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The main purpose in the present paper is to build a Hamiltonian theory for fields which is consistent with the principles of relativity. For this we consider detailed geometric pictures of Lepage theories in the spirit of Dedecker and try…
Metamaterials made of periodic collections of dielectric nanorods are considered theoretically. When quantum resonators are embedded within the nanorods, one obtains a quantum metamaterial, whose electromagnetic properties depend upon the…
We present a master equation describing the interaction of light with dielectric objects of arbitrary sizes and shapes. The quantum motion of the object, the quantum nature of light, as well as scattering processes to all orders in…
We propose a concatenated approach for implementing transitionless quantum driving regardless of adiabatic conditions while being robustness with respect to all kinds of systematic errors induced by pulse duration, pulse amplitude,…
A variational method is discussed, based on the principle of minimal variance. The method seems to be suited for gauge interacting fermions, and the simple case of quantum electrodynamics is discussed in detail. The issue of renormalization…
Cutting out and object and estimate its transparency mask is a key task in many applications. We take on the work on closed-form matting by Levin et al., that is used at the core of many matting techniques, and propose an alternative…
We evaluate the full opacity dependence of collective flow in high-energy heavy-ion collisions within a microscopic kinetic description based on the Boltzmann equation in the conformal relaxation time approximation. By comparing kinetic…
Motivated by new technologies for designing and tailoring metamaterials, we seek properties for certain classes of nonlinear optical materials that allow room for a reversibly controlled opacity-to-transparency phase transition through the…
We use covariant methods to analyse the nonlinear evolution of self-gravitating, non-relativistic media. The formalism is first applied to imperfect fluids, aiming at the kinematic effects of viscosity, before extended to inhomogeneous…
Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi…
The ability to create dynamic, tailored optical potentials has become important across fields ranging from biology to quantum science. We demonstrate a method for the creation of arbitrary optical tweezer potentials using the broadband…
The covariantization procedure is usually referred to the translation operator, that is the derivative. Here we introduce a general method to covariantize arbitrary differential operators, such as the ones defining the fundamental group of…
It is commonly assumed that if the optical metric of a dielectric medium is identical to the metric of a vacuum space-time then light propagation through the dielectric mimics light propagation in the vacuum. However, just as the curved…
We present an algorithm for holographic shaping of partially coherent light, bridging the gap between traditional coherent and geometric optical approaches. The description of partially coherent light relies on a mode expansion formalism,…
We introduce a valuation-theoretic approach to the problem of semistable reduction (i.e., existence of logarithmic extensions on suitable covers) of overconvergent isocrystals with Frobenius structure. The key tool is the quasicompactness…
The path integral formulation of quantum mechanics, i.e., the idea that the evolution of a quantum system is determined as a sum over all the possible trajectories that would take the system from the initial to its final state of its…
Investigating nanoplasmonics using time-dependent approaches permits shedding light on the dynamic optical properties of plasmonic structures, which are intrinsically connected with their potential applications in photochemistry and…
Leveraging the quantum information processing ability of superconducting circuits and long-distance distribution ability of optical photons promises the realization of complex and large-scale quantum networks. In such a scheme, a coherent…
The cooperative electromagnetic interactions between discrete resonators have been widely used to modify the optical properties of metamaterials. Here we propose a general evolutionary approach for engineering these interactions in…
This paper introduces and studies a field theoretic analogue of the Clebsch variational principle of classical mechanics. This principle yields an alternative derivation of the covariant Euler-Poincar\'e equations that naturally includes…