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Path integral approach to the quantum fidelity amplitude
The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscop...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
The Royal Society Publishing
2016
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4855403/ https://www.ncbi.nlm.nih.gov/pubmed/27140973 http://dx.doi.org/10.1098/rsta.2015.0164 |
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author | Vaníček, Jiří Cohen, Doron |
author_facet | Vaníček, Jiří Cohen, Doron |
author_sort | Vaníček, Jiří |
collection | PubMed |
description | The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. |
format | Online Article Text |
id | pubmed-4855403 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2016 |
publisher | The Royal Society Publishing |
record_format | MEDLINE/PubMed |
spelling | pubmed-48554032016-06-13 Path integral approach to the quantum fidelity amplitude Vaníček, Jiří Cohen, Doron Philos Trans A Math Phys Eng Sci Articles The Loschmidt echo is a measure of quantum irreversibility and is determined by the fidelity amplitude of an imperfect time-reversal protocol. Fidelity amplitude plays an important role both in the foundations of quantum mechanics and in its applications, such as time-resolved electronic spectroscopy. We derive an exact path integral formula for the fidelity amplitude and use it to obtain a series of increasingly accurate semiclassical approximations by truncating an exact expansion of the path integral exponent. While the zeroth-order expansion results in a remarkably simple, yet non-trivial approximation for the fidelity amplitude, the first-order expansion yields an alternative derivation of the so-called ‘dephasing representation,’ circumventing the use of a semiclassical propagator as in the original derivation. We also obtain an approximate expression for fidelity based on the second-order expansion, which resolves several shortcomings of the dephasing representation. The rigorous derivation from the path integral permits the identification of sufficient conditions under which various approximations obtained become exact. The Royal Society Publishing 2016-06-13 /pmc/articles/PMC4855403/ /pubmed/27140973 http://dx.doi.org/10.1098/rsta.2015.0164 Text en © 2016 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited. |
spellingShingle | Articles Vaníček, Jiří Cohen, Doron Path integral approach to the quantum fidelity amplitude |
title | Path integral approach to the quantum fidelity amplitude |
title_full | Path integral approach to the quantum fidelity amplitude |
title_fullStr | Path integral approach to the quantum fidelity amplitude |
title_full_unstemmed | Path integral approach to the quantum fidelity amplitude |
title_short | Path integral approach to the quantum fidelity amplitude |
title_sort | path integral approach to the quantum fidelity amplitude |
topic | Articles |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4855403/ https://www.ncbi.nlm.nih.gov/pubmed/27140973 http://dx.doi.org/10.1098/rsta.2015.0164 |
work_keys_str_mv | AT vanicekjiri pathintegralapproachtothequantumfidelityamplitude AT cohendoron pathintegralapproachtothequantumfidelityamplitude |