Dynamics of the order parameter in symmetry breaking phase transitions
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911295666651136 |
|---|---|
| author | Suzuki, Fumika Zurek, Wojciech H. |
| author_facet | Suzuki, Fumika Zurek, Wojciech H. |
| contents | The formation of topological defects in second-order phase transitions can be investigated by solving partial differential equations for the evolution of the order parameter in space and time, such as the Langevin equation. We demonstrate that the ordinary differential equations governing either the temporal or spatial dependence in the Langevin equation provide surprisingly substantial insights into the dynamics of the phase transition. The temporal evolution of the order parameter predicts the essence of the adiabatic-impulse scenario, including the scaling of the freeze-out time, which is crucial to the Kibble-Zurek mechanism (KZM). In particular, Bernoulli differential equations that arise in the overdamped case can be solved analytically. The spatial part of the evolution, in turn, leads to the characteristic size of domains that choose the same broken symmetry. Apart from the fundamental insights into the KZM, this finding enables the exploration of Kibble-Zurek scaling using ordinary differential equations over a large range of quench timescales, which would otherwise be difficult to achieve with numerical simulations of the full partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15568 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of the order parameter in symmetry breaking phase transitions Suzuki, Fumika Zurek, Wojciech H. Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Quantum Physics The formation of topological defects in second-order phase transitions can be investigated by solving partial differential equations for the evolution of the order parameter in space and time, such as the Langevin equation. We demonstrate that the ordinary differential equations governing either the temporal or spatial dependence in the Langevin equation provide surprisingly substantial insights into the dynamics of the phase transition. The temporal evolution of the order parameter predicts the essence of the adiabatic-impulse scenario, including the scaling of the freeze-out time, which is crucial to the Kibble-Zurek mechanism (KZM). In particular, Bernoulli differential equations that arise in the overdamped case can be solved analytically. The spatial part of the evolution, in turn, leads to the characteristic size of domains that choose the same broken symmetry. Apart from the fundamental insights into the KZM, this finding enables the exploration of Kibble-Zurek scaling using ordinary differential equations over a large range of quench timescales, which would otherwise be difficult to achieve with numerical simulations of the full partial differential equations. |
| title | Dynamics of the order parameter in symmetry breaking phase transitions |
| topic | Statistical Mechanics General Relativity and Quantum Cosmology High Energy Physics - Phenomenology High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2412.15568 |