Observables in quantum mechanics are represented by self-adjoint operators on Hilbert space. Such ubiquitous, well-known, and very foundational fact, however, is traditionally subtle to be explained typical first classes mechanics, as well senior physicists who have grown up with the lesson that self-adjointness “just technical”. The usual difficulties clarify connection between demand for cert...

Analysis of stability under linearized dynamics is central to ecology. We highlight two key limitations of the widely used traditional analysis. First, we note that while stability at fixed points is often the focus, ecological systems may spend less time near fixed points, and more time responding to stochastic environmental forcing by exhibiting wide zero-mean fluctuations about those states....

We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of − λ, λ / ∈ R, in Lsc when acting on an appropriate subdomain.

We examine the detail of the analytic structure of an exact analytic solution of three anyons, which interpolates to the fermion ground state in a harmonic potential well. The analysis is done on the fundamental domain with appropriate boundary conditions. Some remarks on the hard-core conditions and self-adjointness are made.