Spectral Theory of Non-Markovian Dissipative Phase Transitions

To date, dissipative phase transitions (DPTs) have mostly been studied for quantum systems coupled to idealized Markovian (memoryless) environments, where the closing of the Liouvillian gap constitutes a hallmark. Here, we extend the spectral theory of DPTs to arbitrary non-Markovian systems and present a general and systematic method to extract their signatures, which is fundamental for the understanding of realistic materials and experiments such as in the solid-state, cold atoms, cavity or circuit QED. We first illustrate our theory to show how memory effects can be used as a resource to control phase boundaries in a model exhibiting a first-order DPT, and then demonstrate the power of the method by capturing all features of a challenging second-order DPT in a two-mode Dicke model for which previous attempts had failed up to now.Comment: 7 pages and 3 figures (main), 12 pages and 6 figures (SM

Théorie spectrale des transitions de phase dissipatives non-markoviennes

So far, dissipative phase transitions (DPTs) have been mostly studied for quantum systems coupled to idealized Markovian (memoryless) environments, where the closing of the Liouvillian gap consitutes a hallmark. Here, we extend the spectral theory of DPTs to arbitrary non-Markovian systems and present a general and systematic numerical method to extract their signatures, which is fundamental for the understanding of realistic materials and experimental platforms such as in the solid-state, cold atoms, or cavity and circuit QED

Spectral Theory of Non-Markovian Dissipative Phase Transitions

To date, dissipative phase transitions (DPTs) have mostly been studied for quantum systems coupled to idealized Markovian (memoryless) environments, where the closing of the Liouvillian gap constitutes a hallmark. Here, we extend the spectral theory of DPTs to arbitrary non-Markovian systems and present a general and systematic method to extract their signatures, which is fundamental for the understanding of realistic materials and experiments such as in the solid-state, cold atoms, cavity or circuit QED. We first illustrate our theory to show how memory effects can be used as a resource to control phase boundaries in a model exhibiting a first-order DPT, and then demonstrate the power of the method by capturing all features of a challenging second-order DPT in a two-mode Dicke model for which previous attempts had fail up to now