Related papers: Super-operator Linear Equations and their Applicat…
Operator quantum error correction provides a unified framework for the known techniques of quantum error correction such as the standard error correction model, the method of decoherence-free subspaces, and the noiseless subsystem method.…
Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…
This paper establishes several new inequalities for the $A$-norm and $A$-numerical radius of operator sums in semi-Hilbertian spaces, significantly advancing the existing theory. We present two fundamental refinements of the generalized…
The purely algebraic technique associated with the creation and annihilation operators to resolve the radial equation of Hydrogen-like atoms (HLA) for generating the bound energy spectrum and the corresponding wave functions is suitable for…
Two semi-analytical approaches to solve the problem of light scattering on nanowire antennas are developed and compared. The derivation is based on the exact solution of the plane wave scattering problem in case of an infinite cylinder. The…
In this paper, we consider an elliptic operator obtained as the superposition of a classical second-order differential operator and a nonlocal operator of fractional type. Though the methods that we develop are quite general, for…
We study the global hypoellipticity and solvability of strongly invariant operators and systems of strongly invariant operators on closed manifolds. Our approach is based on the Fourier analysis induced by an elliptic pseudo-differential…
Building up on classical linear formulations, we posit that a broad class of problems in signal synthesis and in signal recovery are reducible to the basic task of finding a point in a closed convex subset of a Hilbert space that satisfies…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…
A notion of super operator system is defined which generalizes the usual notion of operator systems to include certain unital involutive operator spaces which cannot be represented completely isometric as a concrete operator system on some…
Extensions of standard one-dimensional supersymmetric quantum mechanics are discussed. Supercharges involving higher order derivatives are introduced leading to an algebra which incorporates a higher order polynomial in the Hamiltonian. We…
Recent advances in quantum computing have opened new pathways for enhancing deep learning architectures, particularly in domains characterized by high-dimensional and context-rich data such as natural language processing (NLP). In this…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, such particles can…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
Accurately predicting response properties of molecules such as the dynamic polarizability and hyperpolarizability using quantum mechanics has been a long-standing challenge with widespread applications in material and drug design. Classical…
We propose the construction of equations of motion based on symmetries in quantum-mechanical systems, using Heisenberg's uncertainty principle as a minimal foundation. From canonical operators, two spaces of conjugate operators are…
Entanglement in quantum many-body systems is the key concept for future technology and science, opening up a possibility to explore uncharted realms in an enormously large Hilbert space. The hybrid quantum-classical algorithms have been…
We consider the Schroedinger operator with a complex delta interaction supported by two parallel hypersurfaces in the Euclidean space of any dimension. We analyse spectral properties of the system in the limit when the distance between the…