1,254 research outputs found
Inverse eigenvalue problem for normal J-hamiltonian matrices
A complex square matrix A is called J-hamiltonian if AJ is hermitian where J is a normal real matrix such that J^2=−I_n. In this paper we solve the problem of finding J-hamiltonian normal solutions for the inverse eigenvalue problem
Procrustes problem for the inverse eigenvalue problem of normal (skew) -Hamiltonian matrices and normal -symplectic matrices
A square complex matrix is called (skew) -Hamiltonian if is
(skew) hermitian where is a real normal matrix such that , where
is the identity matrix. In this paper, we solve the Procrustes problem to
find normal (skew) -Hamiltonian solutions for the inverse eigenvalue
problem. In addition, a similar problem is investigated for normal
-symplectic matrices.Comment: 25 page
From the Equations of Motion to the Canonical Commutation Relations
The problem of whether or not the equations of motion of a quantum system
determine the commutation relations was posed by E.P.Wigner in 1950. A similar
problem (known as "The Inverse Problem in the Calculus of Variations") was
posed in a classical setting as back as in 1887 by H.Helmoltz and has received
great attention also in recent times. The aim of this paper is to discuss how
these two apparently unrelated problems can actually be discussed in a somewhat
unified framework. After reviewing briefly the Inverse Problem and the
existence of alternative structures for classical systems, we discuss the
geometric structures that are intrinsically present in Quantum Mechanics,
starting from finite-level systems and then moving to a more general setting by
using the Weyl-Wigner approach, showing how this approach can accomodate in an
almost natural way the existence of alternative structures in Quantum Mechanics
as well.Comment: 199 pages; to be published in "La Rivista del Nuovo Cimento"
(www.sif.it/SIF/en/portal/journals
Efficient Algorithms for Solving Structured Eigenvalue Problems Arising in the Description of Electronic Excitations
Matrices arising in linear-response time-dependent density functional theory and many-body perturbation theory, in particular in the Bethe-Salpeter approach, show a 2 × 2 block structure. The motivation to devise new algorithms, instead of using general purpose eigenvalue solvers, comes from the need to solve large problems on high performance computers. This requires parallelizable and communication-avoiding algorithms and implementations. We point out various novel directions for diagonalizing structured matrices. These include the solution of skew-symmetric eigenvalue problems in ELPA, as well as structure preserving spectral divide-and-conquer schemes employing generalized polar decompostions
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