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Based on the technique of the discrete one-turn transfer maps, the problem of linear coupling between horizontal and vertical betatron oscillations in an accelerator has been treated exactly and entirely in explicit form. The stability…
Sufficient conditions for synchronization of coupled Lienard-type oscillators are investigated via averaging technique. Coupling considered here is pairwise, unidirectional, and described by a nonlinear function (whose graph resides in the…
Synthetic photonic lattice with temporally controlled potentials is a versatile platform for realizing wave dynamics associated with physical areas of optics and quantum physics. Here, discrete optics in one-dimensionally synthetic photonic…
We present a methodology that extends invariant manifold theory to a class of autonomous piecewise linear systems with nonsmoothness at the equilibrium, providing a framework for model order reduction in mechanical structures with compliant…
Inter-orbital coupling refers to the possibility of exciting orbital states by otherwise orthogonal non-interacting modes, a forbidden process in photonic lattices due to an intrinsic propagation constant detuning. In this work, using a…
Acousto-optic interaction in optomechanical crystals allows unidirectional control of elastic waves over optical waves. However, as a result of this nonlinear interaction, infinitely many optical modes are born. This article presents an…
In this paper, we present a cooperative odometry scheme based on the detection of mobile markers in line with the idea of cooperative positioning for multiple robots [1]. To this end, we introduce a simple optimization scheme that realizes…
Applications of normalizing flows to the sampling of field configurations in lattice gauge theory have so far been explored almost exclusively in two space-time dimensions. We report new algorithmic developments of gauge-equivariant flow…
We study theoretically a BEC loaded into an optical lattice in the tight-binding regime, with a second, weak incommensurate lattice acting as a perturbation. We find, using direct diagonalization of small systems and a large scale, number…
We suggest a technique for the observation of a predicted supersolid phase in extended Bose-Hubbard models which are potentially realizable in cold atom optical lattice systems. In particular, we discuss important subtleties arising from…
Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions…
A new device to generate polarization-entangled light in the continuous variable regime is introduced. It consists of an Optical Parametric Oscillator with two type-II phase-matched non-linear crystals orthogonally oriented, associated with…
Precise collaboration in vision-based dual-arm robot systems requires accurate system calibration. Recent dual-robot calibration methods have achieved strong performance by simultaneously solving multiple coordinate transformations.…
Given a finite connected graph $\Lambda$, the space of $SU(2)$ lattice gauge-fields on $\Lambda$, modulo gauge transformations, is a Lagrangian submanifold -- with mild singularities -- of the $SU(2)$ character variety (= phase-space of…
The quantization of the SU(2)$\times $U(1) gauge-symmetric electroweak theory is performed in the Hamiltonian path-integral formalism. In this quantization, we start from the Lagrangian given in the unitary gauge in which the unphysical…
A basic problem in linear particle optics is to find a symplectic transformation that brings the (symmetric) beam matrix to a special diagonal form, called normal form. The conventional way to do this involves an eigenvalue-decomposition of…
We recall the groundwork of spinoptics based on the coadjoint orbits, of given color and spin, of the group of isometries of Euclidean three-space; this model has originally been put forward by Souriau in his treatise "Structure des…
We illustrate how the notion of asymptotic coupling provides a flexible and intuitive framework for proving the uniqueness of invariant measures for a variety of stochastic partial differential equations whose deterministic counterpart…
We define a new parameter about Laguerre-Gaussian (LG) beams, named $Q^{l}_{p}$, which is only related to mode indices $p$ and $l$. This parameter is able to both evaluate and distinguish LG beams. The $Q^{l}_{p}$ values are first…
We report on a high-resolution double-channel imaging method used to synchronously map the intensity- and optical-frequency-distribution of a laser beam in the plane orthogonal to the propagation direction. The synchronous measurement…