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We generalize the conformally invariant topological quantum mechanics of a particle propagating on a punctured plane by introducing a potential that breaks both the rotational and the conformal invariance down to a ${\bf Z}_2$…
A rigorous application of the correspondence rules shows that the operator of the angular momentum of a quantum particle---corresponding to the classical magnitude $\mathbf{l}= m \mathbf{r} \wedge \mathbf{v}$---is given by…
It is known that the momentum operator canonically conjugated to the position operator for a particle moving in some bounded interval of the line {(with Dirichlet boundary conditions) is not essentially self-adjoint}: it has a continuous…
We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre…
The properties which give quantum mechanics its unique character - unitarity, complementarity, non-commutativity, uncertainty, nonlocality - derive from the algebraic structure of Hermitian operators acting on the wavefunction in complex…
We experimentally generate cylindrically polarized wavepackets with transverse orbital angular momentum, demonstrating the coexistence of spatiotemporal optical vortex with spatial polarization singularity. The results in this paper extend…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
In this work, momentum-space decoherence using minimum and nonminimum-uncertainty-product (stretched) Gaussian wave packets in the framework of Caldeira-Leggett formalism and under the presence of a linear potential is studied. As a…
In this diploma thesis we study the characteristics of electromagnetic fields carrying orbital angular momentum (OAM) by analyzing and utilizing results achieved in optics and then apply them to the radio domain to enable innovative radio…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…
We define a set of fully Lorentz-invariant wave packets and show that it spans the corresponding one-particle Hilbert subspace, and hence the whole Fock space as well, with a manifestly Lorentz-invariant completeness relation (resolution of…
We study the dynamics of space-time non-diffracting wavepackets, commonly known as light bullets, in a spatiotemporally varying medium. We show that by spatiotemporal refraction, a monochromatic focused beam can be converted to a light…
Although time-reversal and inversion symmetry constrain the angular momentum of each phonon mode to vanish, we show that the vacuum state of crystals with such symmetries can nevertheless exhibit finite angular momentum fluctuations, which…
Complex and spinorial techniques of general relativity are used to determine all the states of the $SU(2)$ invariant quantum mechanical systems in which the equality holds in the uncertainty relations for the components of the angular…
Variable mass systems are a classic example of open systems in classical mechanics. The reaction forces due to mass variation propel ships, balloons, and rockets. Unlike free constant mass systems, the angular momentum of these systems is…
The time evolution of wave packets in a harmonic oscillator potential is studied. Some new results for the most general case are obtained. A natural number, called ``degree of rigidity'', is introduced to describe qualitatively how much the…
We present a theoretical study of linear wave scattering in one-dimensional nonlinear lattices by intrinsic spatially localized dynamic excitations or discrete breathers. These states appear in various nonlinear systems and present a…
In quantum theory, observables with a continuous spectrum are known to be fundamentally different from those with a discrete and finite spectrum. While some fundamental tests and applications of quantum mechanics originally formulated for…
We present an elementary discussion of the momentum transferred by an electromagnetic wave propagating in a dispersive medium. Our analysis is based on Minkowski's electromagnetic momentum density which have been recently seen to be…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…