Related papers: Path integrals for awkward actions
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
Consistent dynamics which couples classical and quantum degrees of freedom exists. This dynamics is linear in the hybrid state, completely positive and trace preserving. Starting from completely positive classical-quantum master equations,…
The fermion sign problem, the biggest obstacle in quantum Monte Carlo calculations, is completely solved in this paper. Here, we find a strategy, in which the contribution from those negative-weighted paths is thoroughly cancelled or…
A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt = - F(q) + e(q) xi, where e(q) xi is Gaussian white noise whose amplitude e(q) depends on q itself. I show how to convert such equations into path…
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational bottleneck is the sampling from the Gibbs density of the…
Path integral Monte Carlo (PIMC) simulations are used to calculate the momentum distribution of the homogeneous electron gas at finite temperature. This is done by calculating the off-diagonal elements of the real-space density matrix,…
Thermodynamics is independent of a description at a microscopic level consequently statistical thermodynamics must produce results independent of the coordinate system used to describe the particles and their interactions. In the path…
Path integral Monte Carlo approach is used to study the coupled quantum dynamics of the electron and nuclei in hydrogen molecule ion. The coupling effects are demonstrated by comparing differences in adiabatic Born--Oppenheimer and…
The Hamiltonian counterpart of classical Lagrangian field theory is covariant Hamiltonian field theory where momenta correspond to derivatives of fields with respect to all world coordinates. In particular, classical Lagrangian and…
We formulate Lagrangian descriptors (LDs) in the path integral framework. Averaging the classical LD over fluctuations about extremal trajectories defines a quantum LD that incorporates quantum effects. Invariant manifolds, which sharply…
Monte Carlo techniques have been widely employed in statistical physics as well as in quantum theory in the Lagrangian formulation. However, in some areas of application to quantum theories computational progress has been slow. Here we…
A simple and efficient method for quantum Monte Carlo simulation is presented, based on discretization of the action in the path integral, and a Gaussian averaging of the potential, which works well e.g. with the Coulomb potential.
The stochastization of the Jacobi second equality of classical mechanics, by Gaussian white noises for the Lagrangian of a particle in an arbitrary field is considered. The quantum mechanical Hamilton operator similar to that in Euclidian…
We introduce modifications to Monte Carlo simulations of the Feynman path integral that improve sampling of localised interactions. The new algorithms generate trajectories in simple background potentials designed to concentrate them about…
A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the…
A novel generative machine learning approach for the simulation of sequences of financial price data with drawdowns quantifiably close to empirical data is introduced. Applications such as pricing drawdown insurance options or developing…
Monte Carlo studies of many quantum systems face exponentially severe signal-to-noise problems. We show that noise arising from complex phase fluctuations of observables can be reduced without introducing bias using path integral contour…
There are a number of situations where, when computing prices of financial derivatives using quasi-Monte Carlo (QMC), it turns out to be beneficial to apply an orthogonal transform to the standard normal input variables. Sometimes those…
The predictions of the standard model of particle physics are highly successful in spite of the fact that several parts of the underlying quantum field theoretical framework are analytically problematic. Indeed, it has long been suggested,…
The discrete time path integral Monte Carlo (PIMC) with a one-particle density matrix approximation is applied to study the quantum phase transition in the coupled double-well chain. To improve the convergence properties, the exact action…