Related papers: Density Matrix Reconstructions in Ultrafast Transm…
The quantum state of a light beam can be represented as an infinite dimensional density matrix or equivalently as a density on the plane called the Wigner function. We describe quantum tomography as an inverse statistical problem in which…
We consider the inverse problem of determining the density coefficient appearing in the wave equation from separated point source and point receiver data. Under some assumptions on the coefficients, we prove uniqueness results.
We present the first wavelet-based all-electron density-functional calculations to include gradient corrections and the first in a solid. Direct comparison shows this approach to be unique in providing systematic ``transparent''…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
The properties of coherence and polarization of light has been the subject of intense investigations and form the basis of many technological applications. These concepts which historically have been treated independently can now be…
We introduce an effective numerical method of density matrix determination of fiber coupled single photon generated in process of spontaneous parametric down conversion in type I non-collinear configuration. The presented theory has been…
One of the frontiers in electron scattering is to couple ultrafast temporal resolution with highly localized probes to investigate the role of microstructure on material properties. Here, taking advantage of the unprecedented average…
The density matrix is a positive semidefinite operator of trace 1 characterizing the state of a quantum system. We consider the inverse problem to reconstruct such density matrices from indirect measurements, also known as quantum state…
We lay the foundations for a new fast method to reconstruct the electron density in x-ray scanning applications using measurements in the dark field. This approach is applied to a type of machine configuration with fixed energy sensitive…
In this paper, an inverse method was developed which can, in principle, reconstruct arbitrary permeability, conductivity, thickness, and lift-off with a multi-frequency electromagnetic sensor from inductance spectroscopic measurements. The…
Neutron and X-ray reflectometry are powerful techniques facilitating the study of the structure of interfacial materials. The analysis of these techniques is ill-posed in nature requiring the application of a model-dependent methods. This…
The discretization of the density matrix is proposed as a nonlinear positive map for systems with continuous variables. This procedure is used to calculate the entanglement between two modes through different criteria, such as Tsallis…
In a large class of statistical inverse problems it is necessary to suppose that the transformation that is inverted is known. Although, in many applications, it is unrealistic to make this assumption, the problem is often insoluble without…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
We describe a new method for imaging ultrafast dynamics in condensed matter using inelastic x-ray scattering (IXS). We use the concepts of causality and irreversibility to construct a general solution to the inverse scattering problem (or…
This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…
Phase-space partitioning offers an attractive path for the precise tailoring of complex dynamical systems. In Beam Physics, the proposed approach involves (i) producing beams with cross-plane correlations to control kinematical invariants…
There is a growing interest in reconstructing the density matrix of photoelectron wavepackets, in particular in complex systems where decoherence can be introduced either by a partial measurement of the system or through coupling with a…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
This is a continuation of our study [Uhlmann-Zhai, JMPA, 2021] on an inverse boundary value problem for a nonlinear elastic wave equation. We prove that all the linear and nonlinear coefficients can be recovered from the…