Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/0306168

Numerical path integration with Coulomb potential

Jan Myrheim

Published Jun 24, 2003• 1 citation
arXivHTMLPDF

Abstract

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.
DOI
10.48550/arxiv.physics/0306168

Related papers

Path Integrals in Quantum Physics

Rosenfelder, R.

These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the usual heuristic, non-mathematical way for application in many diverse problems in quantum physics. Three main parts deal with path integrals in non-relativistic quantum mechanics, many-body physics and field theory and contain standard examples (quadratic Lagrangians, tunneling, description of bosons and fermions, quantization of gauge theories etc.) as well as specialized topics (scattering, dissipative systems, spin \& color in the path integral, lattice methods etc.). In each part simple Fortran programs which can be run on a PC, illustrate the numerical evaluation of (Euclidean) path integrals by Monte-Carlo or variational methods. Also included are the set of problems which accompanied the lectures and their solutions.

arXiv:1209.1315•Sep 6, 2012•3 citations

Fast Converging Path Integrals for Time-Dependent Potentials

Antun Balaž, Ivana Vidanović, Aleksandar Bogojević +1 more

We calculate the short-time expansion of the propagator for a general many-body quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte-Carlo simulations for path integrals, or to set up various analytic approximation techniques to study dynamic properties of quantum systems in timedependent potentials. The analytically derived results are numerically verified by treating several simple one-dimensional models.

•Dec 14, 2009•0 citations

Monte Carlo Simulations of Quantum Integrations

Shi You

Integrations in quantum calculations are formulated by a same form equation. Effect of calculations and stability of results are raised by using Monte Carlo method and putting all integrations in a same for-loop.

Journal of Yancheng Institute of Technology•Jan 1, 2002•0 citations

Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

Antun Balaž, Ivana Vidanović, Aleksandar Bogojević +2 more

In this and subsequent paper [1] we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.

•Jan 1, 2011•12 citations

Path Integral Monte-Carlo method for relativistic quantum systems

Oleg Pavlovsky, Aleksandr Ivanov, Alexander Novoselov

Relativistic generalization of Path Integral Monte-Carlo method has been proposed and some possible applications have been discussed.

arXiv:1410.8832•International Symposium on Lattice Field Theory (LATTICE)•May 21, 2015•0 citations

Analytically continued physical states in the path-integral: a sign-problem-free Quantum Monte Carlo simulation of Bell states dynamics

Evgeny Polyakov, Alexey N. Rubtsov

The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This leads to a practical algorithm of sign-problem-free Monte Carlo sampling from the Gaussian path integrals. Moreover, the dynamical influence of Gaussian quantum system (the bath) on any other quantum system can be exactly represented as interaction with classical non-Markovian noise. We discuss the relation of these findings to the Bell's theorem and the Feynman's conjecture on the exponential complexity of the classical simulation of quantum systems. In Feynman's path integral we have quasiprobability distributions for trajectories, and in analitycally continued path integrals we have probability distributions for quasitrajectories.

arXiv:1610.08964•Oct 25, 2016•0 citations
These lectures are intended for graduate students who want to acquire a working knowledge of path integral methods in a wide variety of fields in physics. In general the presentation is elementary and path integrals are developed in the usual heuristic, non-mathematical way for application in many diverse problems in quantum physics. Three main parts deal with path integrals in non-relativistic quantum mechanics, many-body physics and field theory and contain standard examples (quadratic Lagrangians, tunneling, description of bosons and fermions, quantization of gauge theories etc.) as well as specialized topics (scattering, dissipative systems, spin \& color in the path integral, lattice methods etc.). In each part simple Fortran programs which can be run on a PC, illustrate the numerical evaluation of (Euclidean) path integrals by Monte-Carlo or variational methods. Also included are the set of problems which accompanied the lectures and their solutions.
We calculate the short-time expansion of the propagator for a general many-body quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte-Carlo simulations for path integrals, or to set up various analytic approximation techniques to study dynamic properties of quantum systems in timedependent potentials. The analytically derived results are numerically verified by treating several simple one-dimensional models.
In this and subsequent paper [1] we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models.
The derivation of path integrals is reconsidered. It is shown that the expression for the discretized action is not unique, and the path integration domain can be deformed so that at least Gaussian path integrals become probabillistic. This leads to a practical algorithm of sign-problem-free Monte Carlo sampling from the Gaussian path integrals. Moreover, the dynamical influence of Gaussian quantum system (the bath) on any other quantum system can be exactly represented as interaction with classical non-Markovian noise. We discuss the relation of these findings to the Bell's theorem and the Feynman's conjecture on the exponential complexity of the classical simulation of quantum systems. In Feynman's path integral we have quasiprobability distributions for trajectories, and in analitycally continued path integrals we have probability distributions for quasitrajectories.