Study the dynamics of the nonspreading Airy packets from the time evolution operator

TL;DR

This paper analyzes the nonspreading behavior of Airy wave packets under quantum evolution, showing they act like classical particles with acceleration, derived from the time evolution operator and Hamiltonian decomposition.

Contribution

It provides a novel derivation of Airy packet dynamics using the time evolution operator and Hamiltonian decomposition, linking quantum evolution to classical-like motion.

Findings

Airy packets evolve without distortion as shift operators

The Hamiltonian is decomposed into parts, revealing classical acceleration behavior

Airy packets behave like classical particles with specific acceleration

Abstract

Berry and Balazs showed that an initial Airy packet Ai(b x) under time evolution is nonspreading in free space and also in a homogeneous time-varying linear potential V(x,t)=-F(t) x. We find both results can be derived from the time evolution operator U(t). We show that U(t) can be decomposed into ordered product of operators and is essentially a shift operator in x; hence, Airy packets evolve without distortion. By writing the Hamiltonian H as H=H_b+H_i, where H_b is the Hamiltonian such that Ai(b x) is its eigenfunction. Then, H_i is shown to be as an interacting Hamiltonian that causes the Airy packet into an accelerated motion of which the acceleration a=(-H_i/( x))/m. Nonspreading Airy packet then acts as a classical particle of mass m, and the motion of it can be described classically by H_i.