Interference nature of quantum breather oscillation

Abstract

In a system of coupled nonlinear oscillators, the breather (or local mode) solution is studied fully quantum mechanically, as well as by a semiclassical initial value representation of the propagator and classical Wigner dynamics. We show that the initial breather state is a superposition of almost degenerate eigenstates. From this simple observation it follows that the breather must decay and revive (i.e., oscillate with energy localization for extended times). Numerical results are shown for a two degree of freedom system. The fact that the semiclassical real-time result reproduces the full quantum one to a large degree, whereas the classical Wigner dynamics based on a similar set of trajectories does not, indicates that the breather oscillation can be viewed as an interference phenomenon.

Herman-Kluk propagator is free from zero-point energy leakage

“…We note in passing that a related study has been performed for the breather initial condition |1, 0 , i.e., with one oscillator in its first excited state and the second one in its ground state. 90 Having affirmed that a simple averaging over classical trajectories starting from a quantum initial state is not sufficient to prevent the ZPE leakage, we come to the question at the heart of this investigation: is there still a ZPE leakage in a truly semiclassical method that allows for the interference of different trajectories? The answer can be found in the results of the HK simulations, see Fig.…”

The role of tunneling in the ionization of atoms by ultrashort and intense laser pulses

“…The matter of whether classically allowed or forbidden transport is the dominant mechanism for some particular phenomenon is relatively straightforward for the simple systems in the above paragraph, but becomes a lot more blurred in the high-dimensional or time-dependent case: The former is deceptive because splitting phase space into disjoint regions is harder in higher dimensions * lando@universite-paris-saclay.fr [17,18]; The latter involves non-stationary potential barriers, which will often trigger chaos even for a single DoF [19][20][21] and renders the very definition of tunneling quite challenging [16]. In the end, time dependence allows for the possibility of highly intricate classical dynamics even in the simplest of systems, and new classically allowed transport pathways can be created that are unrelated to the Wigner function's tails.…”