Spectral theory of Liouvillians for dissipative phase transitions
By Fabrizio Minganti, Alberto Biella, N. Bartolo, C. Ciuti. Physical Review A, 2018
370 citations recorded by the source corpus.
A state of an open quantum system is described by a density matrix, whose dynamics is governed by a Liouvillian superoperator. Within a general framework, we explore fundamental properties of both first-order dissipative phase transitions and second-order dissipative phase transitions associated with a symmetry breaking. In the critical region, we determine the general form of the steady-state density matrix and of the Liouvillian eigenmatrix whose eigenvalue defines the Liouvillian spectral gap. We illustrate our exact results by studying some paradigmatic quantum optical models exhibiting critical behavior.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/a48c90f9635922aef3062b50bfcdc15fb4185b09
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Adam Miranowicz
- Bernardo Spagnolo
- Davide Valenti
- Franco Nori
- Ravindra W. Chhajlany
- Fabrizio Minganti
- Angelo Carollo
- Sahel Ashhab
In Atomic and Molecular Physics, and Optics
- Adam Miranowicz
- Fabrizio Minganti
- Franco Nori
- Ravindra W. Chhajlany
- Bernardo Spagnolo
- Davide Valenti
- I. Arkhipov
- Angelo Carollo
Citations in the corpus
- Hybrid-Liouvillian formalism connecting exceptional points of non-Hermitian Hamiltonians and Liouvillians via postselection of quantum trajectories (2020, background): “To every Lindblad master equation corresponds a nonHermitian Liouvillian superoperator L which can display Liouvillian exceptional points (LEPs) [12, 23, 46–52].”
- Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps (2019, background): “By diagonalizing it, one obtains the spectral decomposition [39, 52]:”
- Geometry of quantum phase transitions (2019, background): “Beyond zero-temperature and thermal phase transitions, a novel type of criticalities have recently emerged in the context of non-equilibrium steady states (NESSes) of open-driven dissipative systems [123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, ”