Related papers: Invariant quantities of a nondepolarizing Mueller …
In this work, oriented for students with knowledge of basics of linear algebra, we demonstrate, how the use of polar decomposition allows one to understand metric properties of non-degenerate linear operators in $R^2$.
With assumption that an optical element is described by a Mueller matrix of the Lorentzian type, a method to find a 3-dimensional complex vector parameter for a corresponding Mueller matrix from results of four specially chosen polarization…
The paper aims to explore the physical quantities of several invariants, including the basic postulates of some types of crucial coordinate transformations, conservation laws and continuity equations, in the electromagnetic and…
Polarization measurements provide a detailed method to test the Standard Model and to search for new physics. Most previous studies depend on pre-selected coordinates, which blurs the significance of the results. The construction of two…
We present a new model for the propagation of polarized light in a random birefringent medium. This model is based on a decomposition of the higher order statistics of the reduced Stokes parameters along the irreducible representations of…
It was generally assumed that the Stokes parameters are complete characterization for the state of polarization of a plane light wave so that their counterparts in quantum optics, called the Stokes operators, represent the polarization of…
Polarimetric sensing by orthogonality breaking has been recently proposed as an alternative technique for performing direct and fast polarimetric measurements using a specific dual-frequency dual-polarization (DFDP) source. Based on the…
Recently, a remarkable correspondence has been unveiled between a certain class of ordinary linear differential equations (ODE) and integrable models. In the first part of the report, we survey the results concerning the 2nd order…
Over an algebraically closed base field $k$ of characteristic 2, the ring $R^G$ of invariants is studied, $G$ being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring $R$ of the…
For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for…
We work on some general extensions of the formalism for theories which preserve the relativity of inertial frames with a nonlinear action of the Lorentz transformations on momentum space. Relativistic particle models invariant under the…
We consider Noether symmetries within Hamiltonian setting as transformations that preserve Poincar\'e-Cartan form, i.e., as symmetries of characteristic line bundles of nondegenerate 1-forms. In the case when the Poincar\'e-Cartan form is…
It is noted that the Niederer transformation can be used to find the explicit relation between time-dependent linear oscillators, including the most interesting case when one of them is harmonic. A geometric interpretation of this…
Information about the three-dimensional structure of solar magnetic fields is encoded in the polarized spectra of solar radiation by a host of physical processes. To extract this information, solar spectra must be obtained in a variety of…
We identify, for a general physically realizable Mueller transformation, the only intrinsic geometricphase structure that can be assigned to it in an invariant manner: the retarding part of the characteristic pure component selected by the…
Meaningful topological invariants for mixed quantum states are challenging to identify as there is no unique way to define them, and most choices do not directly relate to physical observables. Here, we propose a simple pragmatic approach…
Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…
A character (ordinary or modular) is called orthogonally stable if all non-degenerate quadratic forms fixed by representations with those constituents have the same determinant mod squares. We show that this is the case provided there are…