scholarly journals Symmetry Breaking in Quantum Systems

2021 ◽  
pp. 121-128
Author(s):  
Franco Strocchi
Keyword(s):  
Symmetry Breaking ◽  
Quantum Systems

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.

Electron Localization due to Symmetry Breaking in Nonlinear Coupled-Quantum Systems

1997 ◽  
Vol 36 (Part 2, No. 6B) ◽  
pp. L834-L837 ◽  
Author(s):  
Noriaki Tsukada ◽  
Mitsunobu Gotoda ◽  
Toshiro Isu ◽  
Masahiro Nunoshita ◽  
Taneo Nishino
Keyword(s):  
Symmetry Breaking ◽  
Quantum Systems ◽  
Electron Localization

scholarly journals Reference Frame Induced Symmetry Breaking on Holographic Screens

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 408
Author(s):  
Chris Fields ◽  
James F. Glazebrook ◽  
Antonino Marcianò
Keyword(s):  
Symmetry Breaking ◽  
Reference Frame ◽  
Reference Frames ◽  
A Priori ◽  
Quantum Systems ◽  
Classical Information ◽  
Pointer States ◽  
Finite Quantum Systems ◽  
Holographic Screen ◽  
Holographic Screens

Any interaction between finite quantum systems in a separable joint state can be viewed as encoding classical information on an induced holographic screen. Here we show that when such an interaction is represented as a measurement, the quantum reference frames (QRFs) deployed to identify systems and pick out their pointer states induce decoherence, breaking the symmetry of the holographic encoding in an observer-relative way. Observable entanglement, contextuality, and classical memory are, in this representation, logical and temporal relations between QRFs. Sharing entanglement as a resource requires a priori shared QRFs.

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 Spontaneous symmetry breaking and Nambu–Goldstone modes in open classical and quantum systems

2020 ◽  
Vol 2020 (3) ◽  
Author(s):  
Yoshimasa Hidaka ◽  
Yuki Minami
Keyword(s):  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Type A ◽  
Quantum Systems ◽  
Propagation Mode ◽  
Goldstone Mode ◽  
Type B ◽  
Goldstone Theorem ◽  
Diffusion Type ◽  
Goldstone Modes

Abstract We discuss spontaneous symmetry breaking of open classical and quantum systems. When a continuous symmetry is spontaneously broken in an open system, a gapless excitation mode appears corresponding to the Nambu–Goldstone mode. Unlike isolated systems, the gapless mode is not always a propagation mode, but it is a diffusion one. Using the Ward–Takahashi identity and the effective action formalism, we establish the Nambu–Goldstone theorem in open systems, and derive the low-energy coefficients that determine the dispersion relation of Nambu–Goldstone modes. Using these coefficients, we classify the Nambu–Goldstone modes into four types: type-A propagation, type-A diffusion, type-B propagation, and type-B diffusion modes.

scholarly journals Bulk–edge correspondence and stability of multiple edge states of a $\mathcal{PT}$-symmetric non-Hermitian system by using non-unitary quantum walks

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Makio Kawasaki ◽  
Ken Mochizuki ◽  
Norio Kawakami ◽  
Hideaki Obuse
Keyword(s):  
Symmetry Breaking ◽  
Open Quantum Systems ◽  
Quantum Walk ◽  
Quantum Systems ◽  
Quantum Walks ◽  
Multiple Edge ◽  
Exceptional Point ◽  
Topological Phase ◽  
Edge States ◽  
The Stability

Abstract Topological phases and the associated multiple edge states are studied for parity and time-reversal ($\mathcal{PT}$)-symmetric non-Hermitian open quantum systems by constructing a non-unitary three-step quantum walk retaining $\mathcal{PT}$ symmetry in one dimension. We show that the non-unitary quantum walk has large topological numbers of the $\mathbb{Z}$ topological phase and numerically confirm that multiple edge states appear as expected from the bulk–edge correspondence. Therefore, the bulk–edge correspondence is valid in this case. Moreover, we study the stability of the multiple edge states against a symmetry-breaking perturbation so that the topological phase is reduced to $\mathbb{Z}_2$ from $\mathbb{Z}$. In this case, we find that the number of edge states does not become one unless a pair of edge states coalesce at an exceptional point. Thereby, this is a new kind of breakdown of the bulk–edge correspondence in non-Hermitian systems. The mechanism of the prolongation of edge states against the symmetry-breaking perturbation is unique to non-Hermitian systems with multiple edge states and anti-linear symmetry. Toward experimental verifications, we propose a procedure to determine the number of multiple edge states from the time evolution of the probability distribution.

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