Beugung einer ebenen Welle an einem Spalt von endlicher Breite

Strutt, M. J. O.

doi:10.1007/bf01390776

“…6A) is qualitatively similar to the one obtained for a purely real cosine modulation (Fig. 6D), which is known as a Strutt diagram [39]. Both exhibit the essential features of parametric resonance, namely domains of stability (blue) and instability (yellow) that interpenetrate through several very thin "tongues" of instability (resp.…”

Section: Non-hermitian Parametric Resonancesupporting

confidence: 78%

“…For periodic modulations, Eq.22 is the Hill equation [37], which has no general closed-form solutions. A particularly important sub-case is Mathieu's equation [38], which corresponds to a purely real cosine modulation, giving rise to the phenomenon of parametric resonance [39]. Since our motivation lies in EP encircling, we consider modulations that describe loops in the complex plane instead, with segments for which Eq.22 has analytical solutions.…”

Section: Floquet Non-hermitian Hamiltoniansmentioning

confidence: 99%

Non-hermitian time evolution: from static to parametric instability

Bossart,

Fleury

2021

Preprint

0

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Eigenmode coalescence imparts remarkable properties to non-hermitian time evolution, culminating in a purely non-hermitian spectral degeneracy known as an exceptional point (EP). Here, we revisit time evolution at the EP and classify two-level non-hermitian Hamiltonians in terms of the Möbius group. We then leverage that classification to study dynamical EP encircling, by applying it to periodically-modulated (Floquet) Hamiltonians. This reveals that Floquet non-hermitian systems exhibit rich physics whose complexity is not captured by an EP-encircling rule. For example, Floquet EPs can occur without encircling and vice-versa. Instead, we show that the elaborate interplay between non-hermitian and modulation instabilities is better understood through the lens of parametric resonance.

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“…. There have been several studies for the derivation of the Green function for the single slit [27][28][29]. The technical details of its evaluation are beyond the scope of this paper and are to be published elsewhere.…”

Section: Green Function Of the Single Slitmentioning

confidence: 99%

“…Then the conditions are fixed for that ansatz to actually solve equation (8) with the required boundary conditions. Our derivation follows closely the steps described in [29].…”

Section: Appendix a Derivation And Evaluation Of The Green Function mentioning

confidence: 99%

Scattering theory of walking droplets in the presence of obstacles

Dubertrand

¹

,

Hubert

²

,

Schlagheck

³

et al. 2016

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We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al (2006 Phys. Rev. Lett. 97 154101) there have been many attempts to accurately reproduce the experimental results.We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics.

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“…Then the conditions are fixed for that ansatz to actually solve equation (8) with the required boundary conditions. Our derivation follows closely the steps described in [29].…”

Section: Appendix a Derivation And Evaluation Of The Green Function mentioning

confidence: 99%

Scattering theory of walking droplets in the presence of obstacles

Dubertrand

¹

,

Hubert

²

,

Schlagheck

³

et al. 2016

Proceedings of the 6th International Conference on Nonlinear Science and Complexity

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We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a pilot wave for the droplet. This leads to so called walking droplets or walkers. Since the seminal experiment by Couder et al (2006 Phys. Rev. Lett. 97 154101) there have been many attempts to accurately reproduce the experimental results.We propose to describe the trajectories of a walker using a Green function approach. The Green function is related to the Helmholtz equation with Neumann boundary conditions on the obstacle(s) and outgoing boundary conditions at infinity. For a single-slit geometry our model is exactly solvable and reproduces some general features observed experimentally. It stands for a promising candidate to account for the presence of arbitrary boundaries in the walker's dynamics.

show abstract

Beugung einer ebenen Welle an einem Spalt von endlicher Breite

Cited by 31 publications

References 14 publications

Non-hermitian time evolution: from static to parametric instability

Non-hermitian time evolution: from static to parametric instability

Scattering theory of walking droplets in the presence of obstacles

Scattering theory of walking droplets in the presence of obstacles

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