Related papers: Mass-Energy threshold dynamics for dipolar Quantum…
Quantum droplets have been recently observed in dipolar Bose-Einstein condensates (BECs) and in BEC mixtures. This forms the motivation for us to explore the dynamics of these droplets. We make use of the Extended Gross-Pitaevski equation…
We present a general framework in which we can accurately describe the non-equilibrium dynamics of trapped atomic gases. This is achieved by deriving a single Fokker-Planck equation for the gas. In this way we are able to discuss not only…
We study the Cauchy problem of the mass critical nonlinear Schrodinger equation with derivative with the 4pi mass. One has the global well-posedness in H^1 whenever "the mass is strictly less than 4pi" or whenever "the mass is equal to 4pi…
This is a less technical presentation of the ideas in quant-ph/9804035 [Phys Rev Lett 83 (1999), 1707-1710]. A second order phase transition induced by a rapid quench can lock out topological defects with densities far exceeding their…
We consider the finite-time blow-up dynamics of solutions to the self-dual Chern-Simons-Schr\"odinger (CSS) equation (also referred to as the Jackiw-Pi model) near the radial soliton $Q$ with the least $L^{2}$-norm (ground state). While a…
We present a numerical study of turbulence in Bose-Einstein condensates within the 3D Gross-Pitaevskii equation. We concentrate on the direct energy cascade in forced-dissipated systems. We show that behavior of the system is very sensitive…
We present a family of exact solutions of one-dimensional nonlinear Schr\"odinger equation, which describe the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive…
A uniform dilute Bose gas of known density has a universal behavior as the atomic scattering length tends to infinity at unitarity while most of its properties are determined by a universal parameter $\xi$ relating the energies of the…
Now that the properties of the ground state of quantum-mechanical many-body systems (bosons) at low density, $\rho$, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors 4-5 decades ago.…
We consider the time-dependent Gross-Pitaevskii equation describing the dynamics of rotating Bose-Einstein condensates and its discretization with the finite element method. We analyze a mass conserving Crank-Nicolson-type discretization…
The paper considers a model for Bose gases in the so-called 'high-temperature range' below the temperature Tc, where Bose-Einstein condensation sets in.The model is of non-linear two-component type, consisting of a kinetic equation with…
I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation)…
We utilize a two-gas model to simulate collective oscillations of a Bose-Einstein condensate at finite temperatures. The condensate is described using a generalized Gross-Pitaevskii equation, which is coupled to a thermal cloud modelled by…
An autoresonant approach for exciting space-time quasicrystals in Bose-Einstein condensates is proposed by employing two-component chirped frequency parametric driving or modulation of the interaction strength within Gross-Pitaevskii…
The Gross-Pitaevskii equation, or more generally the nonlinear Schr\"odinger equation, models the Bose-Einstein condensates in a macroscopic gaseous superfluid wave-matter state in ultra-cold temperature. We provide analytical study of the…
We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein-de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we…
In this paper, we consider the Cauchy problem of the 3-component Degasperis-Procesi equation. Firstly, we discuss a local well-posedness result and a blow-up criterion in the low besov space. Secondly, we study the blow-up phenomenon by…
We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space $H^s$…
We derive the time-dependent two-component Gross--Pitaevskii (GP) equation as an effective description of the dynamics of a dilute two-component Bose gas near its ground state, which exhibits a two-component Bose-Einstein condensate, in the…
We develop the number-conserving approach that has previously been used in a single component Bose-Einstein condensed dilute atomic gas, to describe consistent coupled condensate and noncondensate number dynamics, to an $n$-component…