Simulating many-body physics with quantum phase-space methods

Stratonovich Equations✄ Itô stochastic equations, in matrix form:dΩdτdn σdτ= −Ω= − 1 2{}−∑ t i j n i j,σ +U ∑n j j,↓ n j j,↑ − µ∑n j j,σi j,σjj,σ{(I − n σ )∆ (1)σ n σ + n σ ∆ (2)σ (I − n σ )where the stochastic propagator matrix is},∆ (r)i j,σ = [ {−t i j + δ i j Un j j,σ ′ − µ }] √(r)± δ i j 2|U|ξ j✄ ξ (r)jare delta-correlated white noisesSimulating many-body physics with quantum phase-space methods 39