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We present a real-space formulation for coarse-graining Kohn-Sham Density Functional Theory that significantly speeds up the analysis of material defects without appreciable loss of accuracy. The approximation scheme consists of two steps.…
While nonlinear optical spectroscopy is becoming more commonly used to study the excited states of nonlinear-optical systems, a general theory of inhomogeneous broadening is rarely applied in lieu of either a simple Lorentzian or Gaussian…
Controlling the coherent optical response of inhomogeneous ensembles is a key challenge in advancing light-matter interaction engineering. We present a comparative study of two spectral tailoring approaches using two-dimensional coherent…
A simple and efficient method for characterization of multidimensional Gaussian states is suggested and experimentally demonstrated. Our scheme shows analogies with tomography of finite dimensional quantum states, with the covariance matrix…
Diffusing wave spectroscopy (DWS) can be employed as an optical rheology tool with numerous applications for studying the structure, dynamics and linear viscoelastic properties of complex fluids, foams, glasses and gels. To carry out DWS…
We introduce a novel method to perform linear optical random projections without the need for holography. Our method consists of a computationally trivial combination of multiple intensity measurements to mitigate the information loss…
Spectral density estimation is a core problem of system identification, which is an important research area of system control and signal processing. There have been numerous results on the design of spectral density estimators. However to…
In this paper, we develop a systematic theory for high dimensional analysis of variance in multivariate linear regression, where the dimension and the number of coefficients can both grow with the sample size. We propose a new \emph{U}~type…
Processes with almost periodic covariance functions have spectral mass on lines parallel to the diagonal in the two-dimensional spectral plane. Methods have been given for estimation of spectral mass on the lines of spectral concentration…
Coherent two-dimensional spectroscopy in IR or visible region is very effective for studying correlations, energy relaxation/transfer pathways in complex multi-chromophore or multi-mode systems. However it is usually restricted up to…
We propose to study the origin of algebraic decay of two-point correlation functions observed in glasses, proteins, and quantum dots by their nonlinear response to sequences of ultrafast laser pulses. Power-law spectral singularities and…
Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…
We propose and demonstrate an interferometric scheme for measuring the two-dimensional two-point cross-spectral density function in a two-shot manner. Our scheme comprises a Michelson interferometer with a converging lens in one of the arms…
Two-dimensional spectroscopy is discussed for open quantum systems with multiple simultaneously measurable fluxes. In particular, we discuss a junction where optical measurements of photon flux are complemented with simultaneous transport…
Accurate estimation of the covariance matrix of cosmic shear statistics is essential for cosmological analyses using current and upcoming wide-area weak lensing surveys. In this work, we investigate analytical methods for computing the…
The inverse scattering problem from the multi-frequency backscattering data is a long-standing open problem. We advance the theory by proving a local uniqueness result. Moreover, we introduce a direct sampling method for quantitatively…
The ability to resolve and quantify features at submicrometer scales from a single-shot image is crucial for real-time uncovering intricate structures in unlabeled biological samples and analyzing them at the subcellular level. We introduce…
Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete…
The notion of periodic two-scale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillating periodic coefficients. In this paper we are interested in…
In recent years, interesting materials have emerged which are only available as micron-scale flakes, and whose novel physics might be better understood through broadband microwave spectroscopy; examples include twisted bilayer graphene [1],…