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Caldeira–Leggett model, Landau damping, and the Vlasov–Poisson system

2011; Elsevier BV; Volume: 240; Issue: 20 Linguagem: Inglês

10.1016/j.physd.2011.02.007

1872-8022

George I. Hagstrom, P.J. Morrison,

Quantum chaos and dynamical systems

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.