Quantum Brownian Motion — Caldeira-Leggett

A quantum harmonic oscillator coupled to a bosonic bath (Caldeira-Leggett model). The reduced Wigner function W(x,p,t) evolves under quantum diffusion and decoherence — quantum superpositions decay at rate γ·Δx²/2λ²_th.

Controls

Damping γ 0.1 Temperature T 0.5 Oscillator ω₀ 1.0

Purity Tr[ρ²]: —

⟨x⟩: —

Δx: —

t: 0.00

Wigner function W(x,p).
Green: positive (classical).
Red: negative (quantum).
Cat state shows interference
fringes that decohere rapidly.