A new Fourier path integral method, a more general scheme for extrapolation, and comparison of eight path integral methods for the quantum mechanical calculation of free energies

2001 ◽  
Vol 114 (2) ◽  
pp. 621 ◽  
Author(s):  
Steven L. Mielke ◽  
Donald G. Truhlar
Keyword(s):  
Path Integral ◽  
Integral Method ◽  
General Scheme ◽  
Quantum Mechanical Calculation ◽  
Quantum Mechanical ◽  
Free Energies ◽  
Mechanical Calculation ◽  
Integral Methods ◽  
Path Integral Method

Path Integral Methods for the Probabilistic Analysis of Nonlinear Systems Under a White-Noise Process

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta
Keyword(s):  
Path Integral ◽  
Path Integration ◽  
Integral Method ◽  
Degrees Of Freedom ◽  
Kolmogorov Equation ◽  
Integral Methods ◽  
Alternative Approach ◽  
Path Integration Method ◽  
Path Integral Method ◽  
Barrier Problems

Abstract In this paper, the widely known path integral method, derived from the application of the Chapman–Kolmogorov equation, is described in details and discussed with reference to the main results available in literature in several decades of contributions. The most simple application of the method is related to the solution of Fokker–Planck type equations. In this paper, the solution in the presence of normal, α-stable, and Poissonian white noises is first discussed. Then, application to barrier problems, such as first passage problems and vibroimpact problems is described. Further, the extension of the path integral method to problems involving multi-degrees-of-freedom systems is analyzed. Lastly, an alternative approach to the path integration method, that is the Wiener Path integration (WPI), also based on the Chapman–Komogorov equation, is discussed. The main advantages and the drawbacks in using these two methods are deeply analyzed and the main results available in literature are highlighted.

A universal model for the quantum mechanical calculation of free energies of solvation in non-aqueous solvents

1997 ◽  
Vol 98 (2-3) ◽  
pp. 85-109 ◽  
Author(s):  
David J. Giesen ◽  
Gregory D. Hawkins ◽  
Daniel A. Liotard ◽  
Christopher J. Cramer ◽  
Donald G. Truhlar
Keyword(s):  
Quantum Mechanical Calculation ◽  
Quantum Mechanical ◽  
Universal Model ◽  
Free Energies ◽  
Mechanical Calculation
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