Adiabatic dynamics of one-dimensional classical Hamiltonian dissipative systems

摘要

AbstractA linearized plane pendulum with the slowly varying mass and length of string and the suspension point moving at a slowly varying speed is presented as an example of a simple 1D mechanical system described by the generalized harmonic oscillator equation, which is a basic model in discussion of the adiabatic dynamics and geometric phase. The expression for the pendulum geometric phase is obtained by three different methods. The pendulum is shown to be canonically equivalent to the damped harmonic oscillator. This supports the mathematical conclusion, not widely accepted in physical community, of no difference between the dissipative and Hamiltonian 1D systems.Highlights?The presented pendulum with slowly varying parameters is the simplest 1D system described by the generalized harmonic oscillator equation.?The expression for the pendulum geometric phase is obtained by three different methods.?The shown canonical equivalence of the pendulum to the damped oscillator confirms the equivalence of dissipative and Hamiltonian 1D systems.<