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The Schrödinger equation with friction from the quantum trajectory perspective
Sophya Garashchuk1, Vaibhav Dixit, Bing Gu
1Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, USA.
The Journal of Chemical Physics
|February 15, 2013
Summary
This study introduces a quantum friction term into the Schrödinger equation, enabling irreversible energy loss and system evolution towards the ground state, applicable to reaction dynamics.
Area of Science:
- Quantum mechanics
- Chemical physics
- Theoretical chemistry
Background:
- The standard time-dependent Schrödinger equation describes reversible quantum dynamics.
- Modeling irreversible energy transfer in quantum systems remains a challenge.
Purpose of the Study:
- To incorporate a friction term into the time-dependent Schrödinger equation.
- To model irreversible energy loss in quantum systems.
- To investigate quantum trajectory dynamics and system evolution.
Main Methods:
- Utilizing the similarity between classical and quantum trajectory equations of motion.
- Introducing a wavefunction phase-dependent friction term.
- Analyzing the nonlinear Schrödinger equation and its properties.
Main Results:
- The modified Schrödinger equation is nonlinear but conserves wavefunction normalization.
- An arbitrary wavefunction evolves towards the system's ground state.
- Energy decrease is proportional to the average kinetic energy of quantum trajectories.
- The high friction regime models reactions with system-to-environment energy transfer.
Conclusions:
- The introduced quantum friction provides a mechanism for irreversible energy dissipation.
- The model is suitable for simulating reaction dynamics involving energy transfer.
- Demonstrated applicability to single and double well potentials.
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