- Access by Xinjiang University
Tunneling with a hydrodynamic pilot-wave model
Phys. Rev. Fluids 2, 034801 – Published 30 March, 2017
DOI: https://doi.org/10.1103/PhysRevFluids.2.034801
Abstract
Eddi et al. [Phys. Rev Lett. 102, 240401 (2009)] presented experimental results demonstrating the unpredictable tunneling of a classical wave-particle association as may arise when a droplet walking across the surface of a vibrating fluid bath approaches a submerged barrier. We here present a theoretical model that captures the influence of bottom topography on this wave-particle association and so enables us to investigate its interaction with barriers. The coupled wave-droplet dynamics results in unpredictable tunneling events. As reported in the experiments by Eddi et al. and as is the case in quantum tunneling [Gamow, Nature (London) 122, 805 (1928)], the predicted tunneling probability decreases exponentially with increasing barrier width. In the parameter regimes examined, tunneling between two cavities suggests an underlying stationary ergodic process for the droplet's position.
Physics Subject Headings (PhySH)
Article Text
References (19)
- A. Eddi, E. Fort, F. Moisy, and Y. Couder, Unpredictable Tunneling of a Classical Wave-Particle Association, Phys. Rev Lett. 102, 240401 (2009).
- G. Gamow, The quantum theory of nuclear desintegration, Nature (London) 122, 805 (1928).
- G. Pucci, P. Sáenz, L. M. Faria, and J. W. M. Bush, Non-specular reflection of walking droplets, J. Fluid Mech. 804, R3 (2016).
- L. M. Faria, A model for Faraday pilot waves over variable topography, J. Fluid Mech. 811, 51 (2017).
- D. M. Harris, J. Moukhtar, E. Fort, Y. Couder, and J. W. M. Bush, Wavelike statistics from pilot-wave dynamics in a circular corral, Phys. Rev. E 88, 011001 (2013).
- B. Benjamin and F. Ursell, The stability of the plane free surface of a liquid in a vertical periodic motion, Proc. Royal Soc. 225, 505 (1954).
- J. Walker, Drops of liquid can be made to float on the liquid: What enables them to do so? Sci. Am. 238, 151 (1978).
- Y. Couder, S. Protière, E. Fort, and A. Boudaoud, Walking and orbiting droplets, Nature (London) 437, 208 (2005).
- J. W. M. Bush, Pilot-wave hydrodynamics, Ann. Rev. Fluid Mech. 47, 269 (2015).
- P. A. Milewski, C. A. Galeano-Rios, A. Nachbin, and J. W. M. Bush, Faraday pilot-wave dynamics: modelling and computation, J. Fluid Mech. 778, 361 (2015).
- A. Eddi, E. Sultan, J. Moukhtar, E. Fort, M. Rossi, and Y. Couder, Information stored in Faraday waves: The origin of a path memory, J. Fluid Mech. 674, 433 (2011).
- J. Molacek and J. W. M. Bush, Drops walking on a vibrating bath: Towards a hydrodynamic pilot-wave theory, J. Fluid Mech. 727, 612 (2013).
- T. A. Driscoll and L. N. Trefethen, Schwarz-Christoffel Mapping (Cambridge University Press, Cambridge, UK, 2002).
- A. Nachbin, A terrain-following Boussinesq system, SIAM J. Appl. Math. 63, 905 (2003).
- W. Artiles and A. Nachbin, Nonlinear Evolution of Surface Gravity Waves Over Highly Variable Depth, Phys. Rev. Lett. 93, 234501 (2004).
- A. Fokas and A. Nachbin, Water waves over a variable bottom: A non-local formulation and conformal mappings, J. Fluid Mech. 695, 288 (2012).
- F. Grossmann, T. Dittrich, P. Jung, and P. Hanggi, Coherent Destruction of Tunneling, Phys. Rev. Lett. 67, 516 (1991).
- S. Perrard, M. Labousse, M. Miskin, E. Fort, and Y. Couder, Self-organization into quantized eigenstates of a classical wave-driven particle, Nat. Commun. 5, 3219 (2014).
- D. M. Harris and J. W. M. Bush, Droplets walking in a rotating frame: From quantized orbits to multimodal statistics, J. Fluid Mech. 739, 444 (2014).