Simulating many-body physics with quantum phase-space methods

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Wigner Equations✄ get stochastic, Raman-modified nonlinear Schrödinger equation:∂∂x φ(t,x) = − Z ∞✄ noise correlations:+dt ′ g(t −t ′ )φ(t ′ ,x) + Γ(t,x) ± i−∞ 2∂t 2φ(t,x)Z ∞]dt ′ h(t −t ′ )φ ∗ (t ′ ,x)φ(t ′ ,x) + Γ R (t,x) φ(t,x)[i−∞〈Γ(ω,x)Γ ∗ (ω ′ ,x ′ )〉 = αA (ω) + α G (ω)δ(x − x ′ )δ(ω − ω ′ )2n〈Γ R (ω,x)Γ R∗ (ω ′ ,x ′ ) 〉 =[n αRn (|ω|) th (|ω|) + 1 ]δ(x − x ′ )δ(ω − ω ′ )2〈∆φ(t,0)∆φ ∗ (t ′ ,0)〉 = 1 2n δ(t −t′ )∂ 2Simulating many-body physics with quantum phase-space methods 29
Simulating many-body physics with quantum phase-space methods 30
Page 1: Simulating many-body physics with q
Page 4 and 5: Theoretical Methods✄ deterministi
Page 6 and 7: Overview✄introduction to phase-sp
Page 8: Probability distributions✄ many w
Page 11 and 12: Simulating many-body physics with q
Page 13 and 14: Density operators for quantum evolu
Page 15 and 16: Stochastic Gauges✄ Mapping from H
Page 17 and 18: Overview✄ introduction to phase-s
Page 19 and 20: General Gaussian operatorsa general
Page 22 and 23: Gaussian Basis II: Thermal operator
Page 24 and 25: Extended phase space−→ λ = (Ω
Page 26 and 27: Application I: photons in a fibreĤ
Page 28 and 29: Quantum Langevin Equations✄ Raman
Page 32 and 33: +P Equations✄ get two stochastic
Page 34 and 35: Simulations✄ soliton jitter, soli
Page 36 and 37: Solving the Hubbard Model✄ only t
Page 38 and 39: Applying the Gaussian representatio
Page 40 and 41: Stratonovich Equations✄ Itô stoc
Page 42 and 43: Branching✄ averages are weighted,
Page 44 and 45: Application III: Molecules in a wel
Page 46: Summary✄ Generalised phase-space

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