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Updated: May 24, 2026
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
Effect of cusps in time-dependent quantum mechanics.
Zeng-hui Yang1, Neepa T Maitra, Kieron Burke
1Department of Chemistry, University of California-Irvine, Irvine, California 92697, USA.
Physical Review Letters
|March 10, 2012
Summary
Spatial cusps in quantum wave functions cause nonanalytic time behavior. A new method calculates this short-time evolution, showing density deviations from Taylor expansions but preserving time-dependent density functional theory.
Area of Science:
- Quantum mechanics
- Computational physics
Background:
- Nonrelativistic quantum mechanics describes wave function evolution over time.
- Spatial features like cusps in initial wave functions can introduce complexities.
- Nonanalytic behavior in time evolution poses challenges for standard approximations.
Purpose of the Study:
- To develop a method for calculating the short-time behavior of quantum systems with spatial cusps.
- To analyze the implications of nonanalytic time evolution on system density.
- To verify the applicability of time-dependent density functional theory (TDDFT) in these scenarios.
Main Methods:
- Proposed a novel computational method to handle nonanalytic short-time dynamics.
- Analyzed the time evolution of the quantum density.
- Examined the conditions under which the Runge-Gross theorem for TDDFT remains valid.
Main Results:
- Demonstrated that the density may not follow its Taylor expansion in time for systems with spatial cusps.
- Showed that the Runge-Gross proof for TDDFT is still applicable.
- Confirmed that the validity of TDDFT relies on the time-analyticity of the external potential.
Conclusions:
- A method is presented to accurately compute short-time quantum dynamics with nonanalytic initial conditions.
- The study clarifies the behavior of quantum densities under specific nonanalytic conditions.
- The foundational principles of time-dependent density functional theory are robust even with complex initial wave functions.
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