scholarly journals Collectivity, phase transitions, and exceptional points in open quantum systems

1998 ◽  
Vol 58 (3) ◽  
pp. 2894-2901 ◽  
Author(s):  
W. D. Heiss ◽  
M. Müller ◽  
I. Rotter
Keyword(s):  
Phase Transitions ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Exceptional Points

scholarly journals Loss, Gain, and Singular Points in Open Quantum Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Hichem Eleuch ◽  
Ingrid Rotter
Keyword(s):  
Parameter Space ◽  
Critical Points ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Experimental Results ◽  
Open Quantum ◽  
Exceptional Points ◽  
Complex Eigenvalues ◽  
Dynamical Properties

Non-Hermitian quantum physics is used successfully for the description of different puzzling experimental results, which are observed in open quantum systems. Mostly, the influence of exceptional points on the dynamical properties of the system is studied. At these points, two complex eigenvalues Ei≡Ei+iΓi/2 of the non-Hermitian Hamiltonian H coalesce (where Ei is the energy and Γi is the inverse lifetime of the state i). We show that also the eigenfunctions Φi of the two states play an important role, sometimes even the dominant one. Besides exceptional points, other critical points exist in non-Hermitian quantum physics. At these points a=acr in the parameter space, the biorthogonal eigenfunctions of H become orthogonal. For illustration, we show characteristic numerical results.

scholarly journals EXCEPTIONAL POINTS IN OPEN AND PT-SYMMETRIC SYSTEMS

2014 ◽  
Vol 54 (2) ◽  
pp. 106-112 ◽  
Author(s):  
Hichem Eleuch ◽  
Ingrid Rotter
Keyword(s):  
Open Quantum Systems ◽  
Level Density ◽  
Quantum Systems ◽  
Point Of View ◽  
Eigenvalues And Eigenfunctions ◽  
Open Quantum ◽  
Exceptional Points ◽  
Characteristic Features ◽  
High Level ◽  
Symmetric Systems

Exceptional points (EPs) determine the dynamics of open quantum systems and cause also PT symmetry breaking in PT symmetric systems. From a mathematical point of view, this is caused by the fact that the phases of the wavefunctions (eigenfunctions of a non-Hermitian Hamiltonian) relative to one another are not rigid when an EP is approached. The system is therefore able to align with the environment to which it is coupled and, consequently, rigorous changes of the system properties may occur. We compare analytically as well as numerically the eigenvalues and eigenfunctions of a 2 × 2 matrix that is characteristic either of open quantum systems at high level density or of PT symmetric optical lattices. In both cases, the results show clearly the influence of the environment on the system in the neighborhood of EPs. Although the systems are very different from one another, the eigenvalues and eigenfunctions indicate the same characteristic features.

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 Exceptional Points and Dynamical Phase Transitions

10.14311/1273 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
I. Rotter
Keyword(s):  
Phase Transitions ◽  
Quantum Physics ◽  
Open Quantum Systems ◽  
Level Density ◽  
Experimental Studies ◽  
Quantum Systems ◽  
Microwave Cavity ◽  
Exceptional Points ◽  
Dynamical Phase ◽  
Dynamical Phase Transitions

In the framework of non-Hermitian quantum physics, the relation between exceptional points,dynamical phase transitions and the counter intuitive behavior of quantum systems at high level density is considered. The theoretical results obtained for open quantum systems and proven experimentally some years ago on a microwave cavity, may explain environmentally induce deffects (including dynamical phase transitions), which have been observed in various experimental studies. They also agree(qualitatively) with the experimental results reported recently in PT symmetric optical lattices.

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 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
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