Related papers: A Generalized Method for Spatial Operations on Phy…
This paper presents a new method, based on the well-known method of moments (MoM), for the numerical electromagnetic analysis of scattering and radiation from metallic or dielectric structures, or both structure types in the same…
The properties of fluctuation induced interactions like van der Waals and Casimir-Lifshitz forces are of interest in a plethora of fields ranging from biophysics to nanotechnology. Here we describe a general approach to compute these…
Ray optics is an intuitive and computationally efficient model for wave propagation through nonuniform media. However, the underlying geometrical-optics (GO) approximation of ray optics breaks down at caustics, erroneously predicting the…
New iterative methods for solving linear equations are presented that are easy to use, generalize good existing methods, and appear to be faster. The new algorithms mix two kinds of linear recurrence formulas. Older methods have either high…
Recently, neural implicit surfaces have become popular for multi-view reconstruction. To facilitate practical applications like scene editing and manipulation, some works extend the framework with semantic masks input for the…
We generalize entanglement detection with covariance matrices for an arbitrary set of observables. A generalized uncertainty relation is constructed using the covariance and commutation matrices, then a criterion is established by…
A momentum-space approach to conformal field theory offers a new perspective on cosmological correlators and better reveals the underlying connections to scattering amplitudes. This thesis explores the interplay between integral…
Crystalline materials, with symmetrical and periodic structures, exhibit a wide spectrum of properties and have been widely used in numerous applications across electronics, energy, and beyond. For crystalline materials discovery,…
Fewer operators are more fundamental than the position operator in a crystal. But since it is not translationally invariant in crystal momentum representation (CMR), how to properly represent it is nontrivial. Over half a century, various…
The analysis of mathematical structure of the method of operator manifold guides our discussion. The latter is a still wider generalization of the method of secondary quantization with appropriate expansion over the geometric objects. The…
Casimir interactions between macroscopic objects are strongly influenced by their geometrical features as shape and orientation as well as by their material properties. The effect of geometry is commonly obtained from the proximity…
We derive some local properties of abstract crystals with logarithmic poles over a smooth base in positive characteristic and obtain the existence of the canonical coordinates of certain ordinary crystals. We then apply the results to…
In many physical problems or applications one has to study functions that are invariant under the action of a symmetry group G and this is best done in the orbit space of G if one knows the equations and inequalities defining the orbit…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
Different approaches are compared to formulation of quantum mechanics of a particle on the curved spaces. At first, the canonical, quasi-classical and path integration formalisms are considered for quantization of geodesic motion on the…
Linear polarimetric transformations of light polarization states by the action of material media are fully characterized by the corresponding Mueller matrices, which contain in an implicit and intricate manner all measurable information on…
We study the mathematical structure of covariant phase observables. Such an observable can alternatively be expressed as a phase matrix, as a sequence of unit vectors, as a sequence of phase states, or as an equivalent class of covariant…
Autonomous robotic systems heavily rely on environment knowledge to safely navigate. For search & rescue, a flying robot requires robust real-time perception, enabled by complementary sensors. IMU data constrains acceleration and rotation,…
A series of physically motivated operations appearing in the study of composite materials are interpreted in terms of elementary continued fraction transforms of matrix valued, rational Stieltjes functions.
To a generalized tight continuous frame in a Hilbert space $\H$ indexed by a locally compact space $\Si$ endowed with a Radon measure, one associates a coorbit theory converting spaces of functions on $\Si$ in spaces of vectors comparable…