Tommy Byrd

Scattering by an oscillating barrier: Quantum, classical, and semiclassical comparison

We present a detailed study of scattering by an amplitude-modulated potential barrier using three distinct physical frameworks: quantum, classical, and semiclassical. Classical physics gives bounds on the energy and momentum of the scattered particle, while also providing the foundation for semiclassical theory. We use the semiclassical approach to selectively add quantum-mechanical effects such as interference and diffraction. We find good agreement between the quantum and semiclassical momentum distributions. Our methods and results can be used to understand quantum and classical aspects of transport mechanisms involving time-varying potentials, such as quantum pumping.

Ballistic Atom Pumps

We examine a classically chaotic system consisting of two reservoirs of particles connected by a channel containing oscillating potential-energy barriers. We investigate whether such a system can preferentially pump particles from one reservoir to the other, a process often called “quantum pumping.” We show how to make a “particle diode” which under specified conditions permits net particle pumping in only one direction. Then we examine systems having symmetric barriers. We find that if all initial particle energies are considered, a system with symmetric barriers cannot preferentially pump particles. However, if only finite initial energy bands are considered, the system can create net particle transport in either direction. We study the system classically, semiclassically, and quantum mechanically, and find that the quantum description cannot be fully understood without the insight gained from classical and semiclassical analysis.