scholarly journals Topological mode switching in modulated structures with dynamic encircling of an exceptional point

2021 ◽  
Vol 477 (2245) ◽  
pp. 20200766
Author(s):  
Linlin Geng ◽  
Weixuan Zhang ◽  
Xiangdong Zhang ◽  
Xiaoming Zhou
Keyword(s):  
Energy Input ◽  
Normal Modes ◽  
Exceptional Point ◽  
Mode Switching ◽  
Input State ◽  
Dynamic Modulation ◽  
Exceptional Points ◽  
Modulated Structures ◽  
Starting Point ◽  
Open Question

Exceptional points are special degeneracies occurring in non-Hermitian systems at which both eigenfrequencies and eigenmodes coalesce simultaneously. Fascinating phenomena, including topological, non-reciprocal and chiral energy transfer between normal modes, have been envisioned in optical and photonic systems with the exceptional point dynamically encircled in the parameter space. However, it has remained an open question of whether and how topological mode switching relying on exceptional points could be achieved in mechanical systems. The present paper studies a two-mode mechanical system with an exceptional point and implements the dynamic encircling of such a point using dynamic modulation mechanisms with time-driven elasticity and viscosity. Topological mode switching with robustness against the input state and loop trajectories has been demonstrated numerically. It is found that the dynamical encircling of an exceptional point with the starting point near the symmetric phase leads to chiral mode transfer controlled mainly by the encircling direction, while non-chiral dynamics is observed for the starting point near the broken phase. Analyses also show that minor energy input is required in the process of encircling the exceptional point, demonstrating the intrinsically motivated behaviour of topological mode switching.

scholarly journals Chiral mode transfer of symmetry-broken states in anti-parity-time-symmetric mechanical system

2021 ◽  
Vol 477 (2256) ◽  
Author(s):  
Linlin Geng ◽  
Weixuan Zhang ◽  
Xiangdong Zhang ◽  
Xiaoming Zhou
Keyword(s):  
Mechanical Systems ◽  
Pt Symmetry ◽  
Exceptional Point ◽  
Mode Switching ◽  
Symmetric System ◽  
Starting Point ◽  
Spring System ◽  
Mass Spring ◽  
Open Question ◽  
Symmetric Systems

Non-Hermitian systems with parity-time (PT) symmetry reveal rich physics beyond the Hermitian regime. As the counterpart of conventional PT symmetry, anti-parity-time (APT) symmetry may lead to new insights and applications. Complementary to PT-symmetric systems, non-reciprocal and chiral mode switching for symmetry-broken modes have been reported in optics with an exceptional point dynamically encircled in the parameter space of an APT-symmetric system. However, it has remained an open question whether and how the APT-symmetry-induced chiral mode transfer could be realized in mechanical systems. This paper investigates the implementation of APT symmetry in a three-element mass–spring system. The dynamic encircling of an APT-symmetric exceptional point has been implemented using dynamic-modulation mechanisms with time-driven stiffness. It is found that the dynamic encircling of an exceptional point in an APT-symmetric system with the starting point near the symmetry-broken phase leads to chiral mode switching. These findings may provide new opportunities for unprecedented wave manipulation in mechanical systems.

scholarly journals Dynamically encircling an exceptional point in anti-parity-time symmetric systems: asymmetric mode switching for symmetry-broken modes

2019 ◽  
Vol 8 (1) ◽  
Author(s):  
Xu-Lin Zhang ◽  
Tianshu Jiang ◽  
C. T. Chan
Keyword(s):  
Topological Structure ◽  
Optical Signal ◽  
Optical Systems ◽  
Exceptional Point ◽  
Mode Switching ◽  
New Wave ◽  
Asymmetric Mode ◽  
Starting Point ◽  
On Chip ◽  
Symmetric Systems

Abstract Dynamically encircling an exceptional point (EP) in parity-time (PT) symmetric waveguide systems exhibits interesting chiral dynamics that can be applied to asymmetric mode switching for symmetric and anti-symmetric modes. The counterpart symmetry-broken modes (i.e., each eigenmode is localized in one waveguide only), which are more useful for applications such as on-chip optical signal processing, exhibit only non-chiral dynamics and therefore cannot be used for asymmetric mode switching. Here, we solve this problem by resorting to anti-parity-time (anti-PT) symmetric systems and utilizing their unique topological structure, which is very different from that of PT-symmetric systems. We find that the dynamical encircling of an EP in anti-PT-symmetric systems with the starting point in the PT-broken phase results in chiral dynamics. As a result, symmetry-broken modes can be used for asymmetric mode switching, which is a phenomenon and application unique to anti-PT-symmetric systems. We perform experiments to demonstrate the new wave-manipulation scheme, which may pave the way towards designing on-chip optical systems with novel functionalities.

