Related papers: Explicit Thin-Lens Solution for an Arbitrary Four …
We construct exactly solvable models for four particles moving on a real line or on a circle with translation invariant two- and four-particle interactions.
We show that if in the particle beam there are linear correlations between energy of particles and their transverse positions and momenta (linear beam dispersions), then the transverse projected emittances always can be reduced by letting…
The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…
A bilayer lens is proposed based on transformation optics. It is shown that Pendry's perfect lens, perfect bilayer lens made of indefinite media, and the concept of compensated media are well unified under the scope of the proposed bilayer…
Linear optical networks are fundamental to the advancement of quantum technologies, including quantum computing, communication, and sensing. The accurate characterization of these networks, described by unitary matrices, is crucial to their…
While the proposal of the Tri-plane representation has advanced the development of the 3D-aware image generative models, problems rooted in its inherent structure, such as multi-face artifacts caused by sharing the same features in…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…
We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We…
A representation theory of finite electromagnetic beams in free space is formulated by factorizing the field vector of the plane-wave component into a $3 \times 2$ mapping matrix and a 2-component Jones-like vector. The mapping matrix has…
In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with…
In future linear colliders the luminosity will depend on maintaining the small emittance aspect ratio delivered by damping rings. Correction of cross-plane coupling can be important in preventing dilution of the beam emittance. In order to…
In acoustic, ultrasonic or electromagnetic propagation, crossed media are often modelled by linear filters with complex gains in accordance with the Beer-Lambert law. This paper addresses the problem of propagation in media where…
Nonlinear optical processing of ambient natural light is highly desired in computational imaging and sensing applications. A strong optical nonlinear response that can work under weak broadband incoherent light is essential for this…
We consider the problem of matrix completion on an $n \times m$ matrix. We introduce the problem of Interpretable Matrix Completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the…
We present a linear-optical scheme for generation of an arbitrary state of three qubits. It requires only three independent particles in the input and post-selection of the coincidence-type at the output. The success probability of the…
One of the bottlenecks that limit the transition of transformation-optics devices from concepts to practical use is the non-unit magnetic permeability generally required from a mathematical transformation. Simple renormalization of…
Recent advances in metasurfaces and optical nanostructures have enabled complex control of incident light with optically thin devices. However, it has thus far been unclear whether it is possible to achieve complete linear control of…
Recent breakthroughs in photonics-based quantum, neuromorphic and analogue processing have pointed out the need for new schemes for fully programmable nanophotonic devices. Universal optical elements based on interferometer meshes are…
We show that the problem of finding the primary and secondary characteristic directions of a linear lossless optical element can be reformulated in terms of an eigenvalue problem related to the unimodular factor of the transfer matrix of…
A model is presented consisting of triangular trimers on the triangular lattice. In analogy to the dimer problem, these particles cover the lattice completely without overlap. The model has a honeycomb structure of hexagonal cells separated…