I present some rather selective reminiscences of my long career in physics, from my doctoral work to the present. I do not spend time on topics such as the nuclear magnetic resonance behavior of 3He, as I have reviewed the history extensively elsewhere, but rather concentrate, first, on my long-running project to make condensed matter physics relevant to questions in the foundations of quantum mechanics, and second, on various rather “quirky” problems such as an attempt to amplify the effects of the parity violation due to the weak interaction to a macroscopic level, and an unconventional proposal for the mechanism of the first-order phase transition between the A and B phases of superfluid liquid 3He.
A quantum walk is a mathematical model and a quantum version of a random walk. For the past two decades, it has been studied from mathematical and physical viewpoints. It has many desirable properties. This paper reevaluates quantum walk from a quantum mechanical perspective, as Feynman essentially proposed it as a toy model in his path integral method. Then we demonstrate that the quantum walk model exhibits both particle-like and wave-like properties by showing reflection and partial reflection as a particle and interference as a wave. In particular, for an initial state supported at two sites
±ℓ, we explicitly derive the weak limit distribution of the Hadamard walk and show that the Konno distribution is modulated by the interference factor
2cos2(ℓk(x)). The resulting interference profile is reminiscent of far-field (Fraunhofer-type) diffraction.