Quantum Decoherence — Pointer Basis & Einselection

Wigner function evolution of a quantum superposition coupled to an environment. Decoherence selects the pointer (classical) basis.

Wigner function W(x,p) — blue=positive, red=negative
Density matrix ρ(x,x') magnitude

Quantum State

Zurek's einselection (1981): environment-induced superselection. The pointer basis consists of states robust against environmental monitoring. Off-diagonal elements of ρ (quantum coherences) decay as:
ρ(x,x') → ρ(x,x')·exp(−γ(x−x')²t)

The Wigner function interference fringes (oscillating between ±) signify quantum coherence. Decoherence destroys these fringes, leaving a classical mixture.