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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Scaled <strong>quantum</strong> field✄ define a <strong>quantum</strong> photon-density field in terms of mode operators:̂Ψ(t,x) = 1 √2πZdk â(t,k)e i(k−k 0)x+iω 0 t ;[̂Ψ(t,x), ̂Ψ† (t,x ′ )]= δ(x − x ′ )✄ change to propagative reference frame <strong>with</strong> scaled variables:t ⇔ (t − x/v)/t 0 x ⇔ x/x 0̂φ = ̂Ψ √ vt 0 /n➜ t 0 is a typical pulse duration➜ x 0 = t 2 0 /|k′′ | is the dispersion length➜ n = |k ′′ |Ac/(n 2 ω 2 ct 0 ) is a typical photon number<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> 26
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