Related papers: Quantum Mechanical Properties of Bessel Beams
Two entangled electron spins, or qubits, are analyzed in terms of ordinary three-dimensional space geometric properties, as are the angles between their angular momenta. This formulation allows concurrence, a measure of quantum…
The main features of quantum computing are described in the framework of spin resonance methods. Stress is put on the fact that quantum computing is in itself nothing but a re-interpretation (fruitful indeed) of well-known concepts. The…
The interrelations between the two definitions of momentum operator, via the canonical energy-momentum tensorial operator and as translation operator (on the operator space), are studied in quantum field theory. These definitions give rise…
It is known that internal energy flow in a light beam can be divided into the orbital flow, associated with the macroscopic energy redistribution within the beam, and the spin flow originating from instantaneous rotation of the field…
Angular momentum densities of electromagnetic beams are connected to helicity (circular polarization) and topological charge (azimuthal phase shift and vorticity). Computing the electromagnetic fields emitted by a circular antenna array,…
The geometrical description of Quantum Mechanics is reviewed and proposed as an alternative picture to the standard ones. The basic notions of observables, states, evolution and composition of systems are analised from this perspective, the…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
The quantum dynamics of optomechanical systems was mostly studied for their fluctuations around classical steady states. We present a theoretical approach to determining the system observables of optomechanical systems as genuine quantum…
Quantum field theory can be physically regularized by modularizing it on several levels of aggregation. Since computation is already thoroughly modularized, physical experiments are treated here as quantum relativistic cellular computations…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket, and a quasidensity operator. These are analogues of the star product, the Moyal bracket, and…
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum Mechanics in presence of non-interacting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary…
The discussion of the foundations of quantum mechanics is complicated by the fact that a number of different issues are closely entangled. Three of these issues are i) the interpretation of probability, ii) the choice between realist and…
The purpose of this contribution is to give a very brief introduction to Quantum Mechanics for an audience of mathematicians. I will follow Segal's approach to Quantum Mechanics paying special attention to algebraic issues. The usual…
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
We review recent important topics in quantized vortices and quantum turbulence in atomic Bose--Einstein condensates (BECs). They have previously been studied for a long time in superfluid helium. Quantum turbulence is currently one of the…
A general entangled qubit pair is analyzed in the de Broglie-Bohm formalism corresponding to two spin-1/2 quantum rotors. Several spin-spin correlators of Bohm's hidden variables are analyzed numerically and a detailed comparison with…
It has been found that quantum corrections can substantially affect the classical results of tracking for trajectories close to the separatrix. Hence the development of a basic formalism for obtaining the quantum maps for any particle beam…
Given a bounded normal operator $A$ in a Hilbert space and a fixed vector $x$, we elaborate on the problem of finding necessary and sufficient conditions under which $(A^kx)_{k\in\mathbb N}$ constitutes a Bessel sequence. We provide a…
The pure state space of Quantum Mechanics is investigated as Hermitian Symmetric Kaehler manifold. The classical principles of Quantum Mechanics (Quantum Superposition Principle, Heisenberg Uncertainty Principle, Quantum Probability…