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Local Measure of Quantum Effects in Quantum Dynamics
Vitaly Rassolov1, Sophya Garashchuk1
1Department of Chemistry and Biochemistry, University of South Carolina, Columbia, South Carolina 29208, United States.
The Journal of Physical Chemistry. A
|May 20, 2021
Summary
We introduce "quantum power," a new measure of quantum dynamics. This quantum power quantifies how quantum features evolve in time, offering insights into the transition from quantum to classical behavior in systems.
Area of Science:
- Quantum mechanics
- Physical chemistry
- Computational physics
Background:
- The Madelung-de Broglie-Bohm formulation describes quantum systems using Bohmian trajectories.
- This approach allows for a clear separation of energy into classical and quantum components, aiding in understanding quantumness.
- Existing methods may not fully capture the nuances of quantum-classical transitions.
Purpose of the Study:
- To propose a novel, system-independent measure of the quantumness of dynamics.
- To introduce "quantum power" as a metric derived from the time-rate of change of energy.
- To investigate the behavior of quantum features during the quantum-to-classical transition.
Main Methods:
- Utilizing the Madelung-de Broglie-Bohm formulation of the Schrödinger equation.
- Defining and calculating a local measure of quantum dynamics termed "quantum power".
- Applying the measure to model chemical systems to analyze quantum-classical transitions.
Main Results:
- Quantum power is a local measure of the time-change in energy, quantifying quantum dynamics.
- In model chemical systems, quantum features do not vanish during the quantum-to-classical transition but are temporally displaced.
- This temporal displacement of quantum features provides a new perspective on the transition.
Conclusions:
- Quantum power offers a valuable tool for assessing the quantumness of dynamical systems.
- The findings suggest that approximate dynamics methods should account for the temporal evolution of quantum features.
- This work provides a framework for evaluating the validity of semiclassical approximations in anharmonic systems.
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