Related papers: Bound States in Curved Quantum Layers
Bound state formation is a classic feature of quantum mechanics, where a particle localizes in the vicinity of an attractive potential. This is typically understood as the particle lowering its potential energy. In this article, we discuss…
A quantum particle moving under the influence of singular interactions on embedded surfaces furnish an interesting example from the spectral point of view. In these problems, the possible occurrence of a bound state is perhaps the most…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Quantum mechanics is sensitive to the geometry of the underlying space. Here, we present a framework for quantum scattering of a non-relativistic particle confined to a two-dimensional space. When the motion manifold hosts localized…
Quantum systems subjected to a continuous weak measurement process evolve according to stochastic differential equations (SDE). Depending on the outcomes of these stochastic measurements, the quantum state may diffuse in various directions…
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…
We investigate an infinite array of point interactions of the same strength in R^d, d=2,3, situated at vertices of a polygonal curve with a fixed edge length. We demonstrate that if the curve is not a line, but it is asymptotically straight…
We consider the possibility that photons of noncommutative QED can make bound states. Using the potential model, developed based on the constituent gluon picture of QCD glue-balls, arguments are presented in favor of existence of these…
We discuss the dynamics of a classical spinless quantum particle carrying electric charge and constrained to move on a non singular static surface in ordinary three dimensional space in the presence of arbitrary configurations of time…
Given a complete non-compact surface embedded in R^3, we consider the Dirichlet Laplacian in a layer of constant width about the surface. Using an intrinsic approach to the layer geometry, we generalise the spectral results of an original…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
Spatial curvature is one of the fundamental cosmological parameters that is routinely constrained from observations. The forward modelling of observations, in particular of large-scale structure, often relies on large cosmological…
A spinless nonrelativistic quantum particle on the curved surface of a homogeneous spherocylindrical capsule is considered. We apply Costa's formalism to solve the Schr\"{o}dinger equation with only a confined potential forcing the particle…
The operator and the functional formulations of the dynamics of constrained systems are explored for determining unambiguously the quantum Hamiltonian of a nonrelativistic particle in a curved space.
It is demonstrated that two distant quantum wells separated by a reservoir with a continuous spectrum can possess bound eigenstates embedded in the continuum. These represent a linear superposition of quantum states localized in the wells.…
In this work, based on a recently introduced localization scheme for scalar fields, we argue that the geometry of the space-time, where the particle states of a scalar field are localized, is intimately related to the quantum entanglement…
The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement is explored for bi-partite and multi-partite pure and mixed states.…
The formalism of nonrelativistic quantum physics was originally considered in the context of inertial frames. Here, we report on a more general framework that includes noninertial frames and arbitrarily strong gravitational fields. We…
We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get…
The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint $q \to 0$ limit, with $q$ the degree of freedom normal to the surface. In this…