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Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…
Highly reflecting mechanically compliant membranes based on photonic-crystal patterns have recently gained increasing attention within cavity optomechanics due to their prospects of reaching high coupling rates in membrane-in-the-middle…
Light shaping facilitates the preparation and detection of optical states and underlies many applications in communications, computing, and imaging. In this Letter, we generalize light shaping to the quantum domain. We show that patterns of…
Coupled mode theory (CMT) is a powerful framework for decomposing interactions between electromagnetic waves and scattering bodies into resonances and their couplings with power-carrying channels. It has widespread use in few-resonance,…
We obtain several higher order exact periodic solutions of (i) a coupled symmetric phi4 model in an external field, (ii) an asymmetric coupled phi4 model, (iii) an asymmetric-symmetric coupled phi4 model, in terms of Lame polynomials of…
Compton scattering is involved in many astrophysical situations. It is well known and has been studied in detail for the past fifty years. Exact formulae for the different cross sections are often complex, and essentially asymptotic…
Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective…
We describe a method to detect twin-beam multiphoton entanglement based on a beam splitter and weak nonlinearities. For the twin-beam four-photon entanglement, we explore a symmetry detector. It works not only for collecting two-pair…
A simple and general formalism for mode coupling by a spatial, temporal or spatiotemporal perturbation in dispersive materials is developed. This formalism can be used for studying various linear and non-linear optical interactions…
Quasi-equilibrium approximation is a widely used closure approximation approach for model reduction with applications in complex fluids, materials science, etc. It is based on the maximum entropy principle and leads to thermodynamically…
We explore exchange coupling of a pair of spins in a double dot and in an optical lattice. Our algorithm uses the frequency of exchanges in a bosonic path integral, evaluated with Monte Carlo. This algorithm is simple enough to be a "black…
We formulate a new atomistic/continuum (a/c) coupling scheme that employs the boundary element method (BEM) to obtain an improved far-field boundary condition. We establish sharp error bounds in a 2D model problem for a point defect…
We demonstrate the controlled coherent transport and splitting of atomic wave packets in spin-dependent optical lattice potentials. Such experiments open intriguing possibilities for quantum state engineering of many body states. After…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We investigate a system composed of $N$ coupled cavities and two-level atoms interacting one at a time. Adjusting appropriately the atom-field detuning, and make the hopping rate of photons between neighboring cavities, $A$, greater than…
Observations and theoretical calculations have shown the importance of non-spherically symmetric structures in supernovae. Thus, the interpretation of observed supernova spectra requires the ability to solve the transfer equation in 3-D…
Various packing problems and simulations of hard and soft interacting particles, such as microscopic models of nematic liquid crystals, reduce to calculations of intersections and pair interactions between ellipsoids. When constrained to a…
This study proposes a high-order multi-scale method tailored for time-dependent nonlinear thermo-electro-mechanical coupling problems of composite structures with highly spatial heterogeneity, which incorporate temperature-dependent…
We present a novel approach for solving numerically one-dimensional scattering problems and apply it for computing the emission probability of an ultracold atom interacting with an arbitrary field mode of a high-$Q$ cavity. Our method is…
This paper is concerned with efficient representations and approximations of the solution to the scattering problem by a system of strongly coupled plasmonic particles. Three schemes are developed: the first is the resonant expansion which…