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Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
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Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry
12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Exact ground state Monte Carlo method for Bosons without importance sampling.

M Rossi1, M Nava, L Reatto

  • 1Dipartimento di Fisica, Università degli Studi di Milano, via Celoria 16, 20133 Milano, Italy. maurizio.rossi@unimi.it

The Journal of Chemical Physics
|June 24, 2010
PubMed
Summary
This summary is machine-generated.

Path Integral Ground State (PIGS) Monte Carlo simulations for bosons can yield unbiased exact results without importance sampling. The initial wave function does not affect the imaginary time propagator, ensuring accuracy in quantum Monte Carlo computations.

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Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

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Last Updated: Jun 12, 2026

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12:11

Computation of Atmospheric Concentrations of Molecular Clusters from ab initio Thermochemistry

Published on: April 8, 2020

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

Area of Science:

  • Quantum Monte Carlo methods
  • Many-body physics
  • Condensed matter theory

Background:

  • Exact quantum Monte Carlo computations for many-boson ground states typically employ importance sampling.
  • Importance sampling relies on guiding or initial variational wave functions.
  • Path Integral Ground State (PIGS) Monte Carlo uses discrete imaginary time evolution.

Purpose of the Study:

  • To investigate the necessity of importance sampling in PIGS Monte Carlo.
  • To determine if finite-time PIGS computations yield unbiased exact results.
  • To analyze the impact of the initial wave function on PIGS accuracy.

Main Methods:

  • Studied bulk liquid and solid Helium-4 using PIGS.
  • Employed a constant initial wave function (ideal Bose gas ground state) to avoid importance sampling.
  • Compared PIGS results with those from variational (shadow) wave functions.
  • Examined both diagonal and off-diagonal properties.

Main Results:

  • PIGS results converged to those obtained with optimal variational wave functions, even with an improper initial state.
  • Accuracy was maintained for diagonal properties (energy, radial distribution, structure factor) and off-diagonal properties (one-body density matrix).
  • The initial wave function's influence is limited to the start of the path, not affecting the propagator.

Conclusions:

  • Zero-temperature PIGS calculations are as unbiased as finite-temperature path integral Monte Carlo.
  • The robustness of PIGS is due to the initial wave function not influencing the imaginary time propagator.
  • A well-chosen initial wave function can significantly accelerate convergence to exact ground state results.