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We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the quantum-classical correspondence holds for very few bosons. In some parameter regions, the ground state is robust (highly sensitive) to changes in the interaction strength (tilt amplitude), which may be of use for quantum information protocols (quantum sensing).
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Particle Trajectories for Quantum Maps
Abstract We study the trajectories of a semiclassical quantum particle under repeated indirect measurement by Kraus operators, in the setting of the quantized torus. In between measurements, the system evolves via either Hamiltonian propagators or metaplectic operators. We show in both cases the convergence in total variation of the quantum trajectory to its corresponding classical trajectory, as defined by the propagation of a semiclassical defect measure. This convergence holds up to the Ehrenfest time of the classical system, which is larger when the system is “less chaotic.” In addition, we present numerical simulations of these effects. In proving this result, we provide a characterization of a type of semi-classical defect measure we call uniform defect measures. We also prove derivative estimates of a function composed with a flow on the torus.
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- Award ID(s):
- 1952939
- PAR ID:
- 10476003
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Annales Henri Poincaré
- Volume:
- 25
- Issue:
- 8
- ISSN:
- 1424-0637
- Format(s):
- Medium: X Size: p. 3699-3738
- Size(s):
- p. 3699-3738
- Sponsoring Org:
- National Science Foundation
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