Bound Eigenstate dynamics under a sudden shift of the well's wall

TL;DR

This paper studies how eigenstates in an infinite well evolve after an abrupt wall shift, revealing a transition in short-time behavior and a universal fractal structure in the dynamics.

Contribution

It introduces a detailed analysis of eigenstate dynamics under sudden boundary shifts, highlighting a change in short-time behavior and the emergence of a universal fractal pattern.

Findings

Short-time behavior shifts from t^(3/2) to t^(1/2) for small shifts.

The dynamical evolution converges to a universal fractal function.

The fractal structure has a dimensionality of D=1.25.

Abstract

We investigate the dynamics of the eigenstate of an infinite well under an abrupt shift of the well's wall. It is shown that when the shift is small compared to the initial well's dimensions, the short time behavior changes from the well known t^(3/2) behavior to t^(1/2) . It is also shown that the complete dynamical picture converges to a universal function, which has fractal structure with dimensionality D=1.25.