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Title: Path description of coordinate-space amplitudes

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Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 95; Journal Issue: 11; Related Information: CHORUS Timestamp: 2017-06-29 22:14:02; Journal ID: ISSN 2470-0010
American Physical Society
Country of Publication:
United States

Citation Formats

Erdoğan, Ozan, and Sterman, George. Path description of coordinate-space amplitudes. United States: N. p., 2017. Web. doi:10.1103/PhysRevD.95.116015.
Erdoğan, Ozan, & Sterman, George. Path description of coordinate-space amplitudes. United States. doi:10.1103/PhysRevD.95.116015.
Erdoğan, Ozan, and Sterman, George. 2017. "Path description of coordinate-space amplitudes". United States. doi:10.1103/PhysRevD.95.116015.
title = {Path description of coordinate-space amplitudes},
author = {Erdoğan, Ozan and Sterman, George},
abstractNote = {},
doi = {10.1103/PhysRevD.95.116015},
journal = {Physical Review D},
number = 11,
volume = 95,
place = {United States},
year = 2017,
month = 6

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on June 29, 2018
Publisher's Accepted Manuscript

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  • Feynman's laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different to that predicted by the classical Fresnel formula. Exceptmore » for neutrino oscillations, good agreement is otherwise found with previous calculations of spatially dependent quantum interference effects.« less
  • The method of complex coordinates has been long been known to allow L/sup 2/ calculations of t-matrix amplitudes for short-range potentials, but to yield divergent results for long-range forces. Using a spherical long-range potential as an example, it is shown here that the Pade method of summation can be used in conjunction with the diverging complex-coordinate calculations to obtain accurate values of the scattering amplitude.
  • We propose a generalization of the intrinsic reaction coordinate (IRC) for quantum many-body systems described in terms of the mass-weighted ring polymer centroids in the imaginary-time path integral theory. This novel kind of reaction coordinate, which may be called the ''centroid IRC,'' corresponds to the minimum free energy path connecting reactant and product states with a least amount of reversible work applied to the center of masses of the quantum nuclei, i.e., the centroids. We provide a numerical procedure to obtain the centroid IRC based on first principles by combining ab initio path integral simulation with the string method. Thismore » approach is applied to NH{sub 3} molecule and N{sub 2}H{sub 5}{sup -} ion as well as their deuterated isotopomers to study the importance of nuclear quantum effects in the intramolecular and intermolecular proton transfer reactions. We find that, in the intramolecular proton transfer (inversion) of NH{sub 3}, the free energy barrier for the centroid variables decreases with an amount of about 20% compared to the classical one at the room temperature. In the intermolecular proton transfer of N{sub 2}H{sub 5}{sup -}, the centroid IRC is largely deviated from the ''classical'' IRC, and the free energy barrier is reduced by the quantum effects even more drastically.« less