Related papers: On Solving Cubic-Quartic Nonlinear Schr\"odinger E…
The dynamics of Bose-Einstein condensates trapped in a deep optical lattice is governed by a discrete nonlinear equation (DNL). Its degree of nonlinearity and the intersite hopping rates are retrieved from a nonlinear tight-binding…
We predict the existence of double-flattop quantum droplets in atomic Bose-Bose mixtures. Solutions of this type have two flattop regions of nearly uniform atomic density corresponding to a compressed central core surrounded by a rarefied…
We present the theoretical and mathematical foundations of stability analysis for a Bose-Einstein condensate (BEC) at Dirac points of a honeycomb optical lattice. The combination of s-wave scattering for bosons and lattice interaction…
In this work, we investigate the existence and orbital (in)stability of several branches of standing--wave solutions for the cubic nonlinear Schr\"odinger equation (NLS) posed on a looping--edge graph $\mathcal{G}$, consisting of a circle…
The discrete nonlinear Schr\"odinger equation (DNLSE) exhibits a transition from ergodic, delocalized dynamics to a weakly nonergodic regime characterized by breather formation; yet, a precise characterization of this transition has…
We address the existence, stability, and evolution of two-dimensional vortex quantum droplets (VQDs) in binary Bose-Einstein condensates trapped in a ring-shaped potential. The interplay of the Lee-Huang-Yang-amended nonlinearity and…
In this work we presented a derivation of the quantum hydrodynamic equations for neutral bosons. We considered short range interaction between particles. This interaction consist binary interaction $U(\textbf{r}_{i},\textbf{r}_{j})$ and…
We investigate how ultracold atoms in double well potentials can be used to study and put bounds on models describing wave function collapse. We refer in particular to the continuous spontaneous localization (CSL) model, which is the most…
We study the stability of a Bose-Einstein condensate of harmonically trapped atoms with negative scattering length, specifically lithium 7. Our method is to solve the time-dependent nonlinear Schrodinger equation numerically. For an…
We describe recent development of quantum hydrodynamics for ultracold Bose particle studying and consider different kinds of interactions. The method of derivation of equations describing the evolution of the neutral Bose particle system at…
We apply the theory of inhomogeneous Kibble-Zurek mechanism to understand quench dynamics from the Mott insulator to the superfluid in a cold Bose gases confined in both a two-dimensional optical lattice and a harmonic trap. The local…
We consider in this paper a system coupling a linear quantum Boltzmann equation and a defocusing cubic nonlinear Schrodinger equation. The Schrodinger equation reflects the dynamics of the wave function of the Bose-Einstein Condensate and…
Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several…
The phenomenon of Bose-Einstein condensation of dilute gases in traps is reviewed from a theoretical perspective. Mean-field theory provides a framework to understand the main features of the condensation and the role of interactions…
According to the mean-field theory a condensed Bose-Bose mixture collapses when the interspecies attraction becomes stronger than the geometrical average of the intraspecies repulsions, $g_{12}^2>g_{11} g_{22}$. We show that instead of…
In discrete nonlinear systems, the study of nonlinear waves has revealed intriguing phenomena in various fields such as nonlinear optics, biophysics, and condensed matter physics. Discrete nonlinear Schr\"odinger (DNLS) equations are often…
Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and…
In the case when $d<2s$, where $d$ is the space dimension and $s$ is the fractional power of the Laplacian, we study the well-posedness for a cubic nonlinear Schr\"odinger equation (CNLSE) generated by the fractional Laplacian and involving…
We consider the 3d cubic nonlinear Schr\"odinger equation (NLS) with a strong 2d harmonic potential. The model is physically relevant to observe the lower-dimensional dynamics of the Bose-Einstein condensate, but its ground state cannot be…
The variational-JWKB method is used to determine experimentally accessible macroscopic quantum tunneling regimes of quasi-bound Bose-Einstein condensates in two quasi one-dimensional trap configurations. The potentials can be created by…