TY - JOUR
T1 - Spatio-temporal symmetry-Point groups with time translations
AU - Padmanabhan, Haricharan
AU - Kingsland, Maggie L.
AU - Munro, Jason M.
AU - Litvin, Daniel B.
AU - Gopalan, Venkatraman
N1 - Funding Information:
Acknowledgments: The authors thank Latham Boyle and Kendrick Smith for sharing their notes on platonic orbits and the character table method to obtain spatio-temporal groups. The authors also thank Jeremy Karl Cockcroft for giving permission to modify and use the stereographic projections from his online course on powder diffraction [20]. HP and VG acknowledge funding from the National Science Foundation (grants DMR 1210588 and DMR 1420620).
Publisher Copyright:
© 2017 by the authors.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by three-dimensional point group symmetry operations in combination with time translation operations are discussed in this work. The derivation of these 'spatio-temporal' groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing. The groups are presented in a template similar to space group operations, and are visualized using a modified version of conventional stereographic projections. Simple examples of physical processes that simultaneously exhibit symmetry in space and time are identified and used to illustrate the application of spatio-temporal groups.
AB - Spatial symmetries occur in combination with temporal symmetries in a wide range of physical systems in nature, including time-periodic quantum systems typically described by the Floquet formalism. In this context, groups formed by three-dimensional point group symmetry operations in combination with time translation operations are discussed in this work. The derivation of these 'spatio-temporal' groups from conventional point groups and their irreducible representations is outlined, followed by a complete listing. The groups are presented in a template similar to space group operations, and are visualized using a modified version of conventional stereographic projections. Simple examples of physical processes that simultaneously exhibit symmetry in space and time are identified and used to illustrate the application of spatio-temporal groups.
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U2 - 10.3390/sym9090187
DO - 10.3390/sym9090187
M3 - Article
AN - SCOPUS:85029435538
SN - 2073-8994
VL - 9
JO - Symmetry
JF - Symmetry
IS - 9
M1 - 187
ER -