The properties of hydrogen-helium mixtures at high pressure are crucial to address important questions about the interior of Giant planets e.g. whether Jupiter has a rocky core and did it emerge via core accretion? Using path integral Monte Carlo simulations, we study the properties of these mixtures as a function of temperature, density and composition. The equation of state is calculated and ...

This study presents a Feynman-Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...

The changes in the two-dimensional ~2D! He phase diagram due to the introduction of impurities ~Cs atoms! are estimated using path-integral Monte Carlo simulations. Our results indicate that when we increase the concentration of Cs atoms, the liquid-gas coexistence zone decreases in size and eventually disappears for sCs;0.005 Å , so that 2D He gases will be stable at low temperatures. @S0163-1...

A method to perform bosonization of a fermionic theory in (1 + 1) dimensions in a path integral framework is developed. The method relies exclusively on the path integral property of allowing variable shifts, and does not depend on the explicit form of Greens functions. Two examples, the Schwinger model and the massless Thirring model, are worked out. PACS numbers: 11.10.Kk; 11.15.Tk

Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical me...

The path integral formulation in quantum mechanics corresponds to the first quantization since it is just to rewrite the quantum mechanical amplitude into many dimensional integrations over discretized coordinates xn. However, the path integral expression cannot be connected to the dynamics of classical mechanics, even though, superficially, there is some similarity between them. Further, the f...

We present the theory of a two-dimensional conformal scalar field using path integral techniques. We derive the conformal anomaly using an adaptation of the method of Fujikawa, and compare the result with a derivation based on a Pauli-Villars measure, where the anomaly is shifted from the path integral measure to the energy-momentum trace. In the path integral approach the energy-momentum is a ...