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Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
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Fabrication and Characterization of Disordered Polymer Optical Fibers for Transverse Anderson Localization of Light
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Published on: July 29, 2013

Critical Dynamics of the Anderson Transition on Small-World Graphs.

Weitao Chen1,2,3, Ignacio García-Mata4,5, John Martin6

  • 1National University of Singapore, Department of Physics, Singapore.

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|May 15, 2026
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Summary

We studied the Anderson transition on random graphs, a key model for quantum phase transitions and many-body localization. Our findings reveal unique dynamics and critical exponents, paving the way for quantum simulator experiments.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Dynamics
  • Disordered Systems

Background:

  • The Anderson transition on random graphs is a crucial model for high-dimensional quantum phase transitions.
  • It shares key features with many-body localization, a phenomenon in complex quantum systems.

Purpose of the Study:

  • To introduce and investigate a unitary Anderson model on small-world graphs.
  • To enable large-scale, long-time simulations of wave-packet dynamics.
  • To explore critical dynamics and universality classes of exotic transitions.

Main Methods:

  • Development of a unitary Anderson model on small-world graphs.
  • Conducting large-scale, long-time simulations of wave-packet dynamics.
  • Applying finite-time scaling analysis to determine critical exponents.

Main Results:

  • Uncovered logarithmically slow critical dynamics.
  • Identified two distinct localization times.
  • Observed a crossover from localized to ergodic diffusion.
  • Established a new dynamical universality class for the Anderson transition.

Conclusions:

  • The developed model facilitates the study of Anderson transitions and many-body localization.
  • It opens possibilities for experimental realization in quantum simulators.
  • Provides a framework for probing universal features of out-of-equilibrium quantum phenomena.