Related papers: Quantum Mechanical Properties of Bessel Beams
We show how strongly correlated ultracold bosonic atoms loaded in specific orbital angular momentum states of arrays of cylindrically symmetric potentials can realize a variety of spin-1/2 models of quantum magnetism. We consider explicitly…
We study quantum and classical systems associated with the quantum corner symmetry group $\mathrm{QCS}=\widetilde{\mathrm{SL}}(2,\mathbb{R})\ltimes \mathrm{H}_3,$ which arises in the context of quantum gravity. We relate quantum observables…
We propose a version of the non-relativistic quantum mechanics in which the pure states of a quantum system are described as sections of a Hilbert (generally infinitely-dimensional) fibre bundle over the space-time. There evolution is…
Research methods and results from physics and psychology are used to explore a question in quantum mechanics. In this investigation, an observer variable is manipulated in an experimental context concerning the trajectory of electrons…
The effect of the Kerr nonlinearity on linear non-diffractive Bessel beams is investigated analytically and numerically using the nonlinear Schr\"odinger equation. The nonlinearity is shown to primarily affect the central parts of the…
Perfect (optical) vortices (PVs) have the mooted ability to encode orbital angular momentum (OAM) onto the field within a well-defined annular ring. Although this makes the near-field radial profile independent of OAM, the far-field radial…
A class of unitary operations generated by idealized, semiclassical fields is studied. The operations implemented by sharp potential kicks are revisited and the possibility of performing them by softly varying external fields is examined.…
A non-associative algebra of observables cannot be represented as operators on a Hilbert space, but it may appear in certain physical situations. This article employs algebraic methods in order to derive uncertainty relations and…
Mesoscopic physics deals with three fundamental issues: quantum coherence, fluctuations and correlations. Here we analyze these issues for atom optics, using a simplified model of an assembly of atoms (or detectors, which are particles with…
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
Experimental evidene of the last decades has made the status of "collapses of the wave function" even more shaky than it already was on conceptual grounds: interference effects turn out to be detectable even when collapses are typically…
During the recent developments of quantum theory it has been clarified that the observable quantities (like energy or position) may be represented by operators (with real spectra) which are manifestly non-Hermitian. The mathematical…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
The ontology emerging from quantum field theory and the results following from Bell's theorems allowed the development of an intuitive picture of the microscopic world described by quantum mechanics, that is, we can say that we understand…
Quantum information science is a source of task-related axioms whose consequences can be explored in general settings encompassing quantum mechanics, classical theory, and more. Quantum states are compendia of probabilities for the outcomes…
The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…
Covariant integral quantisation using coherent states for semidirect product groups is studied and applied to the motion of a particle on the circle. In the present case the group is the Euclidean group E$(2)$. We implement the quantisation…
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…
It is shown that q-deformed quantum mechanics (q-deformed Heisenberg algebra) can be interpreted as quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first-) class constraints. (Saclay, T93/027).