Caldeira-Leggett Model, Landau Damping, and the Vlasov-Poisson System

Details Caldeira-Leggett Model, Landau Damping, and the Vlasov-Poisson System Caldeira-Leggett Model, Landau Damping, and the Vlasov-Poisson System

2010-08-30

arxiv.org/abs/1008.5190v1

Physics

Plasma Physics

Submitted to Physica D

Scientific paper

The Caldeira-Leggett Hamiltonian (Eq. (1) below) describes the interaction of a discrete harmonic oscillator with a continuous bath of harmonic oscillators. This system is a standard model of dissipation in macroscopic low temperature physics, and has applications to superconductors, quantum computing, and macroscopic quantum tunneling. The similarities between the Caldeira-Leggett model and the linearized Vlasov-Poisson equation are analyzed, and it is shown that the damping in the Caldeira-Leggett model is analogous to that of Landau damping in plasmas [1]. An invertible linear transformation [2, 3] is presented that converts solutions of the Caldeira-Leggett model into solutions of the linearized Vlasov-Poisson system.

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