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This paper studies pattern formations in coupled elliptic PDE systems governed by transparent boundary conditions. Such systems unify diverse areas, including inverse boundary problems (via a single passive/active boundary measurement),…
In this work we investigate the possibility of using the reflection algebra as a source of functional equations. More precisely, we obtain functional relations determining the partition function of the six-vertex model with domain-wall…
The attempt to solve inverse scattering problems often leads to optimization and sampling problems that require handling moderate to large amounts of partial differential equations acting as constraints. We focus here on determining…
A multiple scattering model of a quantum particle interacting with a random Lorentz gas of fixed point scatterers is established in an Euclidean space of arbitrary dimension. At the core of the model, the scattering amplitude for the point…
We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…
We study an inverse random obstacle scattering problems in $\mathbb{R}^2$ where the scatterer is formulated by a Gaussian process defined on the angular parameter domain. Equipped with a modified covariance function which is mathematically…
A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
Three papers describing different methods to solve the inverse scattering problem of the reconstruction of the shape and/or impedance of an obstacle have been chosen for analysis. This literature review consists of an evaluation of these…
In supersymmetric quantum mechanics, exact-solvability of one-dimensional quantum systems can be classified only with an additional assumption of integrability, the so-called shape invariance condition. In this paper we show that in the…
We address the question of the dependence of the bulk free energy on boundary conditions for the six vertex model. Here we compare the bulk free energy for periodic and domain wall boundary conditions. Using a determinant representation for…
We consider the inverse obstacle scattering problem of determining both the shape and the "equivalent impedance" from far field measurements at a fixed frequency. In this work, the surface impedance is represented by a second order surface…
We analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on…
This letter is concerned with the analysis of the six-vertex model with domain-wall boundaries in terms of partial differential equations (PDEs). The model's partition function is shown to obey a system of PDEs resembling the celebrated…
We calculate the joint probability distribution of the Wigner-Smith time-delay matrix $Q=-i\hbar S^{-1} \partial S/\partial \epsilon$ and the scattering matrix $S$ for scattering from a chaotic cavity with ideal point contacts. Hereto we…
In this work we relate the spectral problem of the toroidal six-vertex model's transfer matrix with the theory of integrable non-linear differential equations. More precisely, we establish an analogy between the Classical Inverse Scattering…
The inverse scattering problem is of critical importance in a number of fields, including medical imaging, sonar, sensing, non-destructive evaluation, and several others. The problem of interest can vary from detecting the shape to the…
Transitions between different topologically ordered phases have been studied by artificially creating boundaries between these gapped phases and thus studying their effects relating to condensation and tunneling of particles from one phase…
This paper addresses an inverse cavity scattering problem associated with the biharmonic wave equation in two dimensions. The objective is to determine the domain or shape of the cavity. The Green's representations are demonstrated for the…
We study large deviations in interacting quantum liquids with the polytropic equation of state $P(\rho)\sim \rho^\gamma$, where $\rho$ is density and $P$ is pressure. By solving hydrodynamic equations in imaginary time we evaluate the…