The 3 C's of the Circular Economy for Food. A conceptual framework for circular design in the food system

2021 ◽  
Author(s):  
Franco Fassio
Keyword(s):  
Sustainable Development ◽  
Conceptual Framework ◽  
Circular Economy ◽  
Food System ◽  
Raw Material ◽  
Starting Point ◽  
Development Goals ◽  
Definition Of ◽  
Open Question ◽  
Circular Design

Food, the basic connecting unit of all the UN's Sustainable Development Goals, plays a crucial role in the ecological transition towards a circular economic paradigm. This paper takes scientific considerations as a starting point in order to contribute to the definition of a theoretical-operational framework in which to grow the Circular Economy for Food. This is a still-open question in a sector of the circular economy that is emerging as vital to sustainable development. The 3 C's of Capital, Cyclicality and Co-evolution offer a systemic, holistic vision of the food system's role. Within this conceptual framework, the designers can find the main boundaries of the system, within which to express their creativity. The aim must be to avoid damaging relationships with the best supplier of raw material known to humanity (Nature), respecting planetary boundaries and at the same time offering a fair space to civil society.

scholarly journals Paths of unitary access to exceptional points

2021 ◽  
Vol 2038 (1) ◽  
pp. 012026
Author(s):  
Miloslav Znojil
Keyword(s):  
Hilbert Space ◽  
Phase Transitions ◽  
Quantum Phase Transitions ◽  
Quantum Systems ◽  
Point Of View ◽  
Explicit Description ◽  
Direct Access ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Innovative Idea

Abstract With an innovative idea of acceptability and usefulness of the non-Hermitian representations of Hamiltonians for the description of unitary quantum systems (dating back to the Dyson’s papers), the community of quantum physicists was offered a new and powerful tool for the building of models of quantum phase transitions. In this paper the mechanism of such transitions is discussed from the point of view of mathematics. The emergence of the direct access to the instant of transition (i.e., to the Kato’s exceptional point) is attributed to the underlying split of several roles played by the traditional single Hilbert space of states ℒ into a triplet (viz., in our notation, spaces K and ℋ besides the conventional ℒ ). Although this explains the abrupt, quantum-catastrophic nature of the change of phase (i.e., the loss of observability) caused by an infinitesimal change of parameters, the explicit description of the unitarity-preserving corridors of access to the phenomenologically relevant exceptional points remained unclear. In the paper some of the recent results in this direction are summarized and critically reviewed.

scholarly journals Is there another people? Populism, radical democracy and immanent critique

2020 ◽  
pp. 019145372091045
Author(s):  
Victor Kempf
Keyword(s):  
Radical Democracy ◽  
Political Community ◽  
Right Wing ◽  
Constructivist Approach ◽  
Left Wing ◽  
The People ◽  
Starting Point ◽  
Immanent Critique ◽  
Right Wing Populism ◽  
Open Question

This article explores the possibility of a notion of left-wing populism that is conceptually opposed to the identitarian logic of embodiment that characterises right-populist interpellations of ‘the people’. In the first part, I will demonstrate, that in Laclau’s constructivist approach, any populist embodiment of the people actually has a partial, subaltern and performative origin. On this basis, it becomes possible to distinguish between a radical-democratic version of the people that is self-reflexively aware of this origin and a regressive and reified one that ideologically betrays and negates its own subaltern tradition of democratic struggle by proclaiming to embody a positive, pre-established substance of ‘rooted’, ‘well-born’ community. In the second part of the article, I will focus on this self-negation as a starting point for an immanent critique of right-wing populism. Such an immanent critique is promising, because it could overcome the shortcomings of decisionism and moralism that limit the contemporary critique of right-wing populism. However, it remains still an open question how to defend and define a negativist truth of political community and subjectivation that is necessary for developing such a left-Hegelian critique of regressive and reified notions of ‘the people’.

