<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="script">P</mml:mi><mml:mi mathvariant="script">T</mml:mi></mml:mrow></mml:math>-Symmetric Acoustics

Zhu, Xuefeng; Ramezani, Hamidreza; Shi, Chengzhi; Zhu, Jie; Zhang, Xiang

doi:10.1103/physrevx.4.031042

Cited by 461 publications

(341 citation statements)

References 55 publications

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“…If the material possesses the property of ε(x) = ε * (−x), the system is PT -symmetric because the system restores itself after simultaneous parity and time-reversal operations. Such systems have been extensively studied recently and a great variety of interesting phenomena have been discovered, including unusual beam dynamics within paraxial approximations [4][5][6], lasing effect [7][8][9], unidirectional transmission [10][11][12], negative refraction [13], single-particle sensors [14], and others [15][16][17][18][19][20]. Since it is not easy to achieve PT symmetry experimentally, several ways have been proposed to avoid the use of gain in a system.…”

Section: Introductionmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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Non-Hermitian systems with parity-time-(PT )-symmetric complex potentials can exhibit a phase transition when the degree of non-Hermiticity is increased. Two eigenstates coalesce at a transition point, which is known as the exceptional point (EP) for a discrete spectrum and spectral singularity for a continuous spectrum. The existence of an EP is known to give rise to a great variety of novel behaviors in various fields of physics. In this work, we study the complex band structures of one-dimensional photonic crystals with PT -symmetric complex potentials by setting up a Hamiltonian using the Bloch states of the photonic crystal without loss or gain as a basis. As a function of the degree of non-Hermiticity, two types of PT symmetry transitions are found. One is that a PT -broken phase can reenter into a PT -exact phase at a higher degree of non-Hermiticity. The other is that two EPs, one originating from the Brillouin zone center and the other from the Brillouin zone boundary, can coalesce at some k point in the interior of the Brillouin zone and create a singularity of higher order. Furthermore, we can induce a band inversion by tuning the filling ratio of the photonic crystal, and we find that the geometric phases of the bands before and after the inversion are independent of the amount of non-Hermiticity as long as the PT -exact phase is not broken. The standard concept of topological transition can hence be extended to non-Hermitian systems.

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Section: Introductionmentioning

confidence: 99%

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

2015

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“…where u is the velocity vector, p is the pressure, Re is the Reynolds number, and f is the Eulerian body-force that is used to mimic the effects of the immersed body on the flow [27,28,29]. The direct numerical simulations provide an exact description of the flow-body interaction.…”

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confidence: 99%

Mass and Moment of Inertia Govern the Transition in the Dynamics and Wakes of Freely Rising and Falling Cylinders

et al. 2017

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In this Letter, we study the motion and wake-patterns of freely rising and falling cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid m * ≡ ρp/ρ f and its relative moment-of-inertia I * ≡ Ip/I f . This supersedes the current understanding that a critical mass density (m * ≈ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144 combinations of m * and I * , we comprehensively map out the parameter space covering very heavy (m * > 10) to very buoyant (m * < 0.1) particles. The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, Stt ≈ 0.17. Stt separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical 2S (2-Single) vortex mode to a 2P (2-Pairs) vortex mode. Thus, auto-rotation can have a significant influence on the trajectories and wakes of freely rising isotropic bodies.Path-instabilities are a common observation in the dynamics of buoyant and heavy particles. Common examples are the fluttering of falling leaves and disks, and the cork-screw and spiral trajectories of air-bubbles rising in water [1,2,3]. The oscillatory dynamics of such particles can vary a lot depending on the particle's size, shape and its inertia, and the surrounding flow properties. This can be important in a variety of fields ranging from sediment transport and fluidization to multiphase particleand bubble-column reactors [4,5,6].Examples of organisms that exploit path-instabilities are plants and aquatic animals. These often make use of passive appendages attached to their bodies (plumed seeds, barbs, tails, and protrusions) to generate locomotion [7,8,9]. Recently, Lācis et al. [7] demonstrated that the interaction between the wake of a falling bluff body and a protrusion clamped to its rear end can generate a sidewards drift by means of a symmetry-breaking instability similar to that of an inverted pendulum. Such kinds of passive interactions are advantageous to locomotion, since no energy needs to be spent by the animal. Instead, the energy can be extracted through fluid-structure interaction.

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“…For simplicity, this particular phenomenon can be understood from Eq. (13). Since the CPA requires that at the momentum k 0 there is…”

Section: Cpa-lasermentioning

confidence: 99%

“…This leads to interesting phenomena in many fields, such as in quantum field theories and mathematical physics [2], open quantum systems [3], Anderson models for disorder systems [4][5][6]. The non-Hermitian systems have been experimentally realized in optical materials [7], waveguide arrays [8,9], microresonators [10,11], acoustic sensor [12,13] and LRC circuits [14].…”

Section: Introductionmentioning

confidence: 99%

PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

2016

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We study the PT -symmetry breaking for the scattering problem in a one-dimensional (1D) nonHermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact PT -symmetry phase to the phase with spontaneously breaking PT -symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the PT -symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian PT -symmetric potentials.

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PT-Symmetric Acoustics

Cited by 461 publications

References 55 publications

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

Coalescence of exceptional points and phase diagrams for one-dimensionalPT-symmetric photonic crystals

Mass and Moment of Inertia Govern the Transition in the Dynamics and Wakes of Freely Rising and Falling Cylinders

PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

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