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Glauber model in a quantum representation.

Thomas Michael1, Steffen Trimper, Michael Schulz

  • 1Fachbereich Physik, Martin-Luther-Universität, D-06099 Halle, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 16, 2006
PubMed
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This study revisits the Glauber model using quantum mechanics, revealing a new transition rate formula. The quantum Glauber model shows low-temperature behavior governed by Ising energy, not time scales.

Area of Science:

  • Statistical Mechanics
  • Quantum Mechanics
  • Condensed Matter Physics

Background:

  • The Glauber model is a standard for understanding magnetic systems dynamics.
  • Conventional models often simplify temperature and energy interactions.
  • A quantum approach offers a more rigorous framework for these dynamics.

Purpose of the Study:

  • To re-evaluate the Glauber model using a quantum master equation.
  • To incorporate temperature and Ising energy from the outset.
  • To derive an exact transition rate for single spin-flip processes.

Main Methods:

  • Formulation of a quantum master equation.
  • Introduction of a Heisenberg-like picture for second-quantized operators.
  • Derivation of the single spin-flip transition rate.

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Main Results:

  • An exact expression for the transition rate w(i)(sigma(i)) was obtained.
  • The derived rate adheres to the principle of detailed balance.
  • Significant deviations from the conventional Glauber model were observed at low temperatures.

Conclusions:

  • The quantum formulation provides a more accurate description of the Glauber model.
  • Low-temperature dynamics are primarily dictated by Ising energy.
  • This quantum approach offers new insights into magnetic system behavior.