Related papers: Path integral derivations of novel complex traject…
We propose a trajectory-based quasiclassical method for approximating dynamics in condensed phase systems. Building upon the previously developed Optimized Mean Trajectory (OMT) approximation that has been used to compute linear and…
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…
It is a common belief among field theorists that path integrals can be computed exactly only in a limited number of special cases, and that most of these cases are already known. However recent developments, which generalize the WKBJ method…
The simple physics of a free particle reveals important features of the path-integral formulation of relativistic quantum theories. The exact quantum-mechanical propagator is calculated here for a particle described by the simple…
Building on Paper I of this series, which introduced path integral Monte Carlo (PIMC) estimators for the derivative of the potential of mean force (PMF), we propose two path integral molecular dynamics (PIMD) integrators that can make use…
We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…
In many mobile robotics scenarios, such as drone racing, the goal is to generate a trajectory that passes through multiple waypoints in minimal time. This problem is referred to as time-optimal planning. State-of-the-art approaches either…
We study finite-dimensional integrals in a way that elucidates the mathematical meaning behind the formal manipulations of path integrals occurring in quantum field theory. This involves a proper understanding of how Wick's theorem allows…
This paper introduces the Bidirectional Clustered MPPI (BiC-MPPI) algorithm, a novel trajectory optimization method aimed at enhancing goal-directed guidance within the Model Predictive Path Integral (MPPI) framework. BiC-MPPI incorporates…
We consider a semi-classically scaled Schr\"odinger equation with WKB initial data. We prove that in the classical limit the corresponding Bohmian trajectories converge (locally in measure) to the classical trajectories before the…
Model Predictive Path Integral (MPPI) control has proven to be a powerful tool for the control of uncertain systems (such as systems subject to disturbances and systems with unmodeled dynamics). One important limitation of the baseline MPPI…
We present a semiclassical analysis of the quantum propagator of a particle confined on one side by a steeply, monotonically rising potential. The models studied in detail have potentials proportional to $x^{\alpha}$ for $x>0$; the limit…
We consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold that is the product of the total space of…
In recent years efficient algorithms have been developed for the numerical computation of relativistic single-particle path integrals in quantum field theory. Here, we adapt this "worldline Monte Carlo" approach to the standard problem of…
Optimal sampling based motion planning and trajectory optimization are two competing frameworks to generate optimal motion plans. Both frameworks have complementary properties: Sampling based planners are typically slow to converge, but…
Recently a path integral formalism has been proposed by the author which gives the time evolution of moments of slow variables in a Hamiltonian statistical system. This closure relies on evaluating the informational discrepancy of a time…
Stochastic hybrid systems involve the coupling between discrete and continuous stochastic processes. They are finding increasing applications in cell biology, ranging from modeling promoter noise in gene networks to analyzing the effects of…
Path integrals have, over the years, proven to be an extremely versatile tool for simulating the dynamics of open quantum systems. The initial limitations of applicability of these methods in terms of the size of the system has steadily…
We show that the semi-classical analysis of generic Euclidean path integrals necessarily requires complexification of the action and measure, and consideration of complex saddle solutions. We demonstrate that complex saddle points have a…
Optimization has been widely used to generate smooth trajectories for motion planning. However, existing trajectory optimization methods show weakness when dealing with large-scale long trajectories. Recent advances in parallel computing…