Estimating Lyapunov exponents in billiards

Dynamical billiards are paradigmatic examples of chaotic Hamiltonian dynamical systems with widespread applications in physics. We study how well their Lyapunov exponent, characterizing the chaotic dynamics, and its dependence on external parameters can be estimated from phase space volume arguments, with emphasis on billiards with mixed regular and chaotic phase spaces. We show that in the very diverse billiards considered here the leading contribution to the Lyapunov exponent is inversely proportional to the chaotic phase space volume, and subsequently discuss the generality of this relationship. We also extend the well established formalism by Dellago, Posch, and Hoover to calculate the Lyapunov exponents of billiards to include external magnetic fields and provide a software implementation of it

Low-Temperature Linear Thermal Rectifiers Based on Coriolis forces

We demonstrate that a three-terminal harmonic symmetric chain in the presence of a Coriolis force, produced by a rotating platform which is used to place the chain, can produce thermal rectification. The direction of heat flow is reconfigurable and controlled by the angular velocity $\Omega$ of the rotating platform. A simple three terminal triangular lattice is used to demonstrate the proposed principle

Scaling Theory of Heat Transport in Quasi-1D Disordered Harmonic Chains

We introduce a variant of the Banded Random Matrix ensemble and show, using detailed numerical analysis and theoretical arguments, that the phonon heat current in disordered quasi-one-dimensional lattices obeys a one-parameter scaling law. The resulting beta-function indicates that an anomalous Fourier law is applicable in the diffusive regime, while in the localization regime the heat current decays exponentially with the sample size. Our approach opens a new way to investigate the effects of Anderson localization in heat conduction, based on the powerful ideas of scaling theory.Comment: Supplemental Report on calculation of heat current include

Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers

We employ Random Matrix Theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength $\gamma_{\rm CPA}$ and energy $E_{\rm CPA}$, for which a CPA occurs are expressed in terms of the eigenmodes of the isolated cavity -- thus carrying over the information about the chaotic nature of the target -- and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.Comment: Supplementary material is included. Updated version with minor modification

Branched flows in active random walks and the formation of ant trail patterns

Branched flow governs the transition from ballistic to diffusive motion of waves and conservative particle flows in spatially correlated random or complex environments. It occurs in many physical systems from micrometer to interstellar scales. In living matter systems, however, this transport regime is usually suppressed by dissipation and noise. In this article we demonstrate that, nonetheless, noisy active random walks, characterizing many living systems like foraging animals, and chemotactic bacteria, can show a regime of branched flow. To this aim we model the dynamics of trail forming ants and use it to derive a scaling theory of branched flows in active random walks in random bias fields in the presence of noise. We also show how trail patterns, formed by the interaction of ants by depositing pheromones along their trajectories, can be understood as a consequence of branched flow