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Partial-differential-equation-based approach to classical phase-space deformations.

Emmanuel Tannenbaum¹

¹Harvard University, Cambridge, MA 02138, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|August 22, 2002

Summary

This summary is machine-generated.

Researchers developed a novel partial differential equation method to optimize canonical bases for representing Hamiltonians. This approach simplifies complex quantum calculations by minimizing Hamiltonian dependence and isolating integrable dynamics.

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Area of Science:

Quantum mechanics
Computational physics
Mathematical physics

Background:

Nearly integrable Hamiltonians pose challenges in quantum calculations.
Representing Hamiltonians with canonical bases is crucial for theoretical and computational studies.

Purpose of the Study:

To develop a method for finding an optimal canonical basis for nearly integrable Hamiltonians.
To simplify quantum calculations and gain physical insights into integrable dynamics.

Main Methods:

A partial-differential-equation-based approach is used.
The method continuously deforms an initial canonical basis.
The deformation minimizes the Hamiltonian's dependence on canonical position.

Main Results:

An optimal canonical basis is found, minimizing Hamiltonian dependence.
The new basis incorporates classical dynamics into an integrable Hamiltonian.
A significantly smaller nonintegrable component remains compared to the initial representation.

Conclusions:

The optimized basis aids in minimizing basis set size for quantum calculations.
It provides physical insight by isolating integrable dynamics effects.
Semiclassical wave functions corresponding to the final basis can be constructed.