title: Path integral approach to the quantum fidelity amplitude.
abstract: 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.
authors.affiliation: Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), 1015 Lausanne, Switzerland jiri.vanicek@epfl.ch.
authors.forename: Jiří
authors.identifier: http://orcid.org/0000-0002-2080-4378
authors.initials: J
authors.lastname: Vaníček
authors.affiliation: Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel dcohen@bgu.ac.il.
authors.forename: Doron
authors.identifier: http://orcid.org/0000-0002-3835-3544
authors.initials: D
authors.lastname: Cohen
keywords: Loschmidt echo; dephasing representation; path integral; quantum fidelity