Adiabatic invariants for strings and membranes subjected to slowly-varying tension

Invariants for Strings , Membranes , and Beams of Slowly - Varying Dimensions

From Strings to Membranes

We examine the extent to which the action for the membrane of M-theory (the elevendimensional construct which underlies and unifies all of the known string theories) simplifies in the so-called Open Membrane (OM) limit, a limit which lies at the root of the various manifestations of noncommutativity in the string context. In order for the discussion to be relatively self-contained, we start out...

Adiabatic Invariants and Mixmaster Catastrophes

We present a rigorous analysis of the role and uses of the adiabatic invariant in the Mixmaster dynamical system. We propose a new invariant for the global dynamics which in some respects has an improved behaviour over the commonly used one. We illustrate its behaviour in a number of numerical results. We also present a new formulation of the dynamics via Catastrophe Theory. We find that the ch...

Notes on Adiabatic Invariants

Theory of Adiabatic Invariants

We review the basic theory on adiabatic invariants in classical and quantum mechanics. PACS numbers: 45.30.+s,05.45.-a,03.65.-w, 03.65.Sq