The majority of classical dynamical systems are chaotic and exhibit the butterfly effect: a minute change in initial conditions has exponentially large effects later on. But this phenomenon is difficult to reconcile with quantum mechanics. One of the main goals in the field of quantum chaos is to establish a correspondence between the dynamics of classical chaotic systems and their quantum counterparts. In isolated systems in the absence of decoherence, there is such a correspondence in dynamics, but it usually persists only over a short time window, after which quantum interference washes out classical chaos. We demonstrate that quantum mechanics can also play the opposite role and generate exponential instabilities in classically nonchaotic systems within this early-time window. Our calculations employ the out-of-time-ordered correlator (OTOC)—a diagnostic that reduces to the Lyapunov exponent in the classical limit but is well defined for general quantum systems. We show that certain classically nonchaotic models, such as polygonal billiards, demonstrate a Lyapunov-like exponential growth of the OTOC at early times with Planck’s-constant-dependent rates. This behavior is sharply contrasted with the slow early-time growth of the analog of the OTOC in the systems’ classical counterparts. These results suggest that classical-to-quantum correspondence in dynamics is violated in the OTOC even before quantum interference develops.

We study the Lagrangian trajectories of statistically isotropic, homogeneous, and stationary divergence-free spatiotemporal random vector fields. We design this advecting Eulerian velocity field such that it gets asymptotically rough and multifractal, both in space and time, as it is demanded by the phenomenology of turbulence at infinite Reynolds numbers. We then solve numerically the flow equations for a differentiable version of this field. We observe that trajectories get also rough, characterized by nearly the same Hurst exponent as the one of our prescribed advecting field. Moreover, even when considering the simplest situation of the advection by a fractional Gaussian field, we evidence in the Lagrangian framework additional intermittent corrections. The present approach involves properly defined random fields, and asks for a rigorous treatment that would explain our numerical findings and deepen our understanding of this long lasting problem.

We characterize a process of energy extraction via rectification of strongly turbulent flow by using tools of stochastic thermodynamics. We study the dynamics of an asymmetric autonomous rotor that shows biased direction of rotation when placed in a stream. We give experimental evidence that a fluctuation theorem can be used to describe the work injected in the rotor via its coupling with the turbulent flow structure. This approach allows to measure the mean power extracted from the chaotic fluid motion over a broad range of turbulent kinetic energy. A nontrivial dependence of the rotor power on flow kinetic energy is identified. This observation is described by a model taking into account the dissipation of the rotor energy and the temporal memory of coherent structures present in the turbulent flow.

Optical antennas enable efficient coupling between propagating light and bonding electromagnetic waves like surface plasmon polaritons (SPPs). Under the illumination of inhomogeneous optical fields, propagating SPPs mediated by multimode antennas could be spatially asymmetric and the asymmetry strongly depends on the position of the antennas relative to the illumination field. Here we develop such asymmetric excitation of SPPs through illuminating a pair of slot antennas with the (1,0) mode Hermite-Gaussian beam. The physical scenario of the interaction between the illumination optical field and the paired slot antennas are elaborated by full-wave electromagnetic simulations. We also carry out experiments to monitor the asymmetric SPPs propagation with a back-focal plane imaging technique. By retrieving the asymmetric intensity ratio of the SPP pattern in the back-focal plane image, lateral displacement of the antennas down to angstrom level is demonstrated.

We develop a unified minimal scheme to classify quantum chaos in the Sachdev-Ye-Kitaev (SYK) and supersymmetric (SUSY) SYK models and also work out the structure of the energy levels in one periodic table. The SYK with even $q$-body or SUSY SYK with odd $q$-body interaction, with $N$ even or odd number of sites, are put on an equal footing in the minimal Hilbert space; $N$ (mod 8), $q$ (mod 4) double Bott periodicity, and a reflection condition are identified. Exact diagonalizations (EDs) are performed to study both the bulk energy level statistics and hard-edge behaviors. Excellent agreements between the ED results and the symmetry classifications are demonstrated. Our compact and systematic methods can be transformed to map out more complicated periodic tables of SYK models with more degrees of freedom, tensor models, or symmetry protected topological phases.

Using the recently introduced molecular dynamics lattice gas approach, we test fluctuations of coarse-grained quantities. We show that as soon as the system can no longer be considered an ideal gas fluctuations fail to diminish upon coarse graining as is usually expected. These results suggest that current approaches to simulating fluctuating hydrodynamics may have to be augmented to achieve quantitative results for systems with a nonideal equation of state. The molecular dynamics lattice gas method gives a guidance to the exact nature of the fluctuation in such systems.

