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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Krylov complexity is a measure of operator growth in quantum systems, basedon the number of orthogonal basis vectors needed to approximate the timeevolution of an operator. In this paper, we study the Krylov complexity of a$\mathsf{PT}$-symmetric system of oscillators, which exhibits two phasetransitions that separate a dissipative state, a Rabi-oscillation state, and anultra-strongly coupled regime. We use a generalization of the $su(1,1)$ algebraassociated to the Bateman oscillator to describe the Hamiltonian of the coupledsystem, and construct a set of coherent states associated with this algebra. Wecompute the Krylov (spread) complexity using these coherent states, and findthat it can distinguish between the $\mathsf{PT}$-symmetric and $\mathsf{PT}$symmetry-broken phases. We also show that the Krylov complexity reveals theill-defined nature of the vacuum of the Bateman oscillator, which is a specialcase of our system. Our results demonstrate the utility of Krylov complexity asa tool to probe the properties and transitions of $\mathsf{PT}$-symmetricsystems.

Complexity and Operator Growth for Quantum Systems in Dynamic Equilibrium