Pitaevskii equation that resonance states of Bose-Einstein condensates with attractive interactions can be stabilized into true bound states. A semiclassical variational approximation and an independent quantum…
Motivated by some inconsistencies in the way quantum fluctuations are included beyond the classical treatment of hard-core bosons on a lattice in the recent literature, we revisit the large-S semi-classical approach to hard-core bosons on…
We investigate the creation of a relative phase between two Bose-Einstein condensates, initially in number states, by detection of atoms and show how the system approaches a coherent state. Two very distinct time scales are found: one for…
In this paper a class of higher order finite element methods for the discretization of surface Stokes equations is studied. These methods are based on an unfitted finite element approach in which standard Taylor-Hood spaces on an underlying…
In this paper, for a new Stekloff eigenvalue problem which is non-selfadjoint and not $H^1$-elliptic, we establish and analyze two kinds of two-grid discretization scheme and a local finite element scheme. We present the error estimates of…