Dualities and non-Abelian mechanics

doi:10.1038/s41586-020-1932-6

GSTDTAP > 地球科学

DOI	10.1038/s41586-020-1932-6
	Dualities and non-Abelian mechanics
	Song, Xinyang 1; Sun, Ximei 1; Oh, Sungwhan F.1,2; Wu, Meng 1; Zhang, Yanbo 1; Zheng, Wen 1; Geva-Zatorsky, Naama 1,4; Jupp, Ray 3; Mathis, Diane 1; Benoist, Christophe 1; Kasper, Dennis L.1
	2020-01-16
发表期刊	NATURE
ISSN	0028-0836
EISSN	1476-4687
出版年	2020
卷号	577 期号:7792 页码:636-+
文章类型	Article
语种	英语
国家	USA; Netherlands
英文关键词	Dualities-mathematical mappings between different systems-can act as hidden symmetries that enable materials design beyond that suggested by crystallographic space groups. Dualities are mathematical mappings that reveal links between apparently unrelated systems in virtually every branch of physics(1-8). Systems mapped onto themselves by a duality transformation are called self-dual and exhibit remarkable properties, as exemplified by the scale invariance of an Ising magnet at the critical point. Here we show how dualities can enhance the symmetries of a dynamical matrix (or Hamiltonian), enabling the design of metamaterials with emergent properties that escape a standard group theory analysis. As an illustration, we consider twisted kagome lattices(9-15), reconfigurable mechanical structures that change shape by means of a collapse mechanism(9). We observe that pairs of distinct configurations along the mechanism exhibit the same vibrational spectrum and related elastic moduli. We show that these puzzling properties arise from a duality between pairs of configurations on either side of a mechanical critical point. The critical point corresponds to a self-dual structure with isotropic elasticity even in the absence of spatial symmetries and a twofold-degenerate spectrum over the entire Brillouin zone. The spectral degeneracy originates from a version of Kramers' theorem(16,17) in which fermionic time-reversal invariance is replaced by a hidden symmetry emerging at the self-dual point. The normal modes of the self-dual systems exhibit non-Abelian geometric phases(18,19) that affect the semiclassical propagation of wavepackets(20), leading to non-commuting mechanical responses. Our results hold promise for holonomic computation(21) and mechanical spintronics by allowing on-the-fly manipulation of synthetic spins carried by phonons.
领域	地球科学 ; 气候变化 ; 资源环境
收录类别	SCI-E
WOS记录号	WOS:000508324600002
WOS关键词	WAVE-PACKET DYNAMICS ; BERRY-PHASE ; GEOMETRIC PHASE ; GAUGE STRUCTURE ; CHERN NUMBER ; QUANTUM ; STATISTICS ; REALIZATION ; DEGENERACY ; PHONONS
WOS类目	Multidisciplinary Sciences
WOS研究方向	Science & Technology - Other Topics
引用统计
文献类型	期刊论文
条目标识符	http://119.78.100.173/C666/handle/2XK7JSWQ/281226
专题	地球科学资源环境科学气候变化
作者单位	1.Harvard Med Sch, Blavatnik Inst, Dept Immunol, Boston, MA 02115 USA; 2.Harvard Med Sch, Ctr Expt Therapeut & Reperfus Injury, Brigham & Womens Hosp, Dept Anesthesiol Perioperat & Pain Med, Boston, MA 02115 USA; 3.UCB Pharma, Slough, Berks, England; 4.Technion Israel Inst Technol, Technion Integrated Canc Ctr, Dept Cell Biol & Canc Sci, Rappaport Fac Med, Haifa, Israel
推荐引用方式 GB/T 7714	Song, Xinyang,Sun, Ximei,Oh, Sungwhan F.,et al. Dualities and non-Abelian mechanics[J]. NATURE,2020,577(7792):636-+.
APA	Song, Xinyang.,Sun, Ximei.,Oh, Sungwhan F..,Wu, Meng.,Zhang, Yanbo.,...&Kasper, Dennis L..(2020).Dualities and non-Abelian mechanics.NATURE,577(7792),636-+.
MLA	Song, Xinyang,et al."Dualities and non-Abelian mechanics".NATURE 577.7792(2020):636-+.