Related papers: A uniqueness theorem in potential theory with impl…
In this article, we prove a uniqueness result for a coefficient inverse problems regarding a wave, a heat or a Schr\"odinger equation set on a tree-shaped network, as well as the corresponding stability result of the inverse problem for the…
This paper addresses a factorization method for imaging the support of a wave-number-dependent source function from multi-frequency data measured at a finite pair of symmetric receivers in opposite directions. The source function is given…
We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying…
The inverse acoustic scattering of point objects using multi-frequency sparse measurements are studied. The objects may be a sum of point sources or point like scatterers. We show that the locations and scattering strengths of the point…
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 identify and explore the intriguing property of resource resonance arising within resource theories of entanglement, coherence and thermodynamics. While the theories considered are reversible asymptotically, the same is generally not…
We study the question of how reliably one can distinguish two quantum field theories (QFTs). Each QFT defines a probability distribution on the space of fields. The relative entropy provides a notion of proximity between these distributions…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
Recovering microscopic couplings directly from data provides a route to solving the inverse problem in statistical field theories, one that complements the traditional-often computationally intractable-forward approach of predicting…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
We develop a statistical theory describing the operation of multiplexed single-photon sources equipped with photon-number-resolving detectors that includes the potential use of different input mean photon numbers in each of the multiplexed…
Symmetry restoration in a theory of a self-interacting charged scalar field at finite temperature and in the presence of an external magnetic field is examined. The effective potential is evaluated nonperturbatively in the context of the…
A convergence theorem is proved for a class of Nystrom methods for weakly singular integral equations on surfaces in three dimensions. Fredholm equations of the second kind as arise in connection with linear elliptic boundary value problems…
The discrete Schr\"odinger equation with the Dirichlet boundary condition is considered on a half-line lattice when the potential is real valued and compactly supported. The inverse problem of recovery of the potential from the so-called…
Uniqueness theorems are considered for various types of almost periodic objects: functions, measures, distributions, multisets, holomorphic and meromorphic functions.
The apparent dependence of nuclear matter observables on off-shell properties of the two-nucleon potential is re-examined in the context of the effective field theory (EFT) approach. Finite density (thermodynamic) observables are invariant…
In "Classical Electrodynamics" (Jackson) a theorem is proved on the average of an electrostatic or magnetostatic field over a spherical volume. The proof of the theorem is based on an expansion in spherical harmonics and it is useful for…
The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…
Signal restoration and inverse problems are key elements in most real-world data science applications. In the past decades, with the emergence of machine learning methods, inversion of measurements has become a popular step in almost all…
We demonstrate, in the full vector formulation of electromagnetic fields, that the well-known optical theorem pertinent for the characterization of a scatterer's extinction power and associated cross section can be expressed in a multitude…