arXiv subjects

Tzay-Ming Hong

Publications and source records attributed to Tzay-Ming Hong.

38 records · Page 3Linked to original sources

arXiv2003

Semiclassical Quantization Rule for Bound-State Spectrum in Quantum Dots: Scattering Phase Approximation

We study the quantum propagator in the semiclassical limit with sharp confining potentials. Including the energy-dependent scattering phase due to sharp confining potential, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.

cond-mat↗

arXiv2001

Berry Phases of Classical Trajectories in the Presence of Hard-Wall Boundaries

We study the quantum propagator in the semiclassical limit with hard-wall potentials. We show that, upon each reflection by the hard wall, a Berry phase $π$ is accumulated and leads to interferences between different classical trajectories. Including the Berry phase caused by the hard walls, the modified Van Vleck's formula is derived. We also discuss the close relations among quantum statistics, discrete gauge symmetry, and hard-wall constraints. Most of all, we formulate a new quantization rule that applies to {\it both} smooth and sharp boundary potentials. It provides an easy way to compute quantized energies in the semiclassical limit and is extremely useful for many physical systems.

cond-mat↗