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A unitary perturbation theory approach to real-time evolution problems
1Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany.
Summary
We introduce a new analytical method for real-time quantum many-body system evolution. This approach accurately solves Heisenberg equations of motion for dissipative quantum systems, providing insights into non-equilibrium dynamics.
Area of Science:
- Quantum physics
- Many-body systems
- Quantum dynamics
Background:
- Real-time evolution of quantum systems is computationally challenging.
- Dissipative quantum systems require accurate methods for analyzing dynamics.
- Continuous unitary transformations offer a framework for quantum evolution.
Purpose of the Study:
- To present a novel analytical approach for real-time evolution in quantum many-body systems.
- To extend the continuous unitary transformations framework.
- To demonstrate the accuracy of the proposed method for dissipative systems.
Main Methods:
- Developing a novel solution method for Heisenberg equations of motion.
- Applying the method to study dissipative quantum systems across all timescales.
- Obtaining results for non-equilibrium correlation functions.
Main Results:
- The analytical approach accurately describes real-time evolution in dissipative quantum systems.
- Non-equilibrium correlation functions are derived for general initial conditions.
- The method is illustrated using the exactly solvable dissipative oscillator and the dissipative two-state system.
Conclusions:
- The proposed analytical approach offers a powerful tool for studying quantum many-body dynamics.
- This method provides accurate solutions for dissipative quantum systems.
- The framework is applicable to various quantum systems and initial conditions.
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