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Published on: May 30, 2014
Spectral filters in quantum mechanics: A measurement theory perspective
1Institute for Theoretical Chemistry, Department of Chemistry and Biochemistry, The University of Texas at Austin, Austin, Texas 78712-1167, USA.
Summary
We unify time-domain spectral filter algorithms using selective measurements. Both filter diagonalization (FD) and correlation function methods require similar propagation times, differing mainly in eigenvalue identification techniques.
Area of Science:
- Quantum mechanics
- Spectroscopy
- Computational physics
Background:
- Spectral filters are crucial for analyzing quantum systems.
- Existing time-domain methods lack a unified theoretical framework.
- Selective measurements offer a potential unifying principle.
Purpose of the Study:
- To develop a unified time-domain theory for spectral filters.
- To present parameter-free implementations using correlation functions and filter diagonalization (FD).
- To compare the performance of FD and correlation function methods.
Main Methods:
- Formulating a time-domain theory based on selective measurements.
- Developing parameter-free implementations in correlation function and FD forms.
- Utilizing Chebyshev polynomials for time propagation and analytical integration.
- Conducting numerical experiments on a model system.
Main Results:
- A unified theory for time-domain spectral filters based on selective measurements.
- Analytically derived FD equations in a numerically convenient form.
- Demonstration that FD and correlation function methods have comparable time-propagation requirements.
- Identification of distinct eigenvalue localization strategies: diagonalization for FD, zero-finding for correlation functions.
Conclusions:
- The filter diagonalization (FD) method is a specific realization of the general spectral filter objective.
- Both FD and correlation function methods are constrained by the time-energy uncertainty.
- Numerical experiments highlight the procedural differences in spectral analysis between FD and correlation function methods.
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