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Partial-trace-free time-convolutionless equation of motion for the reduced density matrix.
Irena Knezevic1, David K Ferry
1Department of Electrical Engineering and Center for Solid State Electronics Research, Arizona State University, P.O. Box 876206, Tempe, Arizona 85287-6206, USA. irenak@asu.edu
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 21, 2002
Summary
This study introduces a new time convolutionless equation for reduced system density matrices, simplifying calculations for driven quantum systems. The method offers computational advantages and reveals constraints on time-irreversible approximations in quantum dynamics.
Area of Science:
- Quantum mechanics
- Statistical physics
- Computational physics
Background:
- Understanding the evolution of quantum systems coupled to their environment is a long-standing challenge.
- External driving fields introduce complexity to system dynamics.
- Existing methods often involve computationally intensive partial traces over environmental states.
Purpose of the Study:
- To derive a novel time convolutionless equation for the reduced system density matrix.
- To develop a method that avoids partial traces over environmental states.
- To explore the applicability of the new approach to driven and far-from-equilibrium systems.
Main Methods:
- Extension of the projection-operator technique.
- Incorporation of an isomorphism between system Liouville space and the unit eigenspace of a projection operator.
- Derivation of a partial-trace-free, time convolutionless equation of motion.
Main Results:
- A new equation of motion for the reduced system density matrix is derived, which is time convolutionless and free of partial trace.
- The numerical application is efficient for large, externally driven systems due to smaller submatrices.
- All time convolutionless approaches, including this new one, rely on an assumption of time reversibility.
Conclusions:
- The developed approach offers significant computational advantages for studying complex quantum systems.
- The assumption of time reversibility imposes limitations on the applicability of time convolutionless methods with time-irreversible approximations.
- The approach is suitable for describing far-from-equilibrium quantum systems.