Related papers: Parametrization of degenerate density matrices
In this work we present a framework for studying the eigenvalues of a family of matrices with a particular displacement structure. The family admits a specific decomposition as the product of an upper and a lower triangular matrices having…
We study a renormalizable four dimensional model with two deformed quantized space directions. A one-loop renormalization is performed explicitly. The Euclidean model is connected to the Minkowski version via an analytic continuation. At a…
We consider the uniform approximation of the smallest eigenvalue of a large parameter-dependent Hermitian matrix by that of a smaller counterpart obtained through projections. The projection subspaces are constructed iteratively by means of…
This article is dedicated to the following class of problems. Start with an $N\times N$ Hermitian matrix randomly picked from a matrix ensemble - the reference matrix. Applying a rank-$t$ perturbation to it, with $t$ taking the values $1\le…
We investigate the behavior of various spectral invariants, particularly the determinant of the Laplacian, on a family of smooth Riemannian manifolds which undergo conic degeneration; that is, which converge in a particular way to a…
This paper is concerned with the spectral properties of matrices associated with linear filters for the estimation of the underlying trend of a time series. The interest lies in the fact that the eigenvectors can be interpreted as the…
Magnetic resonance (MR) image re-parameterization refers to the process of generating via simulations of an MR image with a new set of MRI scanning parameters. Different parameter values generate distinct contrast between different tissues,…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which…
We theoretically and numerically prove that under an electromagnetic plane wave with linear polarization incident normally to cylindrical passive scatterers, a single energy diagram can integrate absorption, scattering, and extinction cross…
We study a unitary matrix model with Gross-Witten-Wadia weight function and determinant insertions. After some exact evaluations, we characterize the intricate phase diagram. There are five possible phases: an ungapped phase, two different…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
We study time evolution of a subsystem's density matrix under unitary evolution, generated by a sufficiently complex, say quantum chaotic, Hamiltonian, modeled by a random matrix. We exactly calculate all coherences, purity and…
A phenomenological level density model that has different level density parameter sets for the state densities of the deformed and the spherical states, and the optimization of the parameters using experimental data of the average s-wave…
We study the geometric Uhlmann phase of entangled mixed states in a composite system made of two coupled spin-$\frac 1 2$ particles with a magnetic field acting on one of them. Within a depolarizing channel setup, an exact analytical…
A new analytical formulation is prescribed to solve the Helmholtz equation in 2D with arbitrary boundary. A suitable diffeomorphism is used to annul the asymmetries in the boundary by mapping it into an equivalent circle. This results in a…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
Several key questions remain unanswered regarding overparameterized learning models. It is unclear how (stochastic) gradient descent finds solutions that generalize well, and in particular the role of small random initializations. Matrix…
Unitary matrices are the basis of a large number of signal processing applications. In many of these applications, finding ways to efficiently store, and even transmit these matrices, can significantly reduce memory and throughput…