Related papers: Direct path integral estimators for isotope fracti…

The shift in chemical equilibria due to isotope substitution is often exploited to gain insight into a wide variety of chemical and physical processes. It is a purely quantum mechanical effect, which can be computed exactly using…

Path integral calculations of equilibrium isotope effects and isotopic fractionation are expensive due to the presence of path integral discretization errors, statistical errors, and thermodynamic integration errors. Whereas the…

A general method for computing kinetic isotope effects is described. The method uses the quantum-instanton approximation and is based on the thermodynamic integration with respect to the mass of the isotopes and on the path-integral…

A general and rigorous methodology to compute the quantum equilibrium isotope effect is described. Unlike standard approaches, ours does not assume separability of rotational and vibrational motions and does not make the harmonic…

Background: Path integrals are a powerful tool for solving problems in quantum theory that are not amenable to a treatment by perturbation theory. Most path integral computations require an analytic continuation to imaginary time. While…

Path integral implementation of the quantum instanton approximation currently belongs among the most accurate methods for computing quantum rate constants and kinetic isotope effects, but its use has been limited due to the rather high…

The Feynman path integral approach for computing equilibrium isotope effects and isotope fractionation corrects the approximations made in standard methods, although at significantly increased computational cost. We describe an accelerated…

Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to…

The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the…

Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…

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…

A systematic study of the effect of fragment$-$fragment interaction, quantum statistics, $\gamma$-feeding and collective flow is made in the extraction of the nuclear temperature from the double ratio of the isotopic yields in the…

The quantum instanton approximation is a type of quantum transition state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low order derivatives at time zero. Here we present several…

Fractional derivatives are nonlocal differential operators of real order that often appear in models of anomalous diffusion and a variety of nonlocal phenomena. Recently, a version of the Schr\"odinger Equation containing a fractional…

These lectures are intended as an introduction to the technique of path integrals and their applications in physics. The audience is mainly first-year graduate students, and it is assumed that the reader has a good foundation in quantum…

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…

An algorithm for calculating the spectral intensity of radiation due to the coherent addition of many particles with arbitrary trajectories is described. Direct numerical integration of the Lienard-Wiechert potentials, in the far-field, for…

Ring-polymer instanton theory has been developed to simulate the quantum dynamics of molecular systems at low temperatures. Chemical reaction rates can be obtained by locating the dominant tunneling pathway and analyzing fluctuations around…

Collisional effects are included in the path-integral formulation that was proposed in one of our previous paper for the collisionless Boltzmann gas. In calculating the number of molecules entering a six-dimensional phase volume element due…

We develop a new simulation technique based on path-integral molecular dynamics for calculating ground-state tunneling splitting patterns from ratios of symmetrized partition functions. In particular, molecular systems are rigorously…