Simulating many-body physics with quantum phase-space methods

More documents

Recommendations

Info

Application I: photons in a fibreĤ = Ĥ F + Ĥ L + Ĥ G + Ĥ R✄ Ĥ F :fibre-optic Hamiltonian, including χ (3) nonlinearity✄ Ĥ L , Ĥ G : coupling to absorbing reserviors and fibre amplifier reserviors✄ Ĥ R : nonlinear coupling to non-Markovian phonon reserviors➜ models Raman transitions and Brillouin effect (GAWBS)✄ have 10 2 modes and 10 9 particlesSimulating many-body physics with quantum phase-space methods 25
Scaled quantum field✄ define a quantum 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 with 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 numberSimulating many-body physics with quantum phase-space methods 26
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 28 and 29: Quantum Langevin Equations✄ Raman
Page 30 and 31: Wigner Equations✄ get stochastic,
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

Simulating many-body physics with quantum phase-space methods

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?