相关论文: Tan's contact scaling behaviour for trapped Lieb-L…
For a system of $N$ bosons in one space dimension with two-body $\delta$-interactions the Hamiltonian can be defined in terms of the usual closed semi-bounded quadratic form. We approximate this Hamiltonian in norm resolvent sense by…
We investigate the Lieb-Liniger model of one-dimensional bosons subjected to periodic kicks. In both the non-interacting and strongly interacting limits, the system undergoes dynamical localization, leading to energy saturation at long…
We derive and describe a very accurate variational scheme for the ground state of the system of a few ultra-cold bosons confined in one-dimensional traps of arbitrary shapes. It is based on assumption that all inter-particle correlations…
We unravel the stationary properties and the interaction quench dynamics of two bosons, confined in a two-dimensional anisotropic harmonic trap. A transcendental equation is derived giving access to the energy spectrum and revealing the…
The variational determination of the two-boson reduced density matrix is described for a one-dimensional system of $N$ (where $N$ ranges from $2$ to $10^4$) harmonically trapped bosons interacting via contact interaction. The ground-state…
The two and three-body contacts are central to a set of univeral relations between microscopic few-body physics within an ultracold Bose gas and its thermodynamical properties. They may also be defined in trapped few-particle systems, which…
The main focus of this thesis is the theoretical study of strongly interacting quantum mixtures confined in one dimension and subjected to a harmonic external potential. Such strongly correlated systems can be realized and tested in…
We investigate the quantum dynamics of two bosons, trapped in a two-dimensional harmonic trap, upon quenching arbitrarily their interaction strength thereby covering the entire energy spectrum. Utilizing the exact analytical solution of the…
We consider a one-dimensional, trapped, focusing Bose gas where $N$ bosons interact with each other via both a two-body interaction potential of the form $a N^{\alpha-1} U(N^\alpha(x-y))$ and an attractive three-body interaction potential…
For one-dimensional systems with delta-contact interactions, the convergence of the exact-diagonalization method is tested with a basis of harmonic oscillator eigenfunctions with frequency $\Omega$ optimized through the minimization of the…
The configuration interaction (CI) method for calculating the exact eigenstates of a quantum-mechanical few-body system is problematic when applied to particles interacting through contact forces. In dimensions higher than one the approach…
Motivated by recent experiments we derive an exact expression for the correlation function entering the three-body recombination rate for a one-dimensional gas of interacting bosons. The answer, given in terms of two thermodynamic…
We propose a variational approximation to the ground state energy of a one-dimensional gas of interacting bosons on the continuum based on the Bethe Ansatz ground state wavefunction of the Lieb-Liniger model. We apply our variational…
Tan's contact is a quantity that unifies many different properties of a low-temperature gas with short-range interactions, from its momentum distribution to its spatial two-body correlation function. Here, we use a Ramsey interferometric…
We consider N trapped bosons in R 3 interacting via a pair potential w which has a long range of dipolar type. We show the convergence of the energy and of the minimizers for the many-body problem towards those of the dipolar…
The exactly solvable Lieb-Liniger model of interacting bosons in one-dimension has attracted renewed interest as current experiments with ultra-cold atoms begin to probe this regime. Here we numerically solve the equations arising from the…
We consider a finite number $N$ of interacting bosonic atoms at zero temperature confined in a one-dimensional double-well trap and study this system by using the two-site Bose-Hubbard (BH) Hamiltonian. For systems with $N=2$ and $N=3$, and…
We consider the well-known Lieb-Liniger (LL) model for $N$ bosons interacting pairwise on the line via the $\delta$-potential in the mean-field scaling regime. Assuming suitable asymptotic factorization of the initial wave functions and…
Ultracold atoms provide clues to an important many-body problem regarding the dependence of Bose-Einstein condensation (BEC) transition temperature $T_c$ on interactions. However, cold atoms are trapped in harmonic potentials and…
Strongly interacting systems of dipolar bosons in three dimensions confined by harmonic traps are analyzed using the exact Path Integral Ground State Monte Carlo method. By adding a repulsive two-body potential, we find a narrow window of…