2020/03/31 by Julian Huber, Peter Kirton, Stefan Rotter +1 · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Computer science #Geometry #Mathematics #Mechanical and Optical Resonators #Nonlinear Photonic Systems #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Symmetry (geometry) #Symmetry breaking #cond-mat.mes-hall #physics.optics #quant-ph
paper · pdf · doi:10.21468/scipostphys.9.4.052
published as SciPost Phys. 9, 052 (2020) · 15 pages, 3 figures
arxiv created 2020/05/27 · openalex publication_date 2020/10/19 · arxiv updated 2020/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The effect of PT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> -symmetry breaking in coupled systems with balanced gain and loss has recently attracted considerable attention and has been demonstrated in various photonic, electrical and mechanical systems in the classical regime. However, it is still an unsolved problem how to generalize the concept of PT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> symmetry to the quantum domain, where the conventional definition in terms of non-Hermitian Hamiltonians is not applicable. Here we introduce a symmetry relation for Liouville operators that describe the dissipative evolution of arbitrary open quantum systems. Specifically, we show that the invariance of the Liouvillian under this symmetry transformation implies the existence of stationary states with preserved and broken parity symmetry. As the dimension of the Hilbert space grows, the transition between these two limiting phases becomes increasingly sharp and the classically expected PT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> -symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe PT <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒫</mml:mi> <mml:mi>𝒯</mml:mi> </mml:mstyle> </mml:math> -symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.