Breaking Symmetry with Light: Ultra-Fast Ferroelectricity and Magnetism from Three-Phonon Coupling

A theory describing how ferroic properties can emerge transiently in the ultra-fast regime by breaking symmetry with light through three-phonon coupling is presented. Particular emphasis is placed on the special case when two exactly degenerate mid-infra-red or THz phonons are resonantly pumped, since this situation can give rise to an exactly rectified ferroic response with damping envelopes of ~ 1 ps or less. Light-induced ferroelectricity and ferromagnetism are discussed in this context, and a number of candidate materials that could display these phenomena are proposed. The same analysis is also applied to the interpretation of previous femto-magnetism experiments, performed in different frequency ranges (visible and near-infrared), but sharing similar symmetry characteristics.Comment: 10 page

Groups of virtual and welded links

We define new notions of groups of virtual and welded knots (or links) and we study their relations with other invariants, in particular the Kauffman group of a virtual knot.Comment: 22 pages, 7 figure

Representations of Braid Groups and Generalisations

We define and study extensions of Artin's representation and braid monodromy representation to the case of topological and algebraical generalisations of braid groups. In particular we provide faithful representations of braid groups of oriented surfaces with boundary components as (outer) automorphisms of free groups. We give also similar representations for braid groups of non oriented surfaces with boundary components and we show a representation of braid groups of closed surfaces as outer automorphisms of free groups. Finally, we provide faithful representations of Artin-Tits groups of type $\mathcal{D}$ as automorphisms of free groups.Comment: Few misprints corrected, simpler proof for proposition 1

The Levi Decomposition of a Graded Lie Algebra

We show that a graded Lie algebra admits a Levi decomposition that is compatible with the grading