Theoretical Study of Particle-Surface Wave Interactions: A Hydrodynamic Analog of Quantum Mechanics

Idan Ceausu
Work towards MSc degree under the supervision of Asst Prof. Yuval Dagan (Technion)
Department of Aerospace Engineering
Technion – Israel Institute of Technology

In this talk, we will present a new hydrodynamic model demonstrating quantum mechanical features through a deterministic surface wave framework. First, a real variant of a one-dimensional Schrödinger equation is derived, notably similar to that of shallow-water surface waves in hydrodynamics. The wave equation is then coupled to an equation of motion of a particle generating the wave field and driven by field gradients. We place the particle in an infinite potential well and demonstrate self-excitation of particle motion due to asymmetric wave propagation. The particle exhibits inline oscillations comparable in size to cavity modes of the potential well. Finally, we show how the particle probability density function, and a discrete set of eigen-energies are equivalent to known solutions of quantum particles in an infinite potential well, exhibiting “particle in a box” statistics. Unlike the quantum mechanical system, this hydrodynamic model presents a mechanism for transition between the different stable eigenmodes where the desired statistics are obtained.

Future research will compare the theory of the present study to shallow water wave experiments to validate the similarity to the real Schrödinger equation and extract additional hydrodynamic parameters associated with our new theoretical model.

Furthermore, we may also exploit the same quantum mechanical features of the hydrodynamic system for macroscopic engineering applications such as clustering of droplets and particles in micro-fluidic devices, droplet and spray dynamics in turbulent flows, and controlling particle-wave dynamics in chaotic flows.

The talk will be given in English

Wed, 19-10-2022, 13:30-14:30 (Gathering at 13:30)

Classroom 165, ground floor, Library, Aerospace Eng. &

Light refreshments will be served before the lecture

Theoretical Study of Particle-Surface Wave Interactions: A Hydrodynamic Analog of Quantum Mechanics