scholarly journals Quantum‐classical path integral evaluation of reaction rates with a near‐equilibrium flux formulation

2021 ◽  
Author(s):  
Amartya Bose ◽  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Reaction Rates ◽  
Integral Evaluation ◽  
Classical Path

On the Path Integral Evaluation of the S-Matrix for Noncentral Potentials

2020 ◽  
pp. 187-198
Author(s):  
M. V. Carpio-bernido ◽  
E. B. Gravador ◽  
C. C. Bernido
Keyword(s):  
Path Integral ◽  
Integral Evaluation ◽  
S Matrix

scholarly journals Path integral evaluation of equilibrium isotope effects

2009 ◽  
Vol 131 (2) ◽  
pp. 024111 ◽  
Author(s):  
Tomáš Zimmermann ◽  
Jiří Vaníček
Keyword(s):  
Path Integral ◽  
Isotope Effects ◽  
Integral Evaluation

Blip-summed quantum–classical path integral with cumulative quantum memory

2016 ◽  
Vol 195 ◽  
pp. 81-92 ◽  
Author(s):  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Degrees Of Freedom ◽  
Quantum Memory ◽  
Integral Methods ◽  
Acceleration Techniques ◽  
Classical Path ◽  
Forced Oscillator ◽  
Influence Functional ◽  
Harmonic Bath ◽  
Explicit Enumeration

The quantum-classical path integral (QCPI) offers a rigorous methodology for simulating quantum mechanical processes in condensed-phase environments treated in full atomistic detail. This paper describes the implementation of QCPI on system–bath models, which are frequently employed in studying the dynamics of reactive processes. The QCPI methodology incorporates all effects associated with stimulated phonon absorption and emission as its crudest limit, thus can (in some regimes) converge faster than influence functional-based path integral methods specifically designed for system–bath Hamiltonians. It is shown that the QCPI phase arising from a harmonic bath can be summed analytically with respect to the discrete bath degrees of freedom and expressed in terms of precomputed influence functional coefficients, avoiding the explicit enumeration of forced oscillator trajectories, whose number grows exponentially with the length of quantum memory. Further, adoption of the blip decomposition (which classifies the system paths based on the time length over which their forward and backward components are not identical) and a cumulative treatment of the QCPI phase between blips allows elimination of the majority of system paths, leading to a dramatic increase in efficiency. The generalization of these acceleration techniques to anharmonic environments is discussed.

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