Related papers: Bound states without potentials: localization at s…
We point out that bound states, degenerate in energy but differing in parity, may form in one dimensional quantum systems even if the potential is non-singular in any finite domain. Such potentials are necessarily unbounded from below at…
One-dimensional particle states are constructed according to orthogonality conditions, without requiring boundary conditions. Free particle states are constructed using Dirac's delta function orthogonality conditions. The states (doublets)…
We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…
We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential, by first solving the time-independent Schroedinger equation and then study a time dependent system with an…
The formation of bound states involving multiple particles underlies many interesting quantum physical phenomena, such as Efimov physics or superconductivity. In this work we show the existence of an infinite number of such states for some…
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…
Bound state and time evolution for single excitation in one dimensional XXZ spin chain within non-Markovian reservoir are studied exactly. As for bound state, a common feature is the localization of single excitation, which means the…
In this paper we study the number of bound states for potentials in one and two spatial dimensions. We first show that in addition to the well-known fact that an arbitrarily weak attractive potential has a bound state, it is easy to…
We study the localization of bosonic atoms in an optical lattice, which interact in a spatially confined region. The classical theory predicts that there is no localization below a threshold value for the strength of interaction that is…
At the lower edge of the energy continuum the birth of an isolated quantum bound state is studied as caused by an infinitesimally small change of the interaction. In our model a single, asymptotically free massive quantum particle is…
Stable bound quantum states are ubiquitous in nature. Mostly, they result from the interaction of only pairs of particles, so called two-body interactions, even when large complex many-particle structures are formed. We show that…
We study spontaneous symmetry breaking in one dimensional quantum mechanical problems in terms of two-point boundary problems which lead to singular potentials containing Dirac delta functions and its derivatives. We search for…
Some novel TWO-body effects analogous to the well-known THREE-body Efimov effect are predicted. In the systems considered, particle A is constrained on a TRUNCATED or BENT one-dimensional line or two-dimensional plane, or on one side of a…
We show that the geometry of the set of quantum states plays a crucial role in the behavior of entanglement in different physical systems. More specifically it is shown that singular points at the border of the set of unentangled states…
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…
We establish that the ability of a localized trapping potential to bind weakly-interacting bosons is dramatically enhanced in the vicinity of the threshold of formation of the single-particle bound-state of the trap. Specifically, for…
Defects or junctions in materials serve as a source of interactions for particles, and in idealized limits they may be treated as singular points yielding contact interactions. In quantum mechanics, these singularities accommodate an…
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…
Transition states or quantum states of zero energy appear at the boundary between the discrete part of the spectrum of negative energies and the continuum part of positive energy states. As such, transition states can be regarded as a…
Bound states in the continuum (BICs), referring to spatially localized bound states with energies falling within the range of extended modes, have been extensively investigated in single-particle systems, leading to diverse applications in…