Related papers: Conditions for realizing one-point interactions fr…
We study features of tunneling dynamics in an exactly-solvable model of N=4 supersymmetric quantum mechanics with a multi-well potential and with broken reflective symmetry. Quantum systems with a phenomenological potential of this type…
In this paper, the tunneling mechanism of cavitation in liquid helium for 3He and 4He is considered on the basis of the Schr\"odinger-like equation. It is assumed that the pairwise interactions of helium atoms are determined by the…
We consider physical interpretations of non-trivial boundary conditions of self-adjoint extensions for one-dimensional Schr\"odinger operator of free spinless particle. Despite its model and rather abstract character this question is worth…
The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The…
A system of identical bosons with short-range (contact) interactions is studied. Their motion is confined to one dimension by a tight lateral trapping potential and, additionally, subject to a weak harmonic confinement in the longitudinal…
We study the non-equilibrium steady-states of a one-dimensional ($1D1V$) fluid in a finite space region of length $L$. Particles interact among themselves by multi-particle collisions and are in contact with two thermal-wall heat…
Despite the fact that by now one dimensional and three dimensional systems of interacting particles are reasonably well understood, very little is known on how to go from the one dimensional physics to the three dimensional one. This is in…
It was proposed recently that the Schr\"odinger wave function can be reconstructed exactly from a discrete superposition of classical action branches weighted by associated classical densities, without semiclassical approximations. We…
Complete energy spectrum is obtained for the quantum mechanical problem of N one dimensional equal mass particles interacting via potential $$V(x_1,x_2,...,x_N) = g\sum^N_{i < j}{1\over (x_i-x_j)^2} - {\alpha\over \sqrt{\sum_{i < j}…
We consider a class of one dimensional vector Non-linear Schr$\ddot{o}$dinger Equation(NLSE) in an external complex potential with Balanced Loss-Gain(BLG) and Linear Coupling(LC) among the components of the Schr$\ddot{o}$dinger field. The…
Theoretical studies of self-assembly processes and condensed phases in colloidal systems are often based on effective inter-particle potentials. Here we show that developing an effective potential for particles interacting with a limited…
An exact solution of non-stationary Schrodinger equation is obtained for a one-dimensional movement of electrons in an electromagnetic field with arbitrary intensity and frequency. Using it, the permeability coefficient is calculated for a…
Structural phase transitions in two vertically or horizontally coupled channels of strongly interacting particles are investigated. The particles are free to move in the $x$-direction but are confined by a parabolic potential in the…
The aim of this article is to analyze numerical schemes using two-layer neural networks withinfinite width for the resolution of high-dimensional Schr{\"o}dinger eigenvalue problems with smoothinteraction potentials and Neumann boundary…
The formation of correlated structures is of importance in many diverse contexts such as strongly coupled plasmas, soft matter, and even biological mediums. In all these contexts the dynamics are mainly governed by electrostatic…
Using an analytically tractable lattice model for reaction-diffusion processes of hard-core particles we demonstrate that under nonequilibrium conditions phase coexistence may arise even if the system is effectively one-dimensional as e.g.…
Long-range interacting systems irreversibly relax as a result of their finite number of particles, $N$. At order $1/N$, this process is described by the inhomogeneous Balescu--Lenard equation. Yet, this equation exactly vanishes in…
It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…
The aim of this work is to provide further insight into the qualitative behavior of mechanical systems that are well described by Lennard-Jones type interactions on an atomistic scale. By means of $\Gamma$-convergence techniques, we study…
One-dimensional systems of interacting atoms are an ideal laboratory to study the Kosterlitz-Thouless phase transition. In the renormalization group picture there is essentially a two-parameter phase diagram to explore. We first present how…