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Related Concept Videos

Lattice Energies of Ionic Crystals01:27

Lattice Energies of Ionic Crystals

Lattice energy represents the energy released when gaseous cations and anions combine to form an ionic solid, reflecting the strength of electrostatic interactions within the crystal. This process is fundamentally governed by Coulombic attraction between oppositely charged ions, where the potential energy varies inversely with the interionic distance and directly with the product of ionic charges. As ions approach one another, the electrostatic energy becomes increasingly negative, indicating a...
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The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
Trends in Lattice Energy: Ion Size and Charge02:54

Trends in Lattice Energy: Ion Size and Charge

An ionic compound is stable because of the electrostatic attraction between its positive and negative ions. The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid sodium chloride, the lattice energy is the enthalpy change of the process:
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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The Uncertainty Principle

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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
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Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

Efficient perturbation theory for quantum lattice models.

H Hafermann1, G Li, A N Rubtsov

  • 1I. Institute for Theoretical Physics, University of Hamburg, 20355 Hamburg, Germany.

Physical Review Letters
|June 13, 2009
PubMed
Summary

We introduce a new dual fermion method for studying long-range correlations. This approach improves convergence and accurately predicts critical Néel temperatures, outperforming standard techniques.

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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

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Last Updated: Jun 22, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

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Published on: May 27, 2020

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Area of Science:

  • Condensed matter physics
  • Quantum magnetism

Background:

  • Dynamical mean-field theory (DMFT) is a powerful tool for studying strongly correlated systems.
  • However, DMFT struggles to accurately capture long-range correlations.

Purpose of the Study:

  • To develop a novel method for describing long-range correlations beyond DMFT.
  • To apply this method to the two-dimensional Hubbard model.

Main Methods:

  • Utilizing a ladder approximation to dual fermions.
  • Transforming the perturbation series for nonlocal dual fermions.

Main Results:

  • The new technique demonstrates superior convergence compared to standard diagrammatic methods.
  • The critical Néel temperature is suppressed in the ladder approximation, aligning with quantum Monte Carlo results.
  • The method effectively distinguishes between short- and long-range correlations.

Conclusions:

  • The ladder approximation to dual fermions offers a promising approach for studying complex quantum systems.
  • This method enhances the understanding of magnetic properties in models like the 2D Hubbard model.