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Electrons in periodic potentials are open quantum systems susceptible to decoherence. This study corrects conditions for decoherence and calculates the coherent ion motion length scale in solid state physics.

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Area of Science:

  • Solid state physics
  • Quantum mechanics
  • Condensed matter physics

Background:

  • The Bloch theorem assumes electrons in periodic potentials form closed quantum systems, even in macroscopic crystals.
  • Realistic systems involve electron-ion interactions, leading to decoherence and dissipation.
  • The Ovchinnikov and Erikhman theory addresses decoherence due to ionic motion.

Purpose of the Study:

  • To revisit and correct the Ovchinnikov and Erikhman theory of decoherence.
  • To determine the conditions under which electrons in a periodic potential act as a closed quantum system.
  • To identify the primary causes of decoherence in such systems.

Main Methods:

  • Revisiting the seminal theory of Ovchinnikov and Erikhman.
  • Correcting an oversight in the original authors' work.
  • Calculating the length scale of coherent ion motion.

Main Results:

  • Corrected conditions for decoherence in electron-ion systems.
  • Quantified the length scale for coherent ionic motion.
  • Provided a revised physical picture of decoherence.

Conclusions:

  • Decoherence in periodic potentials is influenced by ionic motion.
  • The effective closed-system behavior of electrons has a finite length scale.
  • Understanding decoherence is crucial for solid-state quantum phenomena.