Related papers: Dual-Level Approach to Instanton Theory

There exist two interpretations of instantons in the literature. The first interpretation regards instanton as divider between the initial and final hypersurfaces. The Coleman-De Luccia instanton is one such an example. The second…

We show why and how the $I\bar I$ valley trajectory commonly used in the literature so far is in fact unsatisfactory. A better $I\bar I$ valley is suggested. We also give analytic expressions for the multiple instanton-antiinstanton…

Recent studies of neutral gas-phase reactions characterized by barriers show that certain complex forming processes involving light atoms are enhanced by quantum mechanical tunneling at low temperature. Here, we performed kinetic…

We generalize the string method, originally designed for the study of thermally activated rare events, to the calculation of quantum tunneling rates. This generalization is based on the analogy between quantum mechanics and statistical…

We propose a new approach for computing tunneling rates in quantum or thermal field theory with multiple scalar fields. It is based on exact analytical solutions of piecewise linear potentials with many segments that describes any given…

We propose an efficient method to compute reaction rate constants of thermally activated processes occurring in many-body systems at finite temperature. The method consists in two steps: first, paths are sampled using a transition path…

We first derive the Hamilton-Jacobi theory underlying continuous-time Markov processes, and then use the construction to develop a variational algorithm for estimating escape (least improbable or first passage) paths for a generic…

Accurately modeling chemical reactions at the atomistic level requires high-level electronic structure theory due to the presence of unpaired electrons and the need to properly describe bond breaking and making energetics. Commonly used…

We derive and implement a second-order adjoint method to compute exact gradients and Hessians for a prototypical quantum optimal control problem, that of solving for the minimal energy applied electric field that drives a molecule from a…

We describe a computational investigation of tunneling at finite energy in a weakly coupled quantum mechanical system with two degrees of freedom. We compare a full quantum mechanical analysis to the results obtained by making use of a…

We propose a class of models exhibiting instanton crystal phase. In this phase, the minimum of the free energy corresponds to a configuration with an imaginary-time-dependent order parameter in a form of a chain of alternating instantons…

A practical and new Runge--Kutta numerical scheme for stochastic differential equations is explored. Numerical examples demonstrate the strong convergence of the method. The first order strong convergence is then proved using Ito integrals…

We extend our previous symmetrized path-integral molecular dynamics approach to calculate tunneling splittings of molecules in rotationally excited states. In this new formalism, the system is rigorously projected onto selected rotational…

The development and implementation of increasingly accurate methods for electronic structure calculations mean that, for many atomistic simulation problems, treating light nuclei as classical particles is now one of the most serious…

Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…

The imaginary part of the one loop effective action in external backgrounds can be efficiently computed using worldline instantons which are closed periodic paths in spacetime. Exact solutions for nonstatic backgrounds are only known in…

Fast and robust quantum control protocols are often based on an idealised approximate description of the relevant quantum system. While this may provide a performance which is close to optimal, improvements can be made by incorporating…

We study a new two-time-scale stochastic gradient method for solving optimization problems, where the gradients are computed with the aid of an auxiliary variable under samples generated by time-varying MDPs controlled by the underlying…

Steepest-entropy-ascent quantum thermodynamics, or SEAQT, is a unified approach of quantum mechanics and thermodynamics that avoids many of the inconsistencies that can arise between the two theories. Given a set of energy levels, i.e.,…

Dielectric microstructures have generated much interest in recent years as a means of accelerating charged particles when powered by solid state lasers. The acceleration gradient (or particle energy gain per unit length) is an important…