Anomalous Spreading of Power-Law Quantum Wave Packets

TL;DR

This paper introduces power-law tail quantum wave packets, analyzes their evolution, and reveals anomalous decay behavior and conserved moments, expanding understanding of quantum dynamics with non-standard initial states.

Contribution

It presents a new class of quantum wave packets with power-law tails, analyzes their free evolution, and uncovers unique decay and conservation properties.

Findings

Asymptotic decay of wave packet maxima is anomalous for certain power-law exponents.

Number of finite moments remains conserved during free evolution.

Power-law tail wave packets can be eigenfunctions of a physical Hamiltonian.

Abstract

We introduce power-law tail quantum wave packets. We show that they can be seen as eigenfunctions of a Hamiltonian with a physical potential. We prove that the free evolution of these packets presents an asymptotic decay of the maximum of the wave packets which is anomalous for an interval of the characterizing power-law exponent. We also prove that the number of finite moments of the wave packets is a conserved quantity during the evolution of the wave packet in the free space.