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

2016 ◽  
Vol 195 ◽  
pp. 81-92 ◽  
Author(s):  
Nancy Makri

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.

Author(s):  
Mario Di Paola ◽  
Gioacchino Alotta

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.


Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.


2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ivan M. Burbano ◽  
T. Rick Perche ◽  
Bruno de S. L. Torres

Abstract Particle detectors are an ubiquitous tool for probing quantum fields in the context of relativistic quantum information (RQI). We formulate the Unruh-DeWitt (UDW) particle detector model in terms of the path integral formalism. The formulation is able to recover the results of the model in general globally hyperbolic spacetimes and for arbitrary detector trajectories. Integrating out the detector’s degrees of freedom yields a line defect that allows one to express the transition probability in terms of Feynman diagrams. Inspired by the light-matter interaction, we propose a gauge invariant detector model whose associated line defect is related to the derivative of a Wilson line. This is another instance where nonlocal operators in gauge theories can be interpreted as physical probes for quantum fields.


2003 ◽  
Vol 119 (23) ◽  
pp. 12119-12128 ◽  
Author(s):  
Cristian Predescu ◽  
Dubravko Sabo ◽  
J. D. Doll ◽  
David L. Freeman

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