We study the electromechanical transduction in nanoelectromechanical actuators and show that the differences in scaling laws for electrical and mechanical effects lead to an overall nontrivial miniaturization behavior. In particular, the previously neglected fringing fields considerably increase electrical forces and improve the stability of nanoscale actuators. This shows that electrostatics does not pose any limitations to the miniaturization of electromechanical systems; in fact, in several respects, nanosystems outperform their microscale counterparts. As a specific example, we consider in-plane actuation of ultrathin slabs and show that devices consisting of a few layers of graphene are feasible, implying that electromechanical resonators operating beyond 40 GHz are possible with currently available technology.

Using large scale molecular dynamics simulations, we study in detail the impact of nanometer droplets of low viscosity on flat substrates versus the wettability of the solid plate. The comparison between the molecular dynamics simulations and different macroscopic models reveals that most of these models do not correspond to the simulation results at the nanoscale, in particular for the maximal contact diameter during the nanodroplet impact ($D_{\max }$). We have developed a new model for $D_{\max }$ that is in agreement with the simulation data and also takes into account the effects of the liquid-solid wettability. We also propose a new scaling for the time required to reach the maximal contact diameter $t_{\max }$ with respect to the impact velocity, which is also in agreement with the observations. With the new model for $D_{\max }$ plus the scaling found for $t_{\max }$, we present a master curve collapsing the evolution of the nanometer drop contact diameter during impact for different wettabilities and different impact velocities. We believe our results may help in designing better nanoprinters since they provide an estimation of the maximum impact velocities required to obtain a smooth and homogenous coverage of the surfaces without dry spots.

The Kerr effect in optical microresonators plays an important role for integrated photonic devices and enables third harmonic generation, four-wave mixing, and the generation of microresonator-based frequency combs. Here we experimentally demonstrate that the Kerr nonlinearity can split ultra-high-$Q$ microresonator resonances for two continuous-wave lasers. The resonance splitting is induced by self- and cross-phase modulation and counterintuitively enables two lasers at different wavelengths to be simultaneously resonant in the same microresonator mode. We develop a pump-probe spectroscopy scheme that allows us to measure power dependent resonance splittings of up to 35 cavity linewidths (corresponding to 52 MHz) at 10 mW of pump power. The required power to split the resonance by one cavity linewidth is only $286\mu \mathrm{W}$. In addition, we demonstrate threefold resonance splitting when taking into account four-wave mixing and two counterpropagating probe lasers. These Kerr splittings are of interest for applications that require two resonances at optically controlled offsets, e.g., for optomechanical coupling to phonon modes, optical memories, and precisely adjustable spectral filters.

Unlike conventional jet and drop breakup, which forms a cylindrical liquid column, the dripping of a viscous film will form a liquid annulus, which then ruptures and heals due to surface tension and the inner surface forms a retracting tip. We apply a one-dimensional model to analyze the thinning dynamics, which predicts a universal thinning curve and shows good agreement with experimental measurements. The shape of the tip is documented to be conical and the retraction speed is determined by the balance of viscous and capillary stresses. We also show that the drop contains an entrained bubble and possible formation of satellite bubbles in the healed thread.

This Letter focuses on the dynamics of a liquid jet impacting the surface of a confined, immersed granular bed. Although previous works have considered the erosion process and surface morphology, less attention has been given to the jet hydrodynamics. Based on laboratory experiments, we show that when the liquid jet forms a crater, two situations arise. For weak or no erosion and for open craters, the jet is stationary. For vertical or overhanging crater walls, the jet displays a wide range of behaviors, from quasiperiodic oscillations to symmetry breaking and exploration of different states in time. An analysis of the different system states leads to the emergence of a bifurcation diagram depending on a dimensionless parameter, $J$, comparing the jet impact force to the force necessary to eject a grain. The frequency of the jet oscillations depends on the inertial velocity, the jet dispersion and the ratio between the injector cross section and the confinement length.

Acoustic streaming is an ubiquitous phenomenon resulting from time-averaged nonlinear dynamics in oscillating fluids. In this theoretical study, we show that acoustic streaming can be suppressed by two orders of magnitude in major regions of a fluid by optimizing the shape of its confining walls. Remarkably, the acoustic pressure is not suppressed in this shape-optimized cavity, and neither is the acoustic radiation force on suspended particles. This basic insight may lead to applications, such as acoustophoretic handling of nm-sized particles, which is otherwise impaired by the streaming.

Multiplication and division of the orbital angular momentum (OAM) of light are important functions in the exploitation of the OAM mode space for such purposes as high-dimensional quantum information encoding and mode division multiplexed optical communications. These operations are possible with optical transformations that reshape optical wave fronts according to azimuthal scaling. However, schemes proposed thus far have been limited to OAM multiplication by integer factors and require complex beam-copying or multitransformation diffraction stages; a result of the limited phase excursion $2\pi \ell$ around the annulus of an OAM state $\exp (i\ell \theta )$. Based on the key idea that the phase excursion along spirals in the transverse plane of a vortex is theoretically unlimited, we propose and experimentally demonstrate a simple yet effective scheme using an azimuth-scaling spiral transformