Related papers: Chaos assisted instanton tunneling in one dimensio…
Quantum tunneling between degenerate ground states through the central barrier of a potential is extended to excited states with the instanton method. This extension is achieved with the help of an LSZ reduction technique as in field theory…
In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative…
Based on a closed form expression for the path integral of quantum transition amplitudes, we suggest rigorous definitions of both, quantum instantons and quantum chaos. As an example we compute the quantum instanton of the double well…
We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the…
The method of detection of the unstable periodic spatio-temporal states of spatial extended chaotic systems has been proposed. The application of this method is illustrated by the consideration of two different systems: i) the fluid model…
The effect of inelastic scattering on quantum tunneling through a rectangular potential barrier, of length $L$, containing randomly distributed impurities, is considered. It is shown that, despite the fact that the inelastic transition…
We derive a trace formula for the splitting-weighted density of states suitable for chaotic potentials with isolated symmetric wells. This formula is based on complex orbits which tunnel through classically forbidden barriers. The theory is…
Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer…
Instanton theory has arisen as a practical tool for calculating tunneling splittings in molecular systems. Unfortunately, the original formulation of instanton theory fundamentally breaks down when trying to calculate the level splitting in…
The existence of quantum tunneling opens the possibility of a sudden spatial relocalization of a system after a minor modification of its parameters. Such a quantum analogue of the Thom's classical catastrophe would manifest itself,…
Tunneling between two classically disconnected regular regions can be strongly affected by the presence of a chaotic sea in between. This phenomenon, known as chaos-assisted tunneling, gives rise to large fluctuations of the tunneling rate.…
The assisted tunneling of a wave packet between square one dimensional barriers is treated analytically. The tunneling rate is calculated exactly for a potential mimicking a constant electric field with arbitrary time dependence. The pole…
The assisted tunneling of a metastable state between barriers is investigated analytically by means of a simplified one dimensional model. A time dependent perturbation changes the pole spectrum of the wave function introducing a larger…
A simple example of quantum transport in a classically chaotic system is studied. It consists in a single state lying on a regular island (a stable primary resonance island) which may tunnel into a chaotic sea and further escape to infinity…
A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between n-th degenerate states of neighboring wells is dominated by a…
A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain…
Statistics of tunneling rates in the presence of chaotic classical dynamics is discussed on a realistic example: a hydrogen atom placed in parallel uniform static electric and magnetic fields, where tunneling is followed by ionization along…
In this paper, we derive a perturbatively-corrected instanton rate theory in the ring-polymer framework (RPI+PC), which significantly enhances the accuracy of instanton theory by using third and fourth derivatives of the potential to…
We study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schr\"odinger equation based on the Cranck-Nicholson finite-difference scheme, shows that the…
A recent quasiclassical description of a tunneling universe model is shown to exhibit chaotic dynamics by an analysis of fractal dimensions in the plane of initial values. This result relies on non-adiabatic features of the quantum…