Simulating many-body physics with quantum phase-space methods
Simulating many-body physics with quantum phase-space methods
Simulating many-body physics with quantum phase-space methods
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Density operators for <strong>quantum</strong> evolutioniĤt/1. Unitary dynamics: ̂ρ(t) = e−iĤt/̂ρ(0)e ]✄ ∂t̂ρ ∂ = − i [Ĥ,̂ρ2. Equilibrium state: ̂ρ un (T ) = e − (Ĥ−µ̂N)/k B T]✄ ∂β̂ρ ∂ = 1 2[Ĥ − µ̂N,̂ρ ; β = 1/k BT+3. Open dynamics: ̂ρ Sys = Tr Res {̂ρ}] ()✄ ∂t̂ρ ∂ = − i [Ĥ,̂ρ + γ 2 ̂R̂ρ ̂R † − ̂R † ̂R̂ρ − ̂ρ ̂R † ̂R✄ each type is equivalent to a Liouville equation for ̂ρ:ddτ̂ρ = ̂L[̂ρ] ; τ = t,β<strong>Simulating</strong> <strong>many</strong>-<strong>body</strong> <strong>physics</strong> <strong>with</strong> <strong>quantum</strong> <strong>phase</strong>-<strong>space</strong> <strong>methods</strong> 12
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