Quantum backflow current in a ring: Optimal bounds and fractality
arXiv:2403.18586 · doi:10.1103/PhysRevA.110.022216
Abstract
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.
11 pages, 3 figures
References in corpus (29)
- A measurement-based approach to quantum arrival times
- Quantum arrival time measurement and backflow effect
- A new approach to quantum backflow
- Analytic Examples, Measurement Models and Classical Limit of Quantum Backflow
- Detecting quantum backflow by the density of a Bose-Einstein Condensate
- Demonstrating backflow in classical two beams' interference
- An Introduction to the Quantum Backflow Effect
- Azimuthal backflow in light carrying orbital angular momentum
- Quantum Backflow States from Eigenstates of the Regularized Current Operator
- Decay of a quasi-stable quantum system and quantum backflow
- Quantum backflow in a ring
- Quantum backflow and scattering
- Equivalence between quantum backflow and classically forbidden probability flow in a diffraction-in-time problem
- Relativistic Quantum Backflow
- A quasi-probability for the arrival time problem with links to backflow and the Leggett-Garg inequalities
- Probability backflow for correlated quantum states
- Interference of spin-orbit coupled Bose-Einstein condensates
- Quantum backflow effect and nonclassicality
- Angular momentum quantum backflow in the noncommutative plane
- Experiment-friendly formulation of quantum backflow
- On the experiment-friendly formulation of quantum backflow
- Dissipative quantum backflow
- Unbounded quantum backflow in two dimensions
- Quantum backflow for many-particle systems
- Quantum backflow in solutions to the Dirac equation of the spin- free particle
- Comment on "Backflow in relativistic wave equations"
- Different routes to the classical limit of backflow
- Quantum backflow for dissipative two-identical-particle systems
- Simulating quantum backflow on a quantum computer