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Coulomb Explosion Imaging as a Tool to Distinguish Between Stereoisomers

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Breakdown of the coherent state path integral: two simple examples.

Justin H Wilson¹, Victor Galitski

¹Joint Quantum Institute and Condensed Matter Theory Center, Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA.

Physical Review Letters

|April 8, 2011

Summary

This summary is machine-generated.

The time-continuous coherent state path integral fails for specific quantum models, unlike its time-discretized counterpart. This breakdown occurs when the Hamiltonian is quadratic in the coherent state generator.

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Area of Science:

Quantum mechanics
Condensed matter physics

Background:

Coherent state path integrals are a powerful tool in quantum mechanics.
The single-site Bose-Hubbard model and spin-path integrals are important quantum systems.
Operator approaches provide a benchmark for path integral calculations.

Purpose of the Study:

To investigate the limitations of the time-continuous coherent state path integral.
To identify the conditions under which this path integral formulation breaks down.
To compare the performance of time-continuous and time-discretized path integrals.

Main Methods:

Analysis of the time-continuous coherent state path integral.
Examination of the single-site Bose-Hubbard model and spin-path integral.
Comparison with results from operator-based methods.

Main Results:

The time-continuous coherent state path integral fails for the single-site Bose-Hubbard model and spin-path integral.
Breakdown occurs when the Hamiltonian is quadratic in the coherent state generator.
The time-discretized path integral does not exhibit these issues.

Conclusions:

The time-continuous coherent state path integral is not universally applicable.
The quadratic nature of the Hamiltonian is a critical factor in the path integral's failure.
Time-discretization offers a robust alternative for these quantum systems.