穿隧時間

Abstract

近年來，由法國物理學家 Couder 與合作者們開啓了行走油滴 (walking droplet)的一系列研究。實驗上，他們發現在瀕臨產生法拉第波的頻率與振幅下，於矽油液面挑起的液滴可以因為共振，存活且以大致固定的速度行走。由於油滴在接觸液面時，會激起局部的（法拉第波 Faraday wave）漣漪，這個粒子與波緊密結合的個體，作爲一個複雜但卻完全古典的系統，許多現象（例如狹縫干涉與繞射、穿隧機率等）和量子系統極其相似。在這份論文中，我們將專注在油滴的穿隧時間（tunnelling time)，除了探討 (1) 它如何隨（減低矽油深度，以致無法產生可以回饋給油滴能量的漣漪的）壓克力（相當於位能壁壘）寬度改變外，並紀錄 (2) 在同樣壁壘寬度下，穿隧時間的分佈，最終且分別藉由建構「水漂 (skipping stone)」模型與多重散射 (multiple scattering) 理論成功解釋兩者的行為。由於這兩個性質恰巧都是哥本哈根學派對於量子力學的詮釋無法置啄的，我們接下來推論：如果這些結論（如 Couder et al. 和其他科學家所宣稱）可以推廣到量子系統，根據過往被忽視的波姆力學 (Bohmmechanics)，大膽提出需要引入什麼修正與新的觀念，才能解釋我們利用數值模擬從波姆力學得到的和實驗一致的結論。

In recent years, French physicist Couder and his collaborators have initiated a series of studies on walking droplets. Experimentally, they found that at frequencies and amplitudes close to the onset of Faraday waves, droplets on the surface of silicone oil can survive and walk at a roughly constant speed due to resonance. Droplets excite local ripples from the Faraday instability when they contact the liquid surface. This tightly coupled particle-wave entity, although a complex yet entirely classical system, exhibits many phenomena, such as slit interference and diffraction, and tunneling probability, that are strikingly similar to those of quantum systems.

In this thesis, we focus on the tunneling time of droplets. Specifically, we will explore (1) how it changes with the width of an acrylic barrier, which gives rise to the potential barrier when the depth of the silicone oil is reduced to prevent the generation of ripples that can feed energy back to the droplet, and (2) the distribution of tunneling times at the same barrier width. Ultimately, we successfully explain both behaviors by constructing a“skipping stone” model and a multiple scattering theory. Since these two characteristics are precisely the aspects that the Copenhagen interpretation of quantum mechanics cannot adequately address, we then infer: Provided that the behavior of walking droplets bears resemblance to that of quantum systems, as claimed by Couder et al. and other scientists, we boldly propose what modifications and new concepts need, based on the previously overlooked Bohmian mechanics, to explain the conclusions consistent with experiments obtained from our numerical simulations using Bohmian mechanics.