Related papers: Quantum mechanical 4-dimensional non-polarizing be…
Partial polarization is the manifestation of the correlation between two mutually orthogonal transverse field components associated with a light beam. We show both theoretically and experimentally that the origin of this correlation can be…
Vector beams are inhomogeneously polarized optical fields with nonseparable, quantum-like correlations between their polarisation and spatial components, and hold tremendous promise for classical and quantum communication across various…
Rotations on the 3-dimensional Euclidean vector-space can be represented by real quaternions, as was shown by Hamilton. Introducing complex quaternions allows us to extend the result to elliptic and hyperbolic rotations on the Minkowski…
We show how the quantum process of splitting light may be modelled in classical optics. A second result is the possibility to engineer specific forms of a classical field.
Relations and isomorphisms between quantum field theories in operator and functional integral formalisms are analyzed from the viewpoint of inequivalent representations of commutator or anticommutator rings of field operators. A functional…
Many basis sets for electronic structure calculations evolve with varying external parameters, such as moving atoms in dynamic simulations, giving rise to extra derivative terms in the dynamical equations. Here we revisit these derivatives…
We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a…
Fusion frames are a very active area of research today because of their myriad of applications in pure mathematics, applied mathematics, engineering, medicine, signal and image processing and much more. They provide a great flexibility for…
To quantify the effect of decoherence in quantum measurements, it is desirable to measure not merely the square modulus of the spatial wavefunction, but the entire density matrix, whose phases carry information about momentum and how pure…
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are…
We present a generalized 4 $\times$ 4 matrix formalism for the description of light propagation in birefringent stratified media. In contrast to previous work, our algorithm is capable of treating arbitrarily anisotropic or isotropic,…
These lecture notes yield an introduction to quantum Hall effects both for non-relativistic electrons in conventional 2D electron gases (such as in semiconductor heterostructures) and relativistic electrons in graphene. After a brief…
Quantum field theory (QFT) describes nature using continuous fields, but physical properties of QFT are usually revealed in terms of measurements of observables at a finite resolution. We describe a multiscale representation of a free…
The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…
An input-output model of a two-level quantum system in the Heisenberg picture is of bilinear form with constant system matrices, which allows the introduction of the concepts of controllability and observability in analogy with those of…
A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…
This work is concerned with two-spin-1/2-fermion relativistic quantum mechanics, and it is about the construction of one-particle projectors using an inherently two(many)-particle, `explicitly correlated' basis representation, necessary for…
The Mueller-Stokes formalism which governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could demand of a $4\times 4$ real matrix $M$ in order that it qualifies to be the Mueller matrix…
Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of…
We get deeper understanding of the role played by boundary conditions in quantum field theory, by studying the structure of a scalar massless quantum field theory bounded by two one dimensional planar crystal plates. The system can also be…