Symmetry (physics)

About: Symmetry (physics) is a research topic. Over the lifetime, 26435 publications have been published within this topic receiving 500189 citations. The topic is also known as: symmetry (physics) & physical symmetry.

Robust heteroclinic cycles

Abstract: One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving perturbations and stable. Cycles have been observed in a number of simulations and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some low codimension bifurcations and in the context of forced symmetry breaking from a larger to a smaller symmetry group. In this article we review the theoretical and the applied research on robust cycles.

Renormalizable models with simple symmetry breaking. i. symmetry breaking by a source term.

Abstract: If to a Lagrangian density with invariance under a continuous group of linear transformations of the fields a term linear or bilinear in the fields is added, the symmetry is in general reduced and the currents associated with the original symmetry are only partially conserved. If the theory without the added term is renormalizable, the theory with that term also is, and the needed renormalization conditions are the essential content of the appropriate Ward-Takahashi-Kazes-Rivers identities. The case of symmetry breaking by a term linear in Bose fields (source term) is here analysed completely, in particular with respect to the nonsymmetric limit of vanishing source term, a particular Goldstone mode, and with respect to properties of the ground state energy density as a function of the strength of the source term. Induced and spontaneous breaking of a discrete symmetry are also treated.

On 2-group global symmetries and their anomalies

Abstract: In general quantum field theories (QFTs), ordinary (0-form) global symmetries and 1-form symmetries can combine into 2-group global symmetries. We describe this phenomenon in detail using the language of symmetry defects. We exhibit a simple procedure to determine the (possible) 2-group global symmetry of a given QFT, and provide a classification of the related ’t Hooft anomalies (for symmetries not acting on spacetime). We also describe how QFTs can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory. Finally, we provide a variety of examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way, we stress that the “obstruction to symmetry fractionalization” discussed in some condensed matter literature is really an instance of 2-group global symmetry.

Electric polarization of heteropolar nanotubes as a geometric phase.

Abstract: The threefold symmetry of planar boron nitride (BN), the III-V analog to graphene, prohibits an electric polarization in its ground state, but this symmetry is broken when the sheet is wrapped to form a BN nanotube. We show that this leads to an electric polarization along the nanotube axis which is controlled by the quantum mechanical boundary conditions on its electronic states around the tube circumference. Thus the macroscopic dipole moment has an intrinsically nonlocal quantum mechanical origin from the wrapped dimension. We formulate this novel phenomenon using the Berry's phase approach and discuss its experimental consequences.