Real-Time Path Integral Methods, Quantum Master Equations, and Classical vs Quantum Memory

2019 ◽  
Vol 123 (49) ◽  
pp. 10470-10482
Author(s):  
Sambarta Chatterjee ◽  
Nancy Makri
Keyword(s):  
Real Time ◽  
Path Integral ◽  
Quantum Memory ◽  
Master Equations ◽  
Time Path ◽  
Integral Methods

Real time path integral methods for a system coupled to an anharmonic bath

1994 ◽  
Vol 101 (8) ◽  
pp. 6708-6716 ◽  
Author(s):  
Gregory Ilk ◽  
Nancy Makri
Keyword(s):  
Real Time ◽  
Path Integral ◽  
Time Path ◽  
Integral Methods

Analysis of the statistical errors in conditioned real time path integral methods

1993 ◽  
Vol 99 (7) ◽  
pp. 5087-5090 ◽  
Author(s):  
Abolfazl M. Amini ◽  
Michael F. Herman
Keyword(s):  
Real Time ◽  
Path Integral ◽  
Time Path ◽  
Statistical Errors ◽  
Integral Methods

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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