Related papers: Interacting particles in two dimensions: numerical…
In this study, we solve analytically the Schrodinger equation for a macroscopic quantum oscillator as a central system coupled to two environmental micro-oscillating particles. Then, the double-slit interference patterns are investigated in…
The problem of two electrons in a two-dimensional random potential is addressed numerically. Specifically, the role of the Coulomb interaction between electrons on localization is investigated by writing the Hamiltonian on a localized basis…
We consider two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we study the two-component plasma in detail. When the coulombic coupling constant $\Gamma=2$ the model is exactly solvable. We…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
We suggest an effective approach to separation of variables in the Schr\"odinger equation with two space variables. Using it we classify inequivalent potentials $V(x_1,x_2)$ such that the corresponding Schr\" odinger equations admit…
We consider the two-dimensional nonlinear Schr\"odinger equation with point interaction and we establish a local well-posedness theory, including blow-up alternative and continuous dependence on the initial data in the energy space. We…
We consider a dispersive equation of Schr{\"o}dinger type with a non-linearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with LHY…
Symmetry classification of two-body central potentials in a two-particle Schr\"{o}dinger equation in terms of contact transformations of the equation has been investigated. Explicit calculation has shown that they are of the same four…
We consider N run and tumble particles in one dimension interacting via a linear 1D Coulomb potential, an active version of the rank diffusion problem. It was solved previously for N = 2 leading to a stationary bound state in the attractive…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schr\"{o}dinger-Newton model in any space dimension $d$. Our result is based on an analysis of the corresponding system of second order…
We investigate the behaviour of a system of particles with the different character of interaction. The approach makes it possible to describe systems of interacting particles by statistical methods taking into account a spatial…
We provide a statistical and correlational analysis of the spatial and energetic properties of equilibrium configurations of a few-body system of two to eight equally charged classical particles that are confined on a one-dimensional…
The simulation of strongly correlated many-electron systems is one of the most promising applications for near-term quantum devices. Here we use a class of eigenvalue solvers (presented in Phys. Rev. Lett. 126, 070504 (2021)) in which a…
We investigate the global existence and scattering for the cubic fourth-order Schr\"{o}dinger equation $iu_t+\Delta^2u+|u|^2u=0$ in the low regularity space $H^s(\R^n)$ with $s<2$. We provide an alternative approach to obtain a new…
We develop a general approach to study three-dimensional Schroedinger operators with confining potentials depending on the distance to a surface. The main idea is to apply parallel coordinates based on the surface but outside its cut locus…
This research investigates the formation and stability of localized states, known as quantum droplets and bubbles, in the quadratic-cubic discrete nonlinear Schr\"odinger equation. Near a Maxwell point, these states emerge from two fronts…
We study the following focusing intercritical nonlinear Schr\"odinger equation with partial harmonic confinement: \begin{equation*} \begin{cases} i\partial_t u+\Delta_{z}u-y^2 u =- |u|^{\alpha}u,\quad t\in \mathbb{R},\newline u(0,z)=…
For the numerical solution of the cubic nonlinear Schr\"{o}dinger equation with periodic boundary conditions, a pseudospectral method in space combined with a filtered Lie splitting scheme in time is considered. This scheme is shown to…
We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schr\"{o}dinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very…