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Related Concept Videos

Atomic Nuclei: Nuclear Relaxation Processes01:23

Atomic Nuclei: Nuclear Relaxation Processes

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...
Atomic Nuclei: Types of Nuclear Relaxation01:28

Atomic Nuclei: Types of Nuclear Relaxation

Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers energy to a nearby...
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...
Fermi Level Dynamics01:12

Fermi Level Dynamics

The vacuum level denotes the energy threshold required for an electron to escape from a material surface. It is usually positioned above the conduction band of a semiconductor and acts as a benchmark for comparing electron energies within various materials.
Electron affinity in semiconductors refers to the energy gap between the minimum of its conduction band and the vacuum level and it is a critical parameter in determining how easily a semiconductor can accept additional electrons.
The work...
Ampere-Maxwell's Law: Problem-Solving01:17

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...
Valence Bond Theory02:42

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

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Related Experiment Video

Updated: May 18, 2026

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

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

Published on: May 27, 2020

Solving condensed-matter ground-state problems by semidefinite relaxations.

Thomas Barthel1, Robert Hübener

  • 1Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany.

Physical Review Letters
|September 26, 2012
PubMed
Summary
This summary is machine-generated.

Researchers developed a new method for solving condensed-matter ground-state problems, offering strict lower bounds for ground-state energy. This approach, using semidefinite programs (SDP), is effective for fermionic and spin systems.

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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
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Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Related Experiment Videos

Last Updated: May 18, 2026

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

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

Published on: May 27, 2020

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
11:21

Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving

Published on: March 30, 2017

Area of Science:

  • Condensed Matter Physics
  • Quantum Many-Body Systems
  • Computational Physics

Background:

  • Variational techniques are common for condensed-matter ground-state problems.
  • Solving these problems directly in the thermodynamic limit is challenging.
  • Strongly correlated fermionic and frustrated spin systems require advanced computational methods.

Purpose of the Study:

  • To present a novel, generic approach to the condensed-matter ground-state problem.
  • To provide a method complementary to existing variational techniques.
  • To enable efficient computation of ground-state properties for various quantum systems.

Main Methods:

  • Relaxing the ground-state problem to formulate semidefinite programs (SDP).
  • Applying the SDP method to the thermodynamic limit.
  • Demonstrating the approach on the XXZ and Hubbard models for spinless fermions.

Main Results:

  • The SDP method yields strict lower bounds to the ground-state energy.
  • Approximations to few-particle Green's functions are obtained.
  • The method is applicable to all particle statistics, including fermions and spins.

Conclusions:

  • The SDP method offers a competitive and efficient route for studying strongly correlated systems.
  • It provides a powerful alternative to existing computational techniques.
  • The approach is particularly valuable for systems in dimensions greater than one.