scholarly journals Continuous Dissipative Phase Transitions with or without Symmetry Breaking

2021 ◽  
Author(s):  
Fabrizio Minganti ◽  
Ievgen Arkhipov ◽  
Adam Miranowicz ◽  
Franco Nori
Keyword(s):  
Phase Transitions ◽  
Symmetry Breaking ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Second Order ◽  
Necessary Condition ◽  
Symmetric Model ◽  
Open Quantum ◽  
Modern Physics ◽  
Laser Model

Abstract The paradigm of second-order phase transitions (PTs) induced by spontaneous symmetry breaking (SSB) in thermal and quantum systems is a pillar of modern physics that has been fruitfully applied to out-of-equilibrium open quantum systems. Dissipative phase transitions (DPTs) of second order are often connected with SSB, in close analogy with well-known thermal second-order PTs in closed quantum and classical systems. That is, a second-order DPT should disappear by preventing the occurrence of SSB. Here, we prove this statement to be wrong, showing that, surprisingly, SSB is not a necessary condition for the occurrence of second-order DPTs in \textit{out-of-equilibrium open quantum systems}. We analytically prove this result using the Liouvillian theory of dissipative phase transitions, and demonstrate this anomalous transition in two exemplary models: a paradigmatic laser model, where we can arbitrarily remove SSB while retaining criticality, and a $Z_2$-symmetric model of a two-photon Kerr resonator.

scholarly journals Emergence of PT-symmetry breaking in open quantum systems

2020 ◽  
Vol 9 (4) ◽  
Author(s):  
Julian Huber ◽  
Peter Kirton ◽  
Stefan Rotter ◽  
Peter Rabl
Keyword(s):  
Symmetry Breaking ◽  
Open Quantum Systems ◽  
Symmetry Transformation ◽  
Quantum Systems ◽  
Coupled Systems ◽  
Physical Systems ◽  
Open Quantum ◽  
Parity Symmetry ◽  
Classical Correspondence ◽  
Liouville Operators

The effect of \mathcal{PT}𝒫𝒯-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 \mathcal{PT}𝒫𝒯 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 \mathcal{PT}𝒫𝒯-symmetry breaking transition is recovered. This quantum-to-classical correspondence allows us to establish a common theoretical framework to identify and accurately describe \mathcal{PT}𝒫𝒯-symmetry breaking effects in a large variety of physical systems, operated both in the classical and quantum regimes.

scholarly journals Symmetry Breaking and Error Correction in Open Quantum Systems

2020 ◽  
Vol 125 (24) ◽  
Author(s):  
Simon Lieu ◽  
Ron Belyansky ◽  
Jeremy T. Young ◽  
Rex Lundgren ◽  
Victor V. Albert ◽  
...  
Keyword(s):  
Symmetry Breaking ◽  
Error Correction ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Tuning the universality class of phase transitions by feedback: Open quantum systems beyond dissipation

2021 ◽  
Vol 104 (3) ◽  
Author(s):  
D. A. Ivanov ◽  
T. Yu. Ivanova ◽  
S. F. Caballero-Benitez ◽  
I. B. Mekhov
Keyword(s):  
Phase Transitions ◽  
Open Quantum Systems ◽  
Universality Class ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Phase transitions in open quantum systems

1999 ◽  
Vol 60 (1) ◽  
pp. 114-131 ◽  
Author(s):  
C. Jung ◽  
M. Müller ◽  
I. Rotter
Keyword(s):  
Phase Transitions ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

Relaxation of interacting open quantum systems

2018 ◽  
Vol 189 (05) ◽  
Author(s):  
Vladislav Yu. Shishkov ◽  
Evgenii S. Andrianov ◽  
Aleksandr A. Pukhov ◽  
Aleksei P. Vinogradov ◽  
A.A. Lisyansky
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Hamiltonian assignment for open quantum systems

2020 ◽  
Vol 2 (3) ◽  
Author(s):  
Eugene F. Dumitrescu ◽  
Pavel Lougovski
Keyword(s):  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum

scholarly journals Perturbation Analysis of Quantum Reset Models

2021 ◽  
Vol 183 (1) ◽  
Author(s):  
Géraldine Haack ◽  
Alain Joye
Keyword(s):  
Steady State ◽  
Perturbation Analysis ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Markov Semigroup ◽  
Coupling Constant ◽  
Coupling Term ◽  
Open Quantum ◽  
Effective Dynamics ◽  
A Chain

AbstractThis paper is devoted to the analysis of Lindblad operators of Quantum Reset Models, describing the effective dynamics of tri-partite quantum systems subject to stochastic resets. We consider a chain of three independent subsystems, coupled by a Hamiltonian term. The two subsystems at each end of the chain are driven, independently from each other, by a reset Lindbladian, while the center system is driven by a Hamiltonian. Under generic assumptions on the coupling term, we prove the existence of a unique steady state for the perturbed reset Lindbladian, analytic in the coupling constant. We further analyze the large times dynamics of the corresponding CPTP Markov semigroup that describes the approach to the steady state. We illustrate these results with concrete examples corresponding to realistic open quantum systems.

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