Table 1 Comparison of observables in Lindblad vs. Wigner trajectory frameworks
From: Chaotic and quantum dynamics in driven-dissipative bosonic chains
Observable | Lindblad | Wigner trajectories |
|---|---|---|
Field \(\langle {\hat{a}}_{\ell }\rangle\) | \({{{\mathrm{Tr}}}}\,[{\hat{a}}_{\ell }\hat{\rho }]\) | 〈αℓ〉 |
Photon number \(\langle {\hat{a}}_{\ell }^{{{\dagger}} }{\hat{a}}_{\ell }\rangle\) | \({{{\mathrm{Tr}}}}\,[{\hat{a}}_{\ell }^{{{\dagger}} }{\hat{a}}_{\ell }\hat{\rho }]\) | 〈∣αℓ∣2〉 − 1/2 |
Spatial correlation \(\langle {\hat{a}}_{k}^{{{\dagger}} }{\hat{a}}_{\ell }\rangle\) | \({{{\mathrm{Tr}}}}\,[{\hat{a}}_{k}^{{{\dagger}} }{\hat{a}}_{\ell }\hat{\rho }]\) | \(\langle {\alpha }_{k}^{* }{\alpha }_{\ell }\rangle -{\delta }_{kl}/2\) |
Kerr nonlinearity \(\langle {\hat{a}}_{\ell }^{{{\dagger}} 2}{\hat{a}}_{\ell }^{2}\rangle\) | \({{{\mathrm{Tr}}}}\,[{\hat{a}}_{\ell }^{{{\dagger}} 2}{\hat{a}}_{\ell }^{2}\hat{\rho }]\) | 〈∣αℓ∣4〉 − 2〈∣αℓ∣2〉 + 1/2 |
