Dissipative quantum dynamics, phase transitions and non-Hermitian random matrices

Understand

We explore the connections between dissipative quantum phase transitions and non-Hermitian random matrix theory.

• For this, we work in the framework of the dissipative Dicke model which is archetypal of symmetry-breaking phase transitions in open quantum systems.
• We establish that the Liouvillian describing the quantum dynamics exhibits distinct spectral features of integrable and chaotic character on the two sides of the critical point.
• We follow the distribution of the spacings of the complex Liouvillian eigenvalues across the critical point.