Related papers: Dual-Level Approach to Instanton Theory
We describe a generalized algorithm for evaluating the steady-state solution of the density matrix equation of motion, for the pump-probe scheme, when two fields oscillating at different frequencies couple the same set of atomic transitions…
Finding optimal pathways in chemical reaction networks is essential for elucidating and designing chemical processes, with significant applications such as synthesis planning and metabolic pathway analysis. Such a chemical pathway-finding…
A space-time adaptive method is presented for the reactive Euler equations describing chemically reacting gas flow where a two species model is used for the chemistry. The governing equations are discretized with a finite volume method and…
Transition state theory is a standard framework for predicting the rate of a chemical reaction. Although the transition state theory has been successfully applied to numerous chemical reaction analyses, many experimental and theoretical…
In these lectures we describe the use of Monte Carlo simulations in understanding the role of tunneling events, instantons, in a quantum mechanical toy model. We study, in particular, a variety of methods that have been used in the QCD…
We consider tunneling to the continuum in a multi-dimensional potential. It is demonstrate that this problem can be treated as two separate problems: a) a bound state and b) a non-resonance scattering problem, by a proper splitting of the…
We provide a field-theoretical description of thermal nucleation in a one-dimensional ferromagnetic superfluid, a quantum-gas analogue of false-vacuum decay. The rate at which ground-state domains nucleate follows an Arrhenius law, with an…
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…
Inverse problem or parameter estimation of ordinary differential equations (ODEs), the iterative process of minimizing the mismatch between model-predicted and experimental states by tuning the parameter values within an optimization…
This paper investigates the impact of the increased reaction rate constant due to tunneling effects on planet-forming disks. Our aim is to quantify the astrophysical implications of atom tunneling for simple molecules that are frequently…
Convergence of path integral simulations requires a substantial number of beads when quantum effects are significant. Traditional Trotter scaling approaches estimate the continuum limit through extrapolation, however they are restricted to…
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the…
The Euclidean path integral method is applied to a quantum tunneling model which accounts for finite size ($L$) effects. The general solution of the Euler Lagrange equation for the double well potential is found in terms of Jacobi elliptic…
In this paper we discuss a master equation applied to the two level system of an atom and derive an exact solution to it in an abstract manner. We also present a problem and a conjecture based on the three level system. Our results may give…
Complex quantum trajectory approach, which arose from a modified de Broglie-Bohm interpretation of quantum mechanics, has attracted much attention in recent years. The exact complex trajectories for the Eckart potential barrier and the soft…
A prime example of quantum tunnelling is the semiclassical 'energy splitting' of the levels of a symmetrical double well potential, or equivalently the flipping rate of an instanton. Curiously the accepted expression for the ground state…
The quantum decay of a metastable vacuum is exponentially suppressed by a tunneling action that can be calculated in the semi-classical approximation as the Euclidean action of a bounce that interpolates between the false and true phases.…
We calculate the instanton corrections to energy spectra of one-dimensional quantum mechanical oscillators to all orders and unify them in a closed form transseries description. Using alien calculus, we clarify the resurgent structure of…
In this paper we show an approach to electron transport in double barrier structures which unifies the well known sequential and resonant tunneling models in the widest range of transport regimes, from completely coherent to completely…
The efficiency of water electrolysis in a photoelectrochemical cell is largely limited by the oxygen evolution reaction (OER) at its semiconductor photoanode. Reaction rate constants are key to investigating the slow kinetics of the…