English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Open quantum systems that interact with a Markovian environment can bedescribed by a Lindblad master equation. The generator of time-translation isgiven by a Liouvillian superoperator $\mathcal{L}$ acting on the density matrixof the system. As the Fock space for a single bosonic mode is alreadyinfinite-dimensional, the diagonalization of the Liouvillian has to be done onthe creation- and annihilation-superoperators, a process called `thirdquantization'. We propose a method to solve the Liouvillian for quadraticsystems using a single symplectic transformation. We show that thenon-Hermitian effective Hamiltonian of the system, next to incorporating thedynamics of the system, is a tool to analyze its symmetries. As an example, weuse the effective Hamiltonian to formulate a $\mathcal{PT}$-`symmetry' of anopen system. We describe how the inclusion of source terms allows us to obtainthe cumulant generating function for observables such as the photon current.

Third quantization for bosons: symplectic diagonalization, non-Hermitian Hamiltonian, and symmetries