Related Experiment Video
Updated: Aug 19, 2025

Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Exploring bifurcations in Bose-Einstein condensates via phase field crystal models.
A B Steinberg1, F Maucher2, S V Gurevich1
1Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany.
We developed a phase field crystal model approximation for Bose-Einstein condensates near the superfluid-supersolid transition. This model simplifies analyzing pattern formation and phase transitions, revealing localized states.
Area of Science:
- Condensed matter physics
- Quantum mechanics
- Nonlinear dynamics
Background:
- Bose-Einstein condensates exhibit complex pattern formation and phase transitions.
- Analyzing these phenomena often involves computationally intensive nonlocal equations like the Gross-Pitaevskii equation.
Purpose of the Study:
- To develop an approximate mapping from the Gross-Pitaevskii equation to a phase field crystal model.
- To facilitate the analysis of pattern formation and phase transitions in Bose-Einstein condensates near the superfluid-supersolid boundary.
Main Methods:
- Approximate mapping of the nonlocal Gross-Pitaevskii equation to a phase field crystal (PFC) model.
- Numerical path continuation using standard software to explore bifurcations and phase transitions.
- Analysis of localized states within the PFC approximation.
Main Results:
- An explicit approximate mapping to a simplified PFC model is established, valid near the superfluid-supersolid phase transition.
- The simplified PFC model allows for the exploration of bifurcations and phase transitions.
- The existence of localized states in the PFC approximation is demonstrated.
- The influence of higher-order nonlinearities on the bifurcation diagram is discussed.
Conclusions:
- The phase field crystal model provides a tractable framework for studying phase transitions in Bose-Einstein condensates.
- The approximation reveals detailed bifurcation structures and the presence of localized states.
- Further investigation into nonlinearities can refine the understanding of system transitions.
More Related Videos
06:26Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
08:44Measurements of Long-range Electronic Correlations During Femtosecond Diffraction Experiments Performed on Nanocrystals of Buckminsterfullerene
Published on: August 22, 2017
Related Concept Videos
Phase Transitions: Vaporization and Condensation
Crystal Field Theory - Octahedral Complexes
To explain the observed behavior of transition metal complexes (such as colors), a model involving electrostatic interactions between the electrons from the ligands and the electrons in the unhybridized d orbitals of the central metal atom has been developed. This electrostatic model is crystal field theory (CFT). It helps to understand, interpret, and predict the colors, magnetic behavior, and some structures of coordination compounds of transition metals.
CFT focuses on...
Crystal Field Theory - Tetrahedral and Square Planar Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Phase Transitions: Melting and Freezing
Phase Transitions
Phase Transitions: Sublimation and Deposition