Simulating many-body physics with quantum phase-space methods

Gaussian Basis I: Coherent-state projectorŝΛ =∣ α〉〈(α + ) ∗∣ ∣〈(α+ ) ∗∣ ∣ ∣ ∣α 〉✄ defines the +P distribution, with a doubled phase space −→ λ = (Ω,α,α + )✄ 〈 moments: O ( â † ,â )〉 = E [O(α + ,α)]✄ successful for many applications in quantum optics✄ successful simulations of short-time quantum dynamics of BECSimulating many-body physics with quantum phase-space methods 19