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Phase transition in space: how far does a symmetry bend before it breaks?
1Theory Division, LANL, MS-B213, Los Alamos, NM 87545, USA. whzurek@gmail.com
Summary
We extend the Kibble-Zurek mechanism (KZM) to spatial phase transitions, revealing how spatial variations influence symmetry breaking. The resulting
Area of Science:
- Condensed Matter Physics
- Quantum Phase Transitions
- Non-equilibrium Dynamics
Background:
- The Kibble-Zurek mechanism (KZM) describes defect formation during non-equilibrium phase transitions.
- Symmetry breaking is fundamental to understanding phase transitions in physical systems.
Purpose of the Study:
- To extend the Kibble-Zurek mechanism (KZM) to spatial phase transitions.
- To analyze symmetry breaking dynamics driven by spatial field variations.
- To investigate the relationship between spatial scales and energy spectra in quantum phase transitions.
Main Methods:
- Theoretical extension of the Kibble-Zurek mechanism (KZM) to spatial transitions.
- Analysis of symmetry breaking in systems with time-independent spatial field gradients.
- Application to the transverse quantum Ising model.
Main Results:
- A KZM-like approach successfully describes the spatial scale of order parameter adjustment ('scar').
- Topological defects are not necessarily formed in spatial transitions.
- The spatial scar size directly correlates with the energy gap in quantum phase transitions.
Conclusions:
- The study provides a framework for understanding symmetry breaking in spatial phase transitions.
- The spatial KZM offers insights into defect-free transitions and their spectral signatures.
- The findings link macroscopic spatial scales to microscopic energy levels in quantum systems.
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