ﻻ يوجد ملخص باللغة العربية
We introduce a new type of models for two-component systems in one dimension subject to exact solutions by Bethe ansatz, where the interspecies interactions are tunable via Feshbach resonant interactions. The applicability of Bethe ansatz is obtained by fine-tuning the resonant energies, and the resulting systems can be described by introducing intraspecies repulsive and interspecies attractive couplings $c_1$ and $c_2$. This kind of systems admits two types of interesting solutions: In the regime with $c_1>c_2$, the ground state is a Fermi sea of two-strings, where the Fermi momentum $Q$ is constrained to be smaller than a certain value $Q^*$, and it provides an ideal scenario to realize BCS-BEC crossover (from weakly attractive atoms to weakly repulsive molecules) in one dimension; In the opposite regime with $c_1<c_2$, the ground state is a single bright soliton even for fermionic atoms, which reveals itself as an embedded string solution.
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have
We investigate one-dimensional three-body systems composed of two identical bosons and one imbalanced atom (impurity) with two-body and three-body zero-range interactions. For the case in the absence of three-body interaction, we give a complete phas
We study the fluctuation properties of a one-dimensional many-body quantum system composed of interacting bosons, and investigate the regimes where quantum noise or, respectively, thermal excitations are dominant. For the latter we develop a semiclas
In this Thesis, we report a detailed study of the ground-state properties of a set of quantum few- and many-body systems in one and two dimensions with different types of interactions by using Quantum Monte Carlo methods. Nevertheless, the main focus
In this paper, we provide the two-body exact solutions of two dimensional (2D) Schr{o}dinger equation with isotropic $pm 1/r^3$ interactions. Analytic quantum defect theory are constructed base on these solutions and are applied to investigate the sc