Dephasing representation: Employing the shadowing theorem to calculate quantum correlation functions.

Area of Science:

• Quantum mechanics
• Statistical physics
• Chaos theory

Background:

• Classical and quantum systems can correspond due to the Heisenberg uncertainty principle.
• Existing semiclassical methods often rely on approximations like the Van Vleck determinant.
• Calculating quantum correlation functions in complex systems is computationally challenging.

Purpose of the Study:

• To develop a unique semiclassical representation for quantum systems.
• To provide a rigorous method for calculating quantum correlation functions.
• To extend the applicability of semiclassical linear-response theory to generic mixed systems.

Main Methods:

• Introduced a 'dephasing representation' based on the Feynman path integral formulation.
• Utilized the correspondence between classical systems and quantum systems.
• Related the approach to the shadowing theorem for rigorous approximation.

Main Results:

• Developed a unique semiclassical representation without the Van Vleck determinant.
• Demonstrated that all contributing trajectories in the dephasing representation have the same amplitude.
• Showed that numerical implementation requires only actions along unperturbed trajectories.

Conclusions:

• The dephasing representation is rigorously applicable to systems where the shadowing theorem holds.
• This method is valid for generic, mixed quantum systems, extending previous theories.
• It offers a practical computational tool for quantum correlation functions in high-dimensional, nonuniversal regimes.