Plasma simulation as eigenvalue problem

The cumulative reaction probability as eigenvalue problem

It is shown that the cumulative reaction probability for a chemical reaction can be expressed (absolutely rigorously) as N(E) =Xkp#>, where {pk} are the eigenvalues of a certain Hermitian matrix (or operator). The eigenvalues {pk} all he between 0 and 1 and thus have the interpretation as probabilities, eigenreaction probabilities which may be thought of as the rigorous generalization of the tr...

The Choptuik spacetime as an eigenvalue problem

By fine-tuning generic Cauchy data, critical phenomena have recently been discovered in the black hole/no black hole “phase transition” of various gravitating systems. For the spherisymmetric real scalar field system, we find the “critical” spacetime separating the two phases by demanding discrete scale-invariance, analyticity, and an additional reflection-type symmetry. The resulting nonlinear...

Quantization as Selection Rather than Eigenvalue Problem

Quantum field theory as eigenvalue problem

A mathematically well-defined, manifestly covariant theory of classical and quantum field is given, based on Euclidean Poisson algebras and a generalization of the Ehrenfest equation, which implies the stationary action principle. The theory opens a constructive spectral approach to finding physical states both in relativistic quantum field theories and for flexible phenomenological few-particl...

The Eigenvalue Problem: Perturbation Theory The Unsymmetric Eigenvalue Problem

The Unsymmetric Eigenvalue Problem Just as the problem of solving a system of linear equations Ax = b can be sensitive to perturbations in the data, the problem of computing the eigenvalues of a matrix can also be sensitive to perturbations in the matrix. We will now obtain some results concerning the extent of this sensitivity. Suppose that A is obtained by perturbing a diagonal matrix D by a ...