研究目的
To extend the semiclassical description of quantum entanglement dynamics by including complex trajectories, thereby improving the accuracy of the approximation for longer time values.
研究成果
The inclusion of complex trajectories in the semiclassical approximation significantly improves the accuracy of the description of quantum entanglement dynamics, extending its validity to longer time values. This approach successfully reproduces the quantum behavior of entanglement, including its oscillatory dynamics, for a specific Hamiltonian system.
研究不足
The approach is limited to systems where the initial state is a product of coherent states and governed by a generic Hamiltonian. The accuracy of the semiclassical approximation may vary depending on the system's complexity and the time scale considered.
1：Experimental Design and Method Selection:
The study employs a semiclassical approach to quantum entanglement dynamics, focusing on the linear entropy of the reduced state as an entanglement quantifier. The methodology involves the use of complex classical trajectories to approximate the quantum propagators in the coherent-state representation.
2：Sample Selection and Data Sources:
The system under study is a pure bipartite state initially prepared in a product of coherent states, governed by a generic Hamiltonian. The initial state is a coherent state associated with harmonic oscillator systems.
3：List of Experimental Equipment and Materials:
The study is theoretical and does not involve physical experimental equipment. The 'materials' are mathematical models and computational tools for solving the equations of motion for complex trajectories.
4：Experimental Procedures and Operational Workflow:
The procedure involves deriving a semiclassical formula for the linear entropy by solving the integral representation of the reduced linear entropy through the steepest descent method, including complex trajectories in the calculation.
5：Data Analysis Methods:
The analysis involves comparing the semiclassical results with exact quantum calculations to assess the accuracy of the approximation, particularly focusing on the reproduction of quantum entanglement dynamics over time.
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