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Register a new userDynamics of Dirac solitons in networks
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We study dynamics of Dirac solitons in prototypical networks modeling them by the nonlinear Dirac equation on metric graphs. Soliton solutions of the nonlinear Dirac equation on simple metric graphs are obtained. It is shown that these solutions provide reflectionless vertex transmission of the Dirac solitons under suitable conditions. The constraints for bond nonlinearity coefficients, allowing reflectionless transmission over a Y-junction are derived. The analytical results are confirmed by direct numerical simulations.
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New functionalities in nonlinear optics will require systems with giant optical nonlinearity as well as compatibility with photonic circuit fabrication techniques. Here we introduce a new platform based on strong light-matter coupling between waveguide photons and quantum-well excitons. On a sub-millimeter length scale we generate sub-picosecond bright temporal solitons at a pulse energy of only 0.5 pico-Joules. From this we deduce an unprecedented nonlinear refractive index 3 orders of magnitude larger than in any other ultrafast system. We study both temporal and spatio-temporal nonlinear effects and for the first time observe dark-bright spatio-temporal solitons. Theoretical modelling of soliton formation in the strongly coupled system confirms the experimental observations. These results show the promise of our system as a high speed, low power, integrated platform for physics and devices based on strong interactions between photons.
Quasiparticle approach to dynamics of dark solitons is applied to the case of ring solitons. It is shown that the energy conservation law provides the effective equations of motion of ring dark solitons for general form of the nonlinear term in the generalized nonlinear Schroedinger or Gross-Pitaevskii equation. Analytical theory is illustrated by examples of dynamics of ring solitons in light beams propagating through a photorefractive medium and in non-uniform condensates confined in axially symmetric traps. Analytical results agree very well with the results of our numerical simulations.
In this paper we present the results of parallel numerical computations of the long-term dynamics of linked vortex filaments in a three-dimensional FitzHugh-Nagumo excitable medium. In particular, we study all torus links with no more than 12 crossings and identify a timescale over which the dynamics is regular in the sense that each link is well-described by a spinning rigid conformation of fixed size that propagates at constant speed along the axis of rotation. We compute the properties of these links and demonstrate that they have a simple dependence on the crossing number of the link for a fixed number of link components. Furthermore, we find that instabilities that exist over longer timescales in the bulk can be removed by boundary interactions that yield stable torus links which settle snugly at the medium boundary. The Borromean rings are used as an example of a non-torus link to demonstrate both the irregular tumbling dynamics that arises in the bulk and its suppression by a tight confining medium. Finally, we investigate the collision of torus links and reveal that this produces a complicated wrestling motion where one torus link can eventually dominate over the other by pushing it into the boundary of the medium.
We study the transverse instability and dynamics of bright soliton stripes in two-dimensional nonlocal nonlinear media. Using a multiscale perturbation method, we derive analytically the first-order correction to the soliton shape, which features an exponential growth in time -- a signature of the transverse instability. The solitons characteristic timescale associated with its exponential growth,is found to depend on the square root of the nonlocality parameter. This, in turn, highlights the nonlocality-induced suppression of the transverse instability. Our analytical predictions are corroborated by direct numerical simulations, with the analytical results being in good agreement with the numerical ones.
We study the multicritical behavior for the semimetal-insulator transitions on graphenes honeycomb lattice using the Gross-Neveu-Yukawa effective theory with two order parameters: the SO(3) (Heisenberg) order parameter describes the antiferromagnetic transition, and the $mathbb{Z}_2$ (Ising) order parameter describes the transition to a staggered density state. Their coupling induces multicritical behavior which determines the structure of the phase diagram close to the multicritical point. Depending on the number of fermion flavors $N_f$ and working in the perturbative regime in vicinity of three (spatial) dimensions, we observe first order or continuous phase transitions at the multicritical point. For the graphene case of $N_f=2$ and within our low order approximation, the phase diagram displays a tetracritical structure.
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