Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics

Flynn, Vincent P.; Cobanera, Emilio; Viola, Lorenza

doi:10.1103/physrevlett.127.245701

Cited by 54 publications

(26 citation statements)

References 46 publications

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“…If nonlinearity is not negligible, on the other hand, the combination of transient amplification and nonlinearity can lead to instability even if the largest imaginary part of the spectrum is negative [4]. In addition to classical systems [4,139], the mathematics of stability/instability is relevant in quantum systems described by the bosonic Bogoliubov-de Gennes equation [141,142,143,144,145]. In addition to the stability analysis, the relaxation process to the non-equilibrium steady state in the Lindblad equation is related to non-normality.…”

Section: Non-hermitian Dynamics and Spec-tral Topologymentioning

confidence: 99%

Non-Hermitian topological phenomena: A review

Okuma¹,

Sato²

2022

Preprint

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The past decades have witnessed an explosion of interest in topological materials, and a lot of mathematical concepts have been introduced in condensed matter physics. Among them, the bulk-boundary correspondence is the central topic in topological physics, which has inspired researchers to focus on boundary physics. Recently, the concepts of topological phases have been extended to non-Hermitian Hamiltonians, whose eigenvalues can be complex. Besides the topology, non-Hermiticity can also cause a boundary phenomenon called the non-Hermitian skin effect, which is an extreme sensitivity of the spectrum to the boundary condition. In this article, we review developments in non-Hermitian topological physics by focusing mainly on the boundary problem. As well as the competition between non-Hermitian and topological boundary phenomena, we discuss the topological nature inherent in non-Hermiticity itself.

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Section: Non-hermitian Dynamics and Spec-tral Topologymentioning

confidence: 99%

Non-Hermitian topological phenomena: A review

Okuma¹,

Sato²

2022

Preprint

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“…A typical mathematical tool is the Lindblad equation [20,21]. For example, a bosonic quadratic Lindblad equation has been studied in terms of topology and skin effect [22]. Another useful mathematical tool is the Green's function [15,23].…”

Section: B Bosonic Green's Function In Nambu Representationmentioning

confidence: 99%

Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect

Okuma

2022

Preprint

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“…These have attracted lots of interest mainly due to their utility for quantum information storage (e.g. [33][34][35][36][37][38][39][40][41][42][43][44]). Even though, in general, they are not necessary for the existence of bistability because degenerate stationary states may emerge in the thermodynamic limit only (without a strong symmetry), nor are they sufficient because all of the degenerate stationary states implied by the strong symmetries may have the same expectation values for local observables.…”

Section: Introductionmentioning

confidence: 99%

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

Alaeian¹,

Buča²

2022

Preprint

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The existence of bistability in quantum optical systems remains a intensely debated open question beyond the mean-field approximation. Quantum fluctuations are finite-size corrections to the mean-field approximation used because the full exact solution is unobtainable. Usually, quantum fluctuations destroy the bistability present on the mean-field level. Here, by identifying and using exact modulated semi-local dynamical symmetries in a certain quantum optical models of drivendissipative fermionic chains we exactly prove bistability in precisely the quantum fluctuations. Surprisingly, rather than destroying bistability, the quantum fluctuations themselves exhibit bistability, even though it is absent on the mean-field level for our systems. Moreover, the models studied acquire additional thermodynamic dynamical symmetries that imply persistent periodic oscillations in the quantum fluctuations, constituting pseudo-variants of boundary time crystals. Physically, these emergent operators correspond to finite-frequency and finite-momentum semi-local Goldstone modes. Our work therefore provides to the best of our knowledge the first example of a provably bistable quantum optical system.

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Topology by Dissipation: Majorana Bosons in Metastable Quadratic Markovian Dynamics

Cited by 54 publications

References 46 publications

Non-Hermitian topological phenomena: A review

Non-Hermitian topological phenomena: A review

Boundary-dependent dynamical instability of bosonic Green's function: Dissipative Bogoliubov-de Gennes Hamiltonian and its application to non-Hermitian skin effect

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

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