相关论文: Geometrical description and Faddeev-Jackiw quantiz…
The study of hidden symmetries within Dirac's formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Faddeev-Jackiw approach, gauge and…
This paper presents a brief review of the newly developed \emph{Extended Electrodynamics}. The relativistic and non-relativistic approaches to the extension of Maxwell equations are considered briefly, and the further study is carried out…
We discuss in general how to geometrically visualize a qudit system, with a particular interest in thermal states. The principle of maximum entropy is used to study the geometric properties of an ensemble of finite dimensional Hamiltonian…
We derive the general circuit equations and system models directly from four Maxwell's equations and develop the electric-charge-based and magnetic-flux-based analysis methodologies to unify the analyses for both phase-independent circuits…
The standard solution to time-harmonic electromagnetic scattering problems in homogeneous layered media relies on the use of the electric field dyadic Green's function. However, for small values of the governing angular frequency $\omega$,…
The complex form of Maxwell equations has been constructed as one equation for 3-dimensional complex A-vector. The real and imaginary parts of this vector are described with use of electric and magnetic tensions accordingly. With using a…
In the present paper we will discuss the Faddeev-Jackiw symplectic approach in the analysis of a charged compressible fluid immersed in a higher-derivative electromagnetic field theory. We have obtained the full set of constraints directly…
We present a Hamiltonian formulation for the linearized Vlasov-Maxwell system with a Maxwellian background distribution function. We discuss the geometric properties of the model at the continuous level, and how to discretize the model in…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
A simple Hamiltonian modeling framework for general models in nonlinear optics is given. This framework is specialized to describe the Hamiltonian structure of electromagnetic phenomena in cubicly nonlinear optical media. The model has a…
In some applications there arises the need of a spatially distributed description of a physical quantity inside a device coupled to a circuit. Then, the in-space discretised system of partial differential equations is coupled to the system…
The aim of this article is to investigate the well-posedness, stability and convergence of solutions to the time-dependent Maxwell's equations for electric field in conductive media in continuous and discrete settings. The situation we…
Interactions and relations between objects may be pairwise or higher-order in nature, and so network-valued data are ubiquitous in the real world. The "space of networks", however, has a complex structure that cannot be adequately described…
We present a multi-level quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external…
Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space…
The formalism of reduced quantum electrodynamics is generalized to the case of heterostructures composed of few atomically thick layers and the corresponding effective (2+1)-dimensional gauge theory is formulated. This dimensionally reduced…
We present a systematic canonical quantization procedure for lumped-element superconducting networks by making use of a redundant configuration-space description. The algorithm is based on an original, explicit, and constructive…
In this paper we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving $2-$ simplicial complexes embedded in $\mathbb{R} ^3$ rather than…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite…