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Related Concept Videos

Crystal Field Theory - Octahedral Complexes02:58

Crystal Field Theory - Octahedral Complexes

Crystal Field Theory
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
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Atomic Force Microscopy

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The de Broglie Wavelength

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Fermi Level Dynamics01:12

Fermi Level Dynamics

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Related Experiment Video

Updated: Jun 8, 2026

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

Exploring complex phenomena using ultracold atoms in bichromatic lattices.

Shuming Li1, Indubala I Satija, Charles W Clark

  • 1JILA, NIST, Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
PubMed
Summary

This study connects the many-body Schrödinger equation in quasiperiodic potentials to classical mechanics

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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Condensed matter physics

Background:

  • The study of systems with competing length scales is crucial in physics.
  • The Kolmogorov-Arnold-Moser (KAM) problem describes the transition from regular to chaotic motion in classical Hamiltonian systems.

Purpose of the Study:

  • To investigate the many-body Schrödinger equation in a quasiperiodic potential.
  • To establish a connection between quantum phenomena and the classical KAM problem.
  • To identify experimentally accessible observables for probing distinct phases and nonlinear phenomena.

Main Methods:

  • Numerical treatment of the many-body Schrödinger equation.
  • Perturbative analysis to gain physical insights.
  • Development of many-body observables for visualization and characterization.

Main Results:

  • Identified a connection between quantum systems in quasiperiodic potentials and the classical KAM problem.
  • Proposed observables that probe metallic, Anderson insulator, and band insulator phases.
  • Observed fingerprints of nonlinear phenomena like bifurcations and devil's staircases.
  • Distinguished Anderson and band insulator phases using perturbation theory and dimerized states.

Conclusions:

  • The proposed observables provide a unified view of quantum and classical dynamics in systems with competing length scales.
  • Experimental measurements of these observables can reveal rich physics, including phase transitions and nonlinear behaviors.
  • Perturbation theory offers a valuable tool for understanding the fundamental differences between insulator phases.