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Updated: Jun 6, 2026
11:03
An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Nonlinear semiclassical dynamics of open systems.
A M Ozorio de Almeida1, O Brodier
1Centro Brasileiro de Pesquisas Fisicas, Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil. ozorio@cbpf.br
Summary
This study reviews a semiclassical approximation for quantum systems, simplifying complex dynamics using the chord function. It presents generalized asymptotic equilibrium solutions, offering new insights into quantum system evolution.
Area of Science:
- Quantum Mechanics
- Statistical Physics
- Theoretical Chemistry
Background:
- The evolution of quantum systems is often described by master equations, which can become complex for open systems.
- Semiclassical approximations offer a way to simplify these descriptions by bridging quantum and classical mechanics.
Purpose of the Study:
- To review and extend a semiclassical approximation for density operator evolution in open quantum systems.
- To introduce a novel approach using the chord function and double phase space for analyzing quantum dynamics.
Main Methods:
- The study reviews a semiclassical approximation based on the chord function, the Fourier transform of the Wigner function.
- It employs a classical double Hamiltonian to interpret semiclassical formulae in a real double phase space.
- The theory is extended to include dissipative Markovian evolution via non-Hermitian Lindblad operators.
Main Results:
- The semiclassical approximation provides an exact solution to the Lindblad master equation for specific quadratic Hamiltonians and linear Lindblad operators.
- Decoherence effects are analyzed, showing how they narrow the relevant phase space region.
- A propagator is defined in both Wigner and chord function representations to overcome difficulties associated with decoherence.
Conclusions:
- Generalized asymptotic equilibrium solutions for open quantum systems are presented for the first time.
- The developed semiclassical approach offers a powerful tool for studying quantum dynamics in the presence of dissipation and decoherence.
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