Adiabatic Invariants in Stellar Dynamics .1. Basic Concepts

Adiabatic Invariants in Stellar Dynamics: I. Basic Concepts

The adiabatic criterion, widely used in astronomical dynamics, is based on the harmonic oscillator. It asserts that the change in action under a slowly varying perturbation is exponentially small. Recent mathematical results precisely deene the conditions for invariance show that this model does not apply in general. In particular, a slowly varying perturbation may cause signiicant evolution st...

Adiabatic Invariants in Stellar Dynamics .2. Gravitational Shocking

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

On the Self-Consistent Response of Stellar Systems to Gravitational Shocks

We study the reaction of a globular star cluster to a time-varying tidal perturbation (gravitational shock) using self-consistent N-body simulations and address two questions. First, to what extent is the cluster interior protected by adiabatic invariants. Second, how much further energy change does the postshock evolution of the cluster potential produce and how much does it affect the dispers...

An Adiabatic Theorem without a Gap Condition

The basic adiabatic theorems of classical and quantum mechanics are overviewed and an adiabatic theorem in quantum mechanics without a gap condition is described. 1 Classical Adiabatic Invariants Consider a (mathematical) pendulum whose period is slowly modulated, for example by shortening the length of the pendulum, fig 1, [1, 18]. Figure 1: An adiabatic pendulum The Hamiltonian describing the...