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Quantum free-energy differences from nonequilibrium path integrals. II. Convergence properties for the harmonic
Ramses van Zon1, Lisandro Hernández de la Peña, Gilles H Peslherbe
1Chemical Physics Theory Group, Department of Chemistry, University of Toronto, 80 Saint George Street, Toronto, Ontario, Canada.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
Summary
Nonequilibrium path-integral methods show work distribution and free energy converge as degrees of freedom increase. Convergence rates depend on regularization, impacting quantum free-energy calculations.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Computational physics
Background:
- Nonequilibrium path-integral methods are crucial for calculating quantum free-energy differences.
- Understanding convergence properties is essential for the accuracy of these calculations.
- The behavior of work distribution and free energy with increasing degrees of freedom (M) needs clarification.
Purpose of the Study:
- To investigate the convergence of work distribution and free energy in a quantum harmonic oscillator with changing well strength.
- To determine how the number of degrees of freedom (M) in regularized path integrals affects these convergence properties.
- To compare the convergence rates for different regularization methods.
Main Methods:
- Application of nonequilibrium path-integral methods to a quantum particle in a time-dependent harmonic potential.
- Analysis of the work distribution and free-energy difference using Jarzynski's and Crooks' fluctuation relations.
- Examination of convergence as the number of degrees of freedom (M) approaches infinity, with specific regularization techniques (Fourier and bead methods).
Main Results:
- The work distribution converges as M approaches infinity, irrespective of the switching speed.
- Finite free-energy differences are obtained using Jarzynski's and Crooks' relations.
- Convergence rates differ: 1/M for the Fourier method and 1/M^2 for the bead regularization method.
Conclusions:
- Nonequilibrium path-integral methods provide reliable quantum free-energy calculations.
- The choice of regularization method significantly influences the convergence rate and efficiency.
- These findings have implications for applying these methods to more complex quantum systems.
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