
During, G., Josserand, C., & Rica, S. (2015). Selfsimilar formation of an inverse cascade in vibrating elastic plates. Phys. Rev. E, 91(5), 10 pp.
Abstract: The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of a timedependent inverse cascade, opening up the possibility of selforganization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the shortwave fluctuations. This dynamics appears to be selfsimilar and possesses a powerlaw behavior in the shortwavelength limit which significantly differs from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a longwave coherent structure in finite time.



Hojman, S. A., & Asenjo, F. A. (2015). Supersymmetric Majorana quantum cosmologies. Phys. Rev. D, 92(8), 7 pp.
Abstract: The Einstein equations for an isotropic and homogeneous FriedmannRobertsonWalker universe in the presence of a quintessence scalar field are shown to be described in a compact way, formally identical to the dynamics of a relativistic particle moving on a twodimensional spacetime. The correct Lagrangian for the system is presented and used to construct a spinor quantum cosmology theory using Breit's prescription. The theory is supersymmetric when written in the Majorana representation. The spinor field components interact through a potential that correlates the spacetime metric and the quintessence. An exact supersymmetric solution for k = 0 case is exhibited. This quantum cosmology model may be interpreted as a theory of interacting universes.



Mellado, P., Petrova, O., & Tchernyshyov, O. (2015). Projective symmetry of partons in the Kitaev honeycomb model. Phys. Rev. B, 91(4), 4 pp.
Abstract: Lowenergy states of quantum spin liquids are thought to involve partons living in a gaugefield background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with halfinteger orbital angular momenta. As a consequence, the multiplicities do not reflect the pointgroup symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.



Petrova, O., Mellado, P., & Tchernyshyov, O. (2013). Unpaired Majorana modes in the gapped phase of Kitaev's honeycomb model. Phys. Rev. B, 88(14), 4 pp.
Abstract: We study the gapped phase of Kitaev's honeycomb model (a Z(2) spin liquid) in the presence of lattice defects. We find that some dislocations and bond defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z(2) gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z(2) vortex around a dislocation. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes.



Petrova, O., Mellado, P., & Tchernyshyov, O. (2014). Unpaired Majorana modes on dislocations and string defects in Kitaev's honeycomb model. Phys. Rev. B, 90(13), 14 pp.
Abstract: We study the gapped phase of Kitaev's honeycomb model (a Z(2) spin liquid) on a lattice with topological defects. We find that some dislocations and string defects carry unpaired Majorana fermions. Physical excitations associated with these defects are (complex) fermion modes made out of two (real) Majorana fermions connected by a Z(2) gauge string. The quantum state of these modes is robust against local noise and can be changed by winding a Z(2) vortex around one of the dislocations. The exact solution respects gauge invariance and reveals a crucial role of the gauge field in the physics of Majorana modes. To facilitate these theoretical developments, we recast the degenerate perturbation theory for spins in the language of Majorana fermions.

