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We generalize electrodynamics with a second interaction in lightcone. The time-reversible equations for two-body motion define a semiflow on $C^2(\mathbb{R})$ with four state-dependent delays of neutral type and nonlinear gyroscopic terms.…
We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison…
Optical cavities with moving mirrors provide a versatile platform for exploring radiation-matter interactions and optically mediated mechanical effects, whose control has wide technological implications. However, capturing the coupled…
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in $\mathbb{R}^d$, that are coupled by a matrix-valued potential $V$, and investigate under which conditions each solution to such…
A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and…
We consider an array of coupled optical cavities, each containing a multi-atom ensemble. We show that the nonlinearity inherent in the cooperative dynamics of the atoms in each ensemble coupled to the respective cavity field allows for the…
We study the time-resolved fluorescence spectrum in two-level systems interacting with an incident coherent field, both in the weak and intermediate coupling regimes. For a single two-level system in the intermediate coupling case, as time…
We present a theoretical study of strong laser-atom interactions, when the laser field parameters are subjected to random processes. The atom is modelled by a two-level and three-level systems, while the statistical fluctuations of the…
A model for the dynamics of a classical point charged particle interacting with higher order jet fields is introduced. In this model, the dynamics of the charged particle is described by an implicit ordinary second order differential…
The moving coframe method is applied to solve the local equivalence problem for the class of linear parabolic equations in two independent variables under an action of the pseudo-group of contact transformations. The structure equations and…
Using a generalized procedure for obtaining the dispersion relation and the equation of motion for a propagating fermionic particle, we examine previous claims for a preferred axis at $n_{\mu}$($\equiv(1,0,0,1)$), $n^{2}=0$ embedded in the…
Periodically-driven quantum systems are currently explored in view of realizing novel many-body phases of matter. This approach is particularly promising in gases of ultracold atoms, where sophisticated shaking protocols can be realized and…
We report on collective non-linear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance…
We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship…
The system of an atom couples to two distinct optical cavities with phase decoherence is studied by making use of a dynamical algebraic method. We adopt the concurrence to characterize the entanglement between atom and cavities or between…
The so-called method of phase synchronization has been advocated in a number of papers as a way of decoupling a system of linear second-order differential equations by a linear transformation of coordinates and velocities. This is a rather…
We investigate theoretically the extension of cavity optomechanics to multiple membrane systems. We describe such a system in terms of the coupling of the collective normal modes of the membrane array to the light fields. We show these…
Bad cavity lasers are experiencing renewed interest in the context of active optical frequency standards, due to their enhanced robustness against fluctuations of the laser cavity. The gain medium would consist of narrow-linewidth atoms,…
A three-level atom in the $\Lambda$-configuration coupled to a microcavity is studied. The two transitions of the atom are assumed couple to different counterpropagating mode pairs in the cavity. We analyze the dynamics both, in the…
The invention of the laser immediately enabled the detection of nonlinear photon-matter interactions, as manifested for example by Franken et al.'s detection of second-harmonic generation. With the recent advancement in high-power,…