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

The Caldeira–Leggett Hamiltonian 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 (Landau, 1946 [1]). An invertible linear transformation (Morrison and Pfirsch, 1992 [18]; Morrison, 2000 [19]) is presented that converts solutions of the Caldeira–Leggett model into solutions of the linearized Vlasov–Poisson system.