Aharonov–Bohm effect in a draining bathtub vortex

Dolan, Sam R.; Oliveira, Érika Arantes de; Crispino, Luís C. B.

doi:10.1016/j.physletb.2011.06.013

Cited by 47 publications

(69 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This pattern is shown on Fig. 1 for various frequencies, and looks very close to what was predicted on theoretical grounds for simple bathtub flow models 10,17 . We also observe that incident waves have more wavefronts on the upper half of the vortex in comparison with the lower half-see the various wave characteristics in Fig.…”

supporting

confidence: 86%

Rotational superradiant scattering in a vortex flow

et al. 2017

View full text Add to dashboard Cite

When an incident wave scatters o of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance [1][2][3][4] . We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole [5][6][7][8][9][10] , as well as to hydrodynamics, due to the close relation to over-reflection instabilities [11][12][13] . In water, perturbations of the free surface manifest themselves by a small change ξ(t, x) of the water height. On a flat bottom, and in the absence of flow, linear perturbations are well described by superpositions of plane waves of definite frequency f (Hz) and wavevector k (rad m −1 ). When surface waves propagate on a changing flow, the surface elevation is generally described by the sum of two contributions ξ = ξ I + ξ S , where ξ I is the incident wave produced by a source, for example, a wave generator, while ξ S is the scattered wave, generated by the interaction between the incident wave and the background flow. In this work, we are interested on the properties of this scattering on a draining vortex flow which is assumed to be axisymmetric and stationary. At the free surface, the velocity field is given in cylindrical coordinates by v = v r e r + v θ e θ + v z e z .Due to the symmetry, it is appropriate to describe ξ I and ξ S using polar coordinates (r, θ). Any wave ξ(t, r, θ ) can be decomposed into partial waves 10,14 ,where m ∈ Z is the azimuthal wavenumber and ϕ f ,m (r) denotes the radial part of the wave. Each component of this decomposition has a fixed angular momentum proportional to m, instead of a fixed wavevector k. (To simplify notation, we drop the indices f ,m in the following.) Since the background is stationary and axisymmetric, waves with different f and m propagate independently. Far from the centre of the vortex, the flow is very slow, and the radial part ϕ(r) becomes a sum of oscillatory solutions,where k = ||k|| 2 is the wavevector norm. This describes the superposition of an inward wave of (complex) amplitude A in propagating towards the vortex, and an outward wave propagating away from it with amplitude A out . These coefficients are not independent. The A in values, one for each f and m component, are fixed by the incident part ξ I . If the incident wave is a plane wave ξ = ξ 0 e −2iπft+ik·x , then the partial amplitudes are given by A in = ξ 0 e imπ+iπ/4 / √ 2πk. In other words, a plane wave is a superposition containing all azimuthal waves, something that we have exploited...

show abstract

supporting

confidence: 86%

Rotational superradiant scattering in a vortex flow

et al. 2017

View full text Add to dashboard Cite

show abstract

“…An interesting system was investigated in [64], where it was shown that planar waves scattered by a draining bathtub vortex develops a modified AB effect that has a dependence on two dimensionless parameters, related to the circulation and draining rates [65]. It has been found an inherent asymmetry even in the low-frequency regime which leads to novel interference patterns.…”

Section: Introductionmentioning

confidence: 99%

“…It has been found an inherent asymmetry even in the low-frequency regime which leads to novel interference patterns. More recently in [66][67][68], the analysis made in [64] was extended to a Lorentz-violating and noncommutative background [69][70][71][72][73][74][75], which allows the system to have persistence of phase shifts even if circulation and draining vanish.…”

Section: Introductionmentioning

confidence: 99%

Aharonov–Bohm effect for a fermion field in a planar black hole “spacetime”

et al. 2017

View full text Add to dashboard Cite

In this paper we consider the dynamics of a massive spinor field in the background of the acoustic black hole spacetime. Although this effective metric is acoustic and describes the propagation of sound waves, it can be considered as a toy model for the gravitational black hole. In this manner, we study the properties of the dynamics of the fermion field in this "gravitational" rotating black hole as well as the vortex background. We compute the differential cross section through the use of the partial wave approach and show that an effect similar to the gravitational AharonovBohm effect occurs for the massive fermion field moving in this effective metric. We discuss the limiting cases and compare the results with the massless scalar field case.

show abstract

“…Recently, it was shown in [20] that the scattering of planar waves by a draining bathtub vortex describes a modified AB effect which depends on two dimensionless parameters associated with the circulation and draining rates [21]. The effect was shown to be inherently asymmetric even in the low-frequency limit and leads to novel interference patterns.…”

Section: Introductionmentioning

confidence: 99%

“…In addition, we consider the acoustic black hole metrics obtained from a relativistic fluid in a noncommutative spacetime [29] via the Seiberg-Witten map and also obtained from the Lorentz-violating Abelian Higgs model [30]. More recently in [25], we have extended the analysis made in [20] to a Lorentz-violating and noncommutative background [22] which allows to have persistence of phase shifts even if circulation and draining vanish.…”

Section: Introductionmentioning

confidence: 99%