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Entanglement entropy, which is a measure of quantum correlations between separate parts of a many-body system, has emerged recently as a fundamental quantity in broad areas of theoretical physics, from cosmology and field theory to…
Consider an inverse problem of the simultaneous recovery of boundary impedance and internal conductivity in the electrical impedance tomography (EIT) model using local internal measurement data, which is governed by a boundary value problem…
We study the Electrical Impedance Tomography Bayesian inverse problem for recovering the conductivity given noisy measurements of the voltage on some boundary surface electrodes. The uncertain conductivity depends linearly on a countable…
In the recent paper [17] the first experimental determination of the density matrix of a free electron beam has been reported. The employed method leads to a linear inverse problem with a positive semidefinite operator as unknown. The…
For a compact Riemannian manifold with boundary, endowed with a magnetic potential $\alpha$, we consider the problem of restoring the metric $g$ and the magnetic potential $\alpha$ from the values of the Ma\~n\'e action potential between…
This paper is concerned with the time-dependent Maxwell's equations for a plane interface between a negative material described by the Drude model and the vacuum, which fill, respectively, two complementary half-spaces. In a first paper, we…
The more information a measurement provides about a quantum system's position statistics, the less information a subsequent measurement can provide about the system's momentum statistics. This information trade-off is embodied in the…
This note extends the modulated entropy and free energy methods for proving mean-field limits/propagation of chaos to the whole space without any confining potential, in contrast to previous work limited to the torus or requiring…
Current theories of massless free particle assume {\sl unitary} space inversion and {\sl anti-unitary} time reversal operators. In so doing robust classes of possible theories are discarded. In the present work theories of massless systems…
We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular…
Maxwell equations provide a complete description of the electromagnetic (EM) phenomena, which have been one of the key fundamental-theories of modern physics, such as electromagnetism, optics, quantum theories, etc. The vacuum permittivity…
We present an alternative approach to the theory of free Gibbs states with convex potentials. Instead of solving SDE's, we combine PDE techniques with a notion of asymptotic approximability by trace polynomials for a sequence of functions…
We study long-range correlations of equilibrium current densities in a two-dimensional mesoscopic system with the time reversal invariance broken by a random or homogeneous magnetic field. Our result is universal, i.e. it does not depend on…
We extend a field theoretic approach for the investigation of the electronic charge-current density response of crystalline systems to arbitrary applied electromagnetic fields. The approach leads to the introduction of microscopic…
We consider resonant vortices around nodal points of the wavefunction in electron transport through a mesoscopic device. With a suitable choice of the device geometry, the dominating role is played by single vortices of a preferred…
A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source…
In this article we study the inverse problem of recovering a space-dependent coefficient of the Moore-Gibson-Thompson (MGT) equation, from knowledge of the trace of the solution on some open subset of the boundary. We obtain the Lipschitz…
The Minkowski's theory is regarded as the classical approach for describing the electromagnetism of uniformly moving objects by elegantly utilizing the format-invariance of the Maxwell's equations in inertia reference frames under Lorentz…
In electrical impedance tomography, algorithms based on minimizing the linearized-data-fit residuum have been widely used due to their real-time implementation and satisfactory reconstructed images. However, the resulting images usually…
Magnetism governs key properties of materials used in energy, data storage, and spintronic technologies, yet its complex coupling to lattice and electronic degrees of freedom challenges conventional first-principles approaches. We introduce…