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Connecting Scrambling and Work Statistics for Short-Range Interactions in the Harmonic Oscillator
M Mikkelsen1,2, T Fogarty1, Th Busch1
1Quantum Systems Unit, OIST Graduate University, Onna, Okinawa 904-0495, Japan.
Physical Review Letters
|March 4, 2022
Summary
Information scrambling in quantum systems requires interactions. Its long-time average directly correlates with work probability distribution variance, a measurable quantity in cold-atom experiments.
Area of Science:
- Quantum physics
- Statistical mechanics
- Condensed matter physics
Background:
- Information scrambling describes how quantum information spreads after a perturbation.
- Work statistics quantify energy changes in quantum systems undergoing a quench.
- Connecting these phenomena is crucial for understanding quantum dynamics.
Purpose of the Study:
- To investigate the relationship between information scrambling and work statistics.
- To explore this connection in a paradigmatic model of interacting particles in a 1D harmonic trap.
- To establish a link between theoretical concepts and experimental observables.
Main Methods:
- Numerical simulations of up to five short-range interacting particles in a 1D harmonic trap.
- Analysis of the long-time average of the squared commutator for canonical operators.
- Mathematical formulation of the N-body system dynamics.
Main Results:
- Information scrambling necessitates finite interactions.
- A direct proportionality was found between the squared commutator average and the work probability distribution variance.
- The mathematical structure of the N-body system explains this outcome.
Conclusions:
- A direct connection is established between quantum information scrambling and work fluctuations.
- Work fluctuations serve as an experimentally accessible probe for scrambling properties.
- Findings are relevant for modern cold-atom experiments and quantum information studies.
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