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Causality and non-equilibrium second-order phase transitions in inhomogeneous systems
A del Campo1, T W B Kibble, W H Zurek
1Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
Journal of Physics. Condensed Matter : an Institute of Physics Journal
|September 13, 2013
Summary
Crossing second-order phase transitions rapidly creates topological defects. Inhomogeneous systems suppress defect formation due to causality, but the defect density still follows a power law with quench rate, aiding experimental tests.
Area of Science:
- Condensed Matter Physics
- Statistical Mechanics
- Cosmic String Formation
Background:
- Second-order phase transitions at finite rates lead to non-adiabatic evolution and critical slowing down.
- Topologically nontrivial vacuum manifolds can result in the formation of topological defects during phase transitions.
- The density of these defects is typically related to the quench rate and critical exponents.
Purpose of the Study:
- To investigate the formation of topological defects in inhomogeneous systems during rapid phase transitions.
- To analyze the interplay between spontaneous symmetry breaking and inherited symmetry breaking in defect formation.
- To understand how causality influences defect density and its dependence on the quench rate.
Main Methods:
- Theoretical analysis of second-order phase transitions in systems with topologically nontrivial vacuum manifolds.
- Modeling the competition between spontaneous symmetry breaking and inherited symmetry breaking in inhomogeneous media.
- Investigating the role of front velocity and sound velocity in restricting defect formation.
Main Results:
- Inhomogeneous systems can substantially suppress the overall number of topological defects.
- Defect formation is restricted to regions where the transition front velocity exceeds the sound velocity.
- For small system fractions, the total defect number still follows a power law of the quench rate, with a more pronounced dependence.
Conclusions:
- Causality plays a crucial role in defect formation during rapid phase transitions in inhomogeneous systems.
- The enhanced dependence of defect density on the quench rate in such systems may facilitate experimental verification of defect formation theories.
- Understanding these dynamics is essential for fields ranging from condensed matter physics to cosmology.
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