Iterative quantum-classical path integral with dynamically consistent state hopping

2016 ◽  
Vol 144 (4) ◽  
pp. 044108 ◽  
Author(s):  
Peter L. Walters ◽  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Classical Path

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.

scholarly journals A NOTE ON (SPIN-) COHERENT-STATE PATH INTEGRAL

1999 ◽  
Vol 13 (02) ◽  
pp. 107-140 ◽  
Author(s):  
JUNYA SHIBATA ◽  
SHIN TAKAGI
Keyword(s):  
Coherent State ◽  
Path Integral ◽  
Continuous Time ◽  
Classical Level ◽  
Classical Action ◽  
Single Spin ◽  
Spin Coherent State ◽  
Classical Path ◽  
Time Formalism ◽  
State Path

It is pointed out that there are some fundamental difficulties with the frequently used continuous-time formalism of the spin-coherent-state path integral. They arise already in a single-spin system and at the level of the "classical action" not to speak of fluctuations around the "classical path". Similar difficulties turn out to be present in the case of the (boson-)coherent-state path integral as well; although partially circumventable by an ingenious trick (Klauder's ∊-prescription) at the "classical level", they manifest themselves at the level of fluctuations. Detailed analysis of the origin of these difficulties makes it clear that the only way of avoiding them is to work with the proper discrete-time formalism. The thesis is explicitly illustrated with a harmonic oscillator and a spin under a constant magnetic field.

Quantum-classical path integral with a harmonic treatment of the back-reaction

2019 ◽  
Vol 150 (18) ◽  
pp. 184102 ◽  
Author(s):  
Fei Wang ◽  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Back Reaction ◽  
Classical Path
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