The Impact of Exceptional Points on the Reliability of Thermoacoustic Stability Analysis

2020 ◽  
Author(s):  
Felicitas Schäfer ◽  
Shuai Guo ◽  
Wolfgang Polifke
Keyword(s):  
Stability Analysis ◽  
Exceptional Point ◽  
Exceptional Points ◽  
Large Sets ◽  
Training Samples ◽  
Numerical Stability Analysis ◽  
Increased Sensitivity ◽  
Positive Growth Rate ◽  
Input Uncertainties ◽  
The Impact

Abstract Exceptional points can be found for specific sets of parameters in thermoacoustic systems. At an exceptional point, two eigenvalues and their corresponding eigenfunctions coalesce. Given that the sensitivity of these eigenvalues to parameter changes becomes infinite at the exceptional point, their occurrence may greatly affect the outcome and reliability of numerical stability analysis. We propose a new method to identify exceptional points in thermoacoustic systems. By iteratively updating the system parameters, two initially selected eigenvalues are shifted towards each other, ultimately colliding and generating the exceptional point. Using this algorithm, we were able to identify for the first time a physically meaningful exceptional point with positive growth rate in a thermoacoustic model. Furthermore, our analysis goes beyond previous studies inasmuch as we employ a more realistic flame transfer function to model flame dynamics. Building on these results, we analyze the effect of exceptional points on the reliability of thermoacoustic stability analysis. In the context of uncertainty quantification, we show that surrogate modeling is not reliable in the vicinity of an exceptional point, even when large sets of training samples are provided. The impact of exceptional points on the propagation of input uncertainties is demonstrated via Monte Carlo computations. The increased sensitivity associated with the exceptional point results in large variances for eigenvalue predictions, which needs to be taken into account for reliable stability analysis.

Topological mode switching in a graphene doublet with exceptional points

2017 ◽  
Vol 49 (6) ◽  
Author(s):  
Shaolin Ke ◽  
Bing Wang ◽  
Hua Long ◽  
Kai Wang ◽  
Peixiang Lu
Keyword(s):  
Mode Switching ◽  
Exceptional Points

scholarly journals SIMPLE MODELS OF THREE COUPLED PT -SYMMETRIC WAVE GUIDES ALLOWING FOR THIRD-ORDER EXCEPTIONAL POINTS

2017 ◽  
Vol 57 (6) ◽  
pp. 454 ◽  
Author(s):  
Jan Schnabel ◽  
Holger Cartarius ◽  
Jörg Main ◽  
Günter Wunner ◽  
Walter Dieter Heiss
Keyword(s):  
Matrix Model ◽  
Theoretical Models ◽  
Exceptional Point ◽  
Third Order ◽  
Exceptional Points ◽  
Symmetric Wave ◽  
Wave Guides ◽  
Delta Functions ◽  
Idealised Model ◽  
Parameter Ranges

We study theoretical models of three coupled wave guides with a <em>PT</em>-symmetric distribution of gain and loss. A realistic matrix model is developed in terms of a three-mode expansion. By comparing with a previously postulated matrix model it is shown how parameter ranges with good prospects of finding a third-order exceptional point (EP3) in an experimentally feasible arrangement of semiconductors can be determined. In addition it is demonstrated that continuous distributions of exceptional points, which render the discovery of the EP3 difficult, are not only a feature of extended wave guides but appear also in an idealised model of infinitely thin guides shaped by delta functions.

scholarly journals Exceptional Points and Asymmetric Mode Switching in Plasmonic Waveguides

2016 ◽  
Vol 34 (22) ◽  
pp. 5258-5262 ◽  
Author(s):  
Shaolin Ke ◽  
Bing Wang ◽  
Chengzhi Qin ◽  
Hua Long ◽  
Kai Wang ◽  
...  
Keyword(s):  
Mode Switching ◽  
Plasmonic Waveguides ◽  
Asymmetric Mode ◽  
Exceptional Points
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