Dynamical signatures of instantons: insights from path-integral studies

Abstract

In thermal quantum systems, the quantum effects arising from the Boltzmann distribution, that governs some of its statistical properties, can be accurately quantified using imaginary-time Feynman path integrals. While traditionally used as a method to account for static quantum effects of atomic nuclei, the path-integral framework has also been augmented to simulate short-time quantum dynamics using essentially classical molecular-dynamics based simulation techniques. These techniques have proved successful in achieving quantitative accuracy in computing diffusion coefficients, dipole absorption spectra, and chemical reaction rates. In systems where quantum tunneling is predominant, the main contribution to the quantum effects can be calculated from closed-loop imaginary-time paths called ‘instantons’. This technique has been successfully employed in computing static properties of systems, such as tunneling splittings of energy levels in large molecules. This thesis explores the dynamical imprints of instantons and presents results from path-integral based dynamics simulation in two different contexts. The first part of the thesis reports results from dynamics simulations using path-integral based approaches in thermal quantum systems which are classically chaotic. It has been found that local quantum information in such chaotic systems is ‘scrambled’ or rendered irretrievable very quickly by quantum dynamics. The rate of scrambling of quantum information in such systems, as quantified using ‘out-of-time-ordered’ correlation functions, has been conjectured to be limited by a temperature-dependent constant. We present results which show that the emergence of the afore-mentioned instantons reduces the rate of information scrambling and is responsible for this ‘bound on chaos’. The second part of the thesis reports the quantitative effects that the emergence of artificial instantonic structures has on constrained path-integral based simulations of infrared vibrational spectra of molecular systems. We find that such unphysical structures are responsible for erroneously shifting the frequencies in infrared spectra from their right (quantum) values. The implication of this result is that any method which approximates the path integral with a representative coordinate (such as its geometric centroid) will possibly be subject to this error and hence care needs to be exercised when comparing the resultant spectra with the exact quantum results.