Multifractality of quantum wave packets
I. Garcia-Mata, J. Martin, O. Giraud, B. Georgeot
TL;DR
This paper investigates the multifractal properties of quantum wave packets in a tunable system, comparing measurement methods, and analyzing how multifractality evolves over time.
Contribution
It introduces a physical interpretation of the Ruijsenaars-Schneider model to study quantum wave packet spreading and identifies the most effective method to measure multifractality.
Findings
Multifractality decreases over time and reaches an asymptotic limit.
The asymptotic multifractality differs from that of eigenvectors but is related to it.
The rate of multifractality decrease is quantitatively characterized.
Abstract
We study a version of the mathematical Ruijsenaars-Schneider model, and reinterpret it physically in order to describe the spreading with time of quantum wave packets in a system where multifractality can be tuned by varying a parameter. We compare different methods to measure the multifractality of wave packets, and identify the best one. We find the multifractality to decrease with time until it reaches an asymptotic limit, different from the mulifractality of eigenvectors, but related to it, as is the rate of the decrease. Our results could guide the study of experimental situations where multifractality is present in quantum systems.
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