Floquet band structure of a semi-Dirac system

In this work we use Floquet-Bloch theory to study the influence of circularly and linearly polarized light on two-dimensional band structures with semi-Dirac band touching points, taking the anisotropic nearest neighbor hopping model on the honeycomb lattice as an example. We find circularly polarized light opens a gap and induces a band inversion to create a finite Chern number in the two-band model. By contrast, linearly polarized light can either open up a gap (polarized in the quadratically dispersing direction) or split the semi-Dirac band touching point into two Dirac points (polarized in the linearly dispersing direction) by an amount that depends on the amplitude of the light. Motivated by recent pump-probe experiments, we investigated the non-equilibrium spectral properties and momentum-dependent spin-texture of our model in the Floquet state following a quench in absence of phonons, and in the presence of phonon dissipation that leads to a steady-state independent of the pump protocol. Finally, we make connections to optical measurements by computing the frequency dependence of the longitudinal and transverse optical conductivity for this two-band model. We analyze the various contributions from inter-band transitions and different Floquet modes. Our results suggest strategies for optically controlling band structures and experimentally measuring topological Floquet systems.Comment: 17 pages, 8 figure

Designing Network Protocols for Good Equilibria

Designing and deploying a network protocol determines the rules by which end users interact with each other and with the network. We consider the problem of designing a protocol to optimize the equilibrium behavior of a network with selfish users. We consider network cost-sharing games, where the set of Nash equilibria depends fundamentally on the choice of an edge cost-sharing protocol. Previous research focused on the Shapley protocol, in which the cost of each edge is shared equally among its users. We systematically study the design of optimal cost-sharing protocols for undirected and directed graphs, single-sink and multicommodity networks, and different measures of the inefficiency of equilibria. Our primary technical tool is a precise characterization of the cost-sharing protocols that induce only network games with pure-strategy Nash equilibria. We use this characterization to prove, among other results, that the Shapley protocol is optimal in directed graphs and that simple priority protocols are essentially optimal in undirected graphs

Authentication with Distortion Criteria

In a variety of applications, there is a need to authenticate content that has experienced legitimate editing in addition to potential tampering attacks. We develop one formulation of this problem based on a strict notion of security, and characterize and interpret the associated information-theoretic performance limits. The results can be viewed as a natural generalization of classical approaches to traditional authentication. Additional insights into the structure of such systems and their behavior are obtained by further specializing the results to Bernoulli and Gaussian cases. The associated systems are shown to be substantially better in terms of performance and/or security than commonly advocated approaches based on data hiding and digital watermarking. Finally, the formulation is extended to obtain efficient layered authentication system constructions.Comment: 22 pages, 10 figure

Is the Kelvin Theorem Valid for High-Reynolds-Number Turbulence?

The Kelvin-Helmholtz theorem on conservation of circulations is supposed to hold for ideal inviscid fluids and is believed to be play a crucial role in turbulent phenomena, such as production of dissipation by vortex line-stretching. However, this expectation does not take into account singularities in turbulent velocity fields at infinite Reynolds number. We present evidence from numerical simulations for the breakdown of the classical Kelvin theorem in the three-dimensional turbulent energy cascade. Although violated in individual realizations, we find that circulations are still conserved in some average sense. For comparison, we show that Kelvin's theorem holds for individual realizations in the two-dimensional enstrophy cascade, in agreement with theory. The turbulent ``cascade of circulations'' is shown to be a classical analogue of phase-slip due to quantized vortices in superfluids and various applications in geophysics and astrophysics are outlined.Comment: 4 pages, 3 figure