Related papers: Characterization of coorbit spaces with phase-spac…
This paper is concerned with frame decompositions of $\alpha$-modulation spaces. These spaces can be obtained as coorbit spaces for square-integrable representations of the affine Weyl-Heisenberg group modulo suitable subgroups. The theory…
We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two-dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally…
For any given algebra of local observables in relativistic quantum field theory there exists an associated scaling algebra which permits one to introduce renormalization group transformations and to construct the scaling (short distance)…
We assume that space-time at the Planck scale is discrete, quantised in Planck units and "qubitsed" (each pixel of Planck area encodes one qubit), that is, quantum space-time can be viewed as a quantum computer. Within this model, one finds…
Dynamical systems associated with a q-deformed two dimensional phase space are studied as effective dynamical systems described by ordinary variables. In quantum theory, the momentum operator in such a deformed phase space becomes a…
Periodic driving of particles can create crystalline structures in their dynamics. Such systems can be used to study solid-state physics phenomena in the time domain. In addition, it is possible to realize photonic time crystals and to…
We demonstrate that the multipoles associated with the density matrix are truly observable quantities that can be unambiguously determined from intensity moments. Given their correct transformation properties, these multipoles are the…
In certain scenarios of deformed relativistic symmetries relevant for non-commutative field theories particles exhibit a momentum space described by a non-abelian group manifold. Starting with a formulation of phase space for such particles…
In this survey, we discuss whether the complex projective space can be characterized by its integral cohomology ring among compact complex manifolds.
It is shown that bunch phase space distribution can be modified by means of RF phase modulation.
Limits and characteristic periods of variations in orbital elements of planets were studied by numerical integration of equations of motion. Interrelations between the characteristic periods of variations in orbital elements of some planets…
This paper is concerned with the study of Besov-type decomposition spaces, which are scales of spaces associated to suitably defined coverings of the euclidean space $\mathbb{R}^d$, or suitable open subsets thereof. A fundamental problem in…
The P-matrix approach for the determination of the orbit spaces of compact linear groups enabled to determine all orbit spaces of compact coregular linear groups with up to 4 basic polynomial invariants and, more recently, all orbit spaces…
Phase space is a framework ideally suited for quantizing superintegrable systems through the use of deformation methods, as illustrated here by applications to de Sitter and chiral particles. Within this framework, Nambu brackets elegantly…
All four dimensional orbit spaces of compact coregular linear groups have been determined. The results are obtained through the integration of a universal differential equation, that only requires as input the number of elements of an…
We introduce a version of Farber's topological complexity suitable for investigating mechanical systems whose configuration spaces exhibit symmetries. Our invariant has vastly different properties to the previous approaches of Colman-Grant,…
Unstable periodic orbits scar wave functions in chaotic systems. This also influences the associated spectra, that follow the otherwise universal Porter--Thomas intensity distribution. We show here how this deviation extend to other longer…
We study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square-integrable quasi-regular representation on ${\rm L}^2(\mathbb{R}^d)$. We first prove that these representations are integrable…
We study the coherence in time and space of electromagnetic fields propagated through complex media. Whether for localization, imaging or telecommunication, the development of dedicated numerical techniques is generally based on the…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…