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Related Concept Videos

First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...
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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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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

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Setting Limits on Supersymmetry Using Simplified Models
07:46

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Published on: November 15, 2013

Odd-particle systems in the shell model Monte Carlo method: circumventing a sign problem.

Abhishek Mukherjee1, Y Alhassid

  • 1Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520, USA.

Physical Review Letters
|August 7, 2012
PubMed
Summary

This study overcomes the sign problem in shell model Monte Carlo simulations for odd-particle systems. The new method accurately calculates ground-state energies and pairing gaps in atomic nuclei.

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Area of Science:

  • Nuclear Physics
  • Computational Physics
  • Quantum Many-Body Systems

Background:

  • Shell Model Monte Carlo (SMMC) is effective for finite-size systems.
  • The sign problem hinders SMMC application to odd-particle number systems.
  • Accurate calculation of ground-state properties for odd-particle systems is challenging.

Purpose of the Study:

  • To develop a method to circumvent the sign problem in SMMC for odd-particle systems.
  • To accurately determine ground-state energies of odd-particle number systems.
  • To calculate pairing gaps in atomic nuclei.

Main Methods:

  • Extracting odd-system ground-state energy from even-system Green's function asymptotics.
  • Utilizing imaginary-time single-particle Green's function.
  • Applying the method to nuclei in the iron region.

Main Results:

  • Successfully circumvented the sign problem for ground-state energy calculations.
  • Calculated pairing gaps for iron region nuclei.
  • Achieved good agreement between calculated and experimental pairing gaps.

Conclusions:

  • The developed method provides a viable solution to the sign problem in SMMC for odd-particle systems.
  • This approach enables accurate predictions of nuclear pairing gaps.
  • The findings have implications for understanding nuclear structure and properties.