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Main Authors: Goussev, Arseni, Quinque, Felix, Joo, Jaewoo, Burbanks, Andrew
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2403.18586
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author Goussev, Arseni
Quinque, Felix
Joo, Jaewoo
Burbanks, Andrew
author_facet Goussev, Arseni
Quinque, Felix
Joo, Jaewoo
Burbanks, Andrew
contents The probability density of a quantum particle moving freely within a circular ring can exhibit local flow patterns inconsistent with its angular momentum, a phenomenon known as quantum backflow. In this study, we examine a quantum particle confined to a ring and prepared in a state composed of a fixed (yet arbitrary) number of lowest energy eigenstates with non-negative angular momentum. We investigate the time-dependent behavior of the probability current at a specified point along the ring's circumference. We establish precise lower and upper bounds for this probability current, thereby delineating the exact scope of the quantum backflow effect. We also present an analytical expression for a quantum state that yields a record-high backflow probability transfer, reaching over 95% of the theoretical bound. Furthermore, our investigation yields compelling numerical and analytical evidence supporting the conjecture that the current-versus-time function associated with states maximizing backflow probability transfer forms a fractal curve with a dimension of 7/4. The observed fractality may provide a characteristic, experimentally-relevant signature of quantum backflow near the probability-transfer bound.
format Preprint
id arxiv_https___arxiv_org_abs_2403_18586
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Quantum backflow current in a ring: Optimal bounds and fractality
Goussev, Arseni
Quinque, Felix
Joo, Jaewoo
Burbanks, Andrew
Quantum Physics
The probability density of a quantum particle moving freely within a circular ring can exhibit local flow patterns inconsistent with its angular momentum, a phenomenon known as quantum backflow. In this study, we examine a quantum particle confined to a ring and prepared in a state composed of a fixed (yet arbitrary) number of lowest energy eigenstates with non-negative angular momentum. We investigate the time-dependent behavior of the probability current at a specified point along the ring's circumference. We establish precise lower and upper bounds for this probability current, thereby delineating the exact scope of the quantum backflow effect. We also present an analytical expression for a quantum state that yields a record-high backflow probability transfer, reaching over 95% of the theoretical bound. Furthermore, our investigation yields compelling numerical and analytical evidence supporting the conjecture that the current-versus-time function associated with states maximizing backflow probability transfer forms a fractal curve with a dimension of 7/4. The observed fractality may provide a characteristic, experimentally-relevant signature of quantum backflow near the probability-transfer bound.
title Quantum backflow current in a ring: Optimal bounds and fractality
topic Quantum Physics
url https://arxiv.org/abs/2403.18586