Related papers: Local density approximation for the almost-bosonic…
A fermion ground state energy functional is set up in terms of particle density, relative pair density, and kinetic energy tensor density. It satisfies a minimum principle if constrained by a complete set of compatibility conditions. A…
We present an analytical approximation for nonlinear dynamics of trapped Bose-co ndensed gases. The new approximation is a substantial improvement over the Thomas-Fermi approximation and is shown to be applicable for systems with a rather…
The statistical mechanics of an anyon gas in a magnetic field is addressed. An harmonic regulator is used to define a proper thermodynamic limit. When the magnetic field is sufficiently strong, only exact $N$-anyon groundstates, where…
We address in this work the problem of minimizing quantum entropies under local constraints. We suppose macroscopic quantities such as the particle density, current, and kinetic energy are fixed at each point of $\Rm^d$, and look for a…
We investigate degenerate quantum gases in one dimension trapped in a harmonic potential that is split in the centre by a pointlike potential. Since the single particle eigenfunctions of such a system are known for all strengths of the…
A Bose-Einstein condensate of atoms, trapped in an axially symmetric harmonic potential, is considered. By averaging the spatial density along the symmetry direction over a length that preserves the aspect ratio, the system may be mapped on…
The essence of the Thomas-Fermi model is the assumption that the local behavior of a many-body system can be approximated by that of a homogeneous system. In this paper, we present the natural extension of the static Thomas-Fermi treatment…
We rely on a variational approach to derive a set of equations governing a trapped self-interacting Bose gas at finite temperature. In this work, we analyze the static situation both at zero and finite temperature in the Thomas-Fermi limit.…
We investigate local and global properties of the one-dimensional Bose-Hubbard model with an external confining potential, describing an atomic condensate in an optical lattice. Using quantum Monte Carlo techniques we demonstrate that a…
We investigate a homogenization problem related to a non-local interface energy with a periodic forcing term. We show the existence of planelike minimizers for such energy. Moreover, we prove that, under suitable assumptions on the…
The ground state properties of a single-component one-dimensional Coulomb gas are investigated. We use Bose-Fermi mapping for the ground state wave function which permits to solve the Fermi sign problem in the following respects (i) the…
We investigate the behavior of a weakly interacting nearly one-dimensional (1D) trapped Bose gas at finite temperature. We perform in situ measurements of spatial density profiles and show that they are very well described by a model based…
The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the…
Using the method of locally equilibrium statistical operator we consider the thermalized relativistic quantum fields in an oscillatory trap. We compare this thermal picture of the confined boson gas with non-relativistic model of…
We consider the quantitative description of a many-particle gas of interacting abelian anyons in the plane, confined in a trapping potential. If the anyons are modeled as bosons with a magnetic flux attachment, and if the total magnetic…
Ultracold gases are a versatile platform to simulate condensed matter physics, as virtually any parameter is experimentally tunable. In particular, highly anisotropic traps allow the realization of low-dimensional systems, where the role of…
We consider a Fermi gas with short-range attractive interactions that is confined along one direction by a tight harmonic potential. For this quasi-two-dimensional (quasi-2D) Fermi gas, we compute the pressure equation of state, radio…
We investigate the particle and kinetic energy densities of harmonically trapped fermion gases at zero temperature in arbitrary dimensions. We derive analytically a differential equation connecting these densities, which so far have been…
We study a nonlinear ground state of the Gross-Pitaevskii equation with a parabolic potential in the hydrodynamics limit often referred to as the Thomas--Fermi approximation. Existence of the energy minimizer has been known in literature…
A thermodynamic argument is proposed in order to discuss the most appropriate form of the local energy balance equation within the Oberbeck-Boussinesq approximation. The study is devoted to establish the correct thermodynamic property to be…