Related papers: Symmetries of Optical Phase Conjugation
The symmetric group on 4 letters has the reflection group $D_{3}$ as an isomorphic image. This fact follows from the coincidence of the root systems $A_{3}$ and $D_{3}$. The isomorphism is used to construct an orthogonal basis of…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
Coupled oscillators are prevalent throughout the physical world. Dynamical system formulations of weakly coupled oscillator systems have proven effective at capturing the properties of real-world systems. However, these formulations usually…
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A method to construct a geometric structure with the same solutions as a given variational principle is presented. The method applies to large families of variational principles. In particular, the known results that assign cosymplectic…
Imposing additional constraints on low-rank optimization has garnered growing interest. However, the geometry of coupled constraints hampers the well-developed low-rank structure and makes the problem intricate. To this end, we propose a…
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We present an entirely new geometric and probabilistic approach to synchronization of correspondences across multiple sets of objects or images. In particular, we present two algorithms: (1) Birkhoff-Riemannian L-BFGS for optimizing the…
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Optical traps and lattices provide a new opportunity to study strongly correlated high spin systems with cold atoms. In this article, we review the recent progress on the hidden symmetry properties in the simplest high spin fermionic…
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Shaping light deep inside complex media, such as biological tissue, is critical to many research fields. Although the coherent control of scattered light via wavefront shaping has made significant advances in addressing this challenge,…
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This article explores the application of the path integral formalism in describing synchronization phenomena in entangled networks, cavities, and reservoirs. We discuss the concept of using Lagrangian mechanics for systems undergoing…
In this work we reformulate the method presented in App. Opt. 53:2297 (2014) as a constrained minimization problem using the augmented Lagrangian method. First we introduce the new method and then describe the numerical solution, which…