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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Equilibration of a one-dimensional Wigner crystal
K A Matveev1, A V Andreev, M Pustilnik
1Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA.
Physical Review Letters
|September 28, 2010
Summary
Slow relaxation in one-dimensional interacting electron systems at low temperatures is studied. We investigate spinless electrons forming a Wigner crystal, finding relaxation rates influenced by phonon umklapp scattering. For specific models, the relaxation rate vanishes.
Area of Science:
- Condensed Matter Physics
- Quantum Mechanics
- Materials Science
Background:
- One-dimensional (1D) interacting electron systems exhibit slow relaxation at low temperatures due to suppressed processes changing particle numbers.
- Understanding these relaxation dynamics is crucial for comprehending the approach to equilibrium in quantum systems.
Purpose of the Study:
- To investigate the relaxation rate of a 1D system of spinless electrons with strong long-range repulsion, specifically when they form a Wigner crystal.
- To analyze the role of umklapp scattering of phonons in the Wigner crystal on the system's relaxation dynamics.
Main Methods:
- Theoretical analysis of a 1D system of interacting spinless electrons.
- Modeling electron behavior as a Wigner crystal due to strong long-range repulsion.
- Incorporating umklapp scattering of phonons within the Wigner crystal model to determine relaxation rates.
Main Results:
- Identified that umklapp scattering of phonons significantly influences the relaxation rate towards equilibrium in the 1D Wigner crystal.
- Determined that for the integrable model with inverse-square repulsion, the relaxation rate vanishes, indicating persistent non-equilibrium behavior.
Conclusions:
- The study elucidates the mechanisms behind slow relaxation in 1D Wigner crystals at low temperatures.
- The vanishing relaxation rate in specific integrable models highlights the importance of interactions and scattering processes in determining system dynamics.
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