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A universal quantum wave equation that yields Dirac, Klein-Gordon, Schrodinger and quantum heat equations is derived. These equations are related by complex transformation of space, time and mass. The new symmetry exhibited by these…
The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker…
The construction of discrete scalar wave propagation equations in arbitrary inhomogeneous media was recently achieved by using elementary dynamical processes realizing a discrete counterpart of the Huygens principle. In this paper, we…
We study the time evolution of a wave function for the spatially flat Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchar dust as a matter…
The paper is devoted to the description a measurable time-interval (``proper time'') in the Hamiltonian version of general relativity with the Dirac-ADM metric. To separate the dynamical parameter of evolution from the space metric we use…
Despite its widespread significance, the temporal coupled-mode theory (CMT) lacks a foundational validation based on electromagnetic principles and stands as a phenomenological theory relying on fitted coupling coefficients. We employ an ab…
In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $\phi(k,E)$ is…
The Arnowitt-Deser-Misner (ADM) evolution equations for the induced metric and the extrinsic-curvature tensor of the spacelike surfaces which foliate the space-time manifold in canonical general relativity are a first-order system of…
We introduce a class of partial differential equations on metric graphs associated with mixed evolution: on some edges we consider diffusion processes, on other ones transport phenomena. This yields a system of equations with possibly…
Within the context of a $5D$ space-time, we construct a unified theory of gravity and electromagnetism from which the Einstein field equations and Maxwell equations emerge, with homogenous Maxwell equations appearing naturally. We also…
The paper addresses the two-point correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian, positive- or negative-definite matrices. A simplified version of the…
It is shown that the decomposition theorems of York, Stewart and Walker for symmetric spatial second-rank tensors, such as the perturbed metric tensor and perturbed Ricci tensor, and the spatial fluid velocity vector imply that, for open,…
We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations…
A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines.…
The propagation of electromagnetic waves through disordered layered system is considered in the paradigm of Maxwell's equations homogenization. In spite of the impossibility to describe the system in terms of effective dielectric…
The paper addresses the space-frequency correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian matrices. The two-frequency Wigner distribution (2f-WD) for polarized…
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a…
We begin this work calculating Halliwell's propagator in the case of a Mixmaster universe with small anisotropy. Afterwards in the context of the Decoherence Model we introduce in our system terms that comprise the self-measurement of the…
The classical and quantum dynamics of the Friedmann-Robertson-Walker Universe with massless scalar and massive fermion matter field as a source is discussed in the framework of the Dirac generalized Hamiltonian formalism. The Hamiltonian…
The paper extends well-posedness results of a previously explored class of time-shift invariant evolutionary problems to the case of non-autonomous media. The Hilbert space setting developed for the time-shift invariant case can be utilized…