Related papers: Particle in a box with a delta-function potential:…
This survey article deals with a delta potential - also known as a point scatterer - on flat 2D and 3D tori. We introduce the main conjectures regarding the spectral and wave function statistics of this model in the so- called weak and…
We investigate whether a 3-$\delta$ system with positive coupling strengths can approximate the transmission spectrum of a 2-$\delta$ resonance system with opposite-sign couplings for $k <3$. Theoretical analysis establishes exact…
Dusty plasma can exist in a wide range, from the laboratory to Saturn's rings. The coupling parameter plays a very important role in diagnosing dusty plasma. There are two ways to deal analytically with the effect of coupling in plasma.…
We restrict a quantum particle under a coulombian potential (i.e., the Schr\"odinger operator with inverse of the distance potential) to three dimensional tubes along the x-axis and diameter $\varepsilon$, and study the confining limit…
The original Thomson problem of "spherical crystallography" seeks the ground state of electron shells interacting via the Coulomb potential; however one can also study crystalline ground states of particles interacting with other…
In the spectral analysis of few one dimensional quantum particles interacting through delta potentials it is well known that one can recast the problem into the spectral analysis of an integral operator (the skeleton) living on the…
Consider operators $L_{V}:=\Delta + V$ in a bounded smooth domain $D$ in $R^N$. Assume that $V\in C^1(D)$ and $V$ may blow up at the boundary at most as $1/\delta^2$ where $\delta$ denotes distance to the boundary. Assume also that $L_{V}$…
The probability of observing a large deviation (LD) in the number of particles in a region $\Lambda$ in a dilute quantum gas contained in a much larger region $V$ is shown to decay as $\exp[-|\Lambda|\Delta F]$, where $|\L|$ is the volume…
The paper discusses the problem of stability of a two-component plasma and proposes a consistent consideration of quantum and long-range effects to calculate the thermodynamic properties of such a plasma. We restrict ourselves by the case…
The effective classical/quantum dynamics of a particle constrained on a closed line embedded in a higher dimensional configuration space is analyzed. By considering explicit examples it is shown how different reduction mechanisms produce…
For finite interacting particle systems with strong repulsing-attracting or general interactions, we prove global weak well-posedness almost up to the critical threshold of the strengths of attracting interactions (independent of the number…
A model physical problem is studied in which a system of two electrons is subject either to soft confinement by means of attractive oscillator potentials or by entrapment within an impenetrable spherical box of finite radius $R.$ When hard…
We study the formation of electron-hole pairs for disordered systems in the limit of weak electron-hole interactions. We find that both attractive and repulsive interactions lead to electron-hole pair states with large localization length…
Continuing the discussion on negative entropy in Casimir-effect like configurations, we consider two simple one-dimensional examples. One is the s-wave contribution to a plasma sphere and the other a single delta function potential. Some…
Energy levels are investigated for two charged particles possessing an attractive, momentum-independent, zero-range interaction in a uniform magnetic field. A transcendental equation governs the spectrum, which is characterized by a…
In this work we discuss about the problem of an electrically charged particle placed on the symmetry axis of an electrically charged ring in a quantum viewpoint. This problem should be an expanded version of the usual quantum ring and…
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…
Dirac delta-function potential is widely studied in quantum mechanics because it usually can be exactly solved and at the same time is useful in modeling various physical systems. Here we study a system of delta-potential trapped spinorbit…
Interaction of waves with point and line defects are usually described by $\delta$-function potentials supported on points or lines. In two dimensions, the scattering problem for a finite collection of point defects or parallel line defects…
We calculate the energy and wave functions of two particles confined to two spatial dimensions interacting via arbitrary anisotropic potentials with negative or zero net volume. The general rigorous analytic expressions are given in the…