Related papers: Quantum exotic: A repulsive and bottomless confini…
We consider classical and quantum dynamics on potentials that are asymptotically unbounded from below. By explicit construction we find that quantum bound states can exist in certain bottomless potentials. The classical dynamics in these…
We consider a particle with a position-dependent mass, moving in a three-dimensional semi-infinite parallelepipedal or cylindrical channel under the influence of some hyperbolic potential. We show that the lack of uniformity in the…
We quantise integrable point-particle systems with opposite-sign kinetic terms and nontrivial interactions. Using methods from separability theory, we show that previously determined classical stability conditions also imply discrete…
We show how a potential that is well-defined everywhere on the positive half-line, but diverges to $-\infty$ as $x\rightarrow 0^+$, may still be able to dynamically confine a particle to the (positive) half-line. We shall call this effect…
We study the classical dynamics of a charged particle in two dimensions, under the influence of a perpendicular magnetic and an in-plane electric field. We prove the surprising fact that there is a finite region in phase space that…
We give a rigorous argument that long--range repulsion stabilizes quantum systems; ground states of such quantum systems exist even when the ground state energy is precisely at the ionization threshold. For atomic systems at the critical…
The existence of bound states in quantum mechanics with no classical counterpart has been a subject of interest for a long time. Cross-wires and cavities connected to infinite leads are typical examples in which open geometries with bulges…
A quantum neutral particle, constrained to move on a conical surface, is used as a toy model to explore bound states due to both a inverse squared distance potential and a $\delta$-function potential, which appear naturally in the model.…
We investigate the confinement properties of solutions of the aggregation equation with repulsive-attractive potentials. We show that solutions remain compactly supported in a large fixed ball depending on the initial data and the…
We consider a quantum droplet which is confined in a ring potential. We investigate the so-called "yrast" state, i.e., the lowest-energy state of the droplet assuming that it has some fixed expectation value of the angular momentum. Two are…
We summarize unusual bound or localized states in quantum mechanics. Our guide through these intriguing phenomena is the classical physics of the upside-down pendulum. Taking advantage of the analogy between the corresponding Newton's…
On a lattice, as the momentum space is compact, the kinetic energy is bounded not only from below but also from above. It is shown that this, somehow removes the distinction between repulsive and attractive forces. In particular, it is seen…
One-dimensional scattering by a Coulomb potential V(x)=lambda/|x| is studied for both repulsive (c>0) and attractive (c<0) cases. Two methods of regularizing the singularity at x=0 are used, yielding the same conclusion, namely, that the…
The quantum-mechanical collapse (alias fall onto the center of particles attracted by potential -1/r^2), or "quantum anomaly", is a well-known issue in the quantum theory. We demonstrate that the mean-field repulsive nonlinearity prevents…
We consider a continuous system of classical particles confined in a finite region $\Lambda$ of $\mathbb{R}^d$ interacting through a superstable and tempered pair potential in presence of non free boundary conditions. We prove that the…
We prove limiting absorption resolvent bounds for the semiclassical Schr\"odinger operator with a repulsive potential in dimension $n\ge 3$, which may have a singularity at the origin. As an application, we obtain time decay for the…
After reviewing the general properties of zero-energy quantum states, we give the explicit solutions of the \seq with $E=0$ for the class of potentials $V=-|\gamma|/r^{\nu}$, where $-\infty < \nu < \infty$. For $\nu > 2$, these solutions…
The quantum mechanical bound states of the $-{\alpha}/x^2$ potential are truly anomalous. We revisit this problem by adopting a slightly modified version of this potential, one that adopts a cutoff in the potential arbitrarily close to the…
This paper considers the possibility that two charged particles with an attractive short-ranged potential between them which is not strong enough to form bound states in free space, may bind in uniform magnetic fields. It is shown that in…
Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which…