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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 on its implementation.

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We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γ_{CPA} and energy E_{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.

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When waves propagate through weakly scattering but correlated, disordered environments they are randomly focused into pronounced branchlike structures, a phenomenon referred to as branched flow, which has been studied in a wide range of isotropic random media. In many natural environments, however, the fluctuations of the random medium typically show pronounced anisotropies. A prominent example is the focusing of tsunami waves by the anisotropic structure of the ocean floor topography. We study the influence of anisotropy on such natural focusing events and find a strong and nonintuitive dependence on the propagation angle which we explain by semiclassical theory.

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

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Waves traveling through weakly random media are known to be strongly affected by their corresponding ray dynamics, in particular in forming linear freak waves. The ray intensity distribution, which, e.g., quantifies the probability of freak waves is unknown, however, and a theory of how it is approached in an appropriate semiclassical limit of wave mechanics is lacking. We show that this limit is not the usual limit of small wavelengths, but that of decoherence. Our theory, which can describe the intensity distribution for an arbitrary degree of coherence is relevant to a wide range of physical systems, as decoherence is omnipresent in real systems.

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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 ß 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.

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Although human musical performances represent one of the most valuable achievements of mankind, the best musicians perform imperfectly. Musical rhythms are not entirely accurate and thus inevitably deviate from the ideal beat pattern. Nevertheless, computer generated perfect beat patterns are frequently devalued by listeners due to a perceived lack of human touch. Professional audio editing software therefore offers a humanizing feature which artificially generates rhythmic fluctuations. However, the built-in humanizing units are essentially random number generators producing only simple uncorrelated fluctuations. Here, for the first time, we establish long-range fluctuations as an inevitable natural companion of both simple and complex human rhythmic performances. Moreover, we demonstrate that listeners strongly prefer long-range correlated fluctuations in musical rhythms. Thus, the favorable fluctuation type for humanizing interbeat intervals coincides with the one generically inherent in human musical performances.

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We show that a harmonic lattice model with amplifying and attenuating elements, when coupled to two thermal baths, exhibits unique heat transport properties. Some of these novel features include anomalous nonequilibrium steady-state heat currents, negative differential thermal conductance, as well as nonreciprocal heat transport. We find that when these elements are arranged in a PT-symmetric manner, the domain of existence of the nonequilibrium steady state is maximized. We propose an electronic experimental setup based on resistive-inductive-capacitive (RLC) transmission lines, where our predictions can be tested.

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Even very weak correlated disorder potentials can cause extreme fluctuations in Hamiltonian flows. In two dimensions this leads to a pronounced branching of the flow. Although present in a great variety of physical systems, a quantitative theory of the branching statistics is lacking. Here, we derive an analytical expression for the number of branches valid for all distances from a source. We also derive the scaling relations that make this expression universal for a wide range of random potentials. Our theory has possible applications in many fields ranging from semiconductor to geophysics.

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We study the effect of localized modes in lattices of size N with parity-time (PT) symmetry. Such modes are arranged in pairs of quasidegenerate levels with splitting delta approximately exp(-N/xi) where xi is their localization length. The level "evolution" with respect to the PT breaking parameter gamma shows a cascade of bifurcations during which a pair of real levels becomes complex. The spontaneous PT symmetry breaking occurs at gammaPT approximately min{delta}, thus resulting in an exponentially narrow exact PT phase. As N/xi decreases, it becomes more robust with gammaPT approximately 1/N2 and the distribution P(gammaPT) changes from log-normal to semi-Gaussian. Our theory can be tested in the frame of optical lattices.

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Recent experiments on symmetry-broken mesoscopic semiconductor structures have exhibited an amazing rectifying effect in the transverse current-voltage characteristics with promising prospects for future applications. We present a simple microscopic model, which takes into account the energy dependence of current-carrying modes and explains the rectifying effect by an interplay of fully quantized and quasiclassical transport channels in the system. It also suggests the design of a ballistic rectifier with an optimized rectifying signal and predicts voltage oscillations which may provide an experimental test for the mechanism considered here.