Wignerian symplectic covariance approach to the interaction-time problem.

Area of Science:

• Quantum mechanics
• Quantum information theory
• Phase-space quantum mechanics

Background:

• The Wigner distribution function exhibits symplectic covariance.
• Wigner-Rényi entropies are invariant under symplectic transformations.
• Estimating interaction times in quantum systems is crucial for understanding scattering processes.

Purpose of the Study:

• To leverage symplectic properties for estimating quantum state interaction times.
• To analyze scattering of a Schrödinger cat state with modified Gaussian potentials.
• To utilize Wigner-Rényi entropies as indicators for interaction duration.

Main Methods:

• Utilizing the phase-space representation of quantum theory.
• Analyzing the time evolution governed by the Moyal equation.
• Employing Wigner-Rényi entropies of order one and one-half as key observables.

Main Results:

• Demonstrated the use of Wigner-Rényi entropies to identify the start and end of quantum state-potential interactions.
• Investigated scattering in the above-barrier regime with modified Gaussian potentials (barrier-to-barrier and barrier-to-well).
• Showcased the effectiveness of the phase-space approach for dynamical scattering centers.

Conclusions:

• The proposed method provides a new framework for estimating interaction times of moving quantum states.
• Wigner-Rényi entropies serve as effective indicators for interaction periods with fast-decaying potentials.
• The approach is applicable to diverse physical systems, including atomic, molecular, and condensed matter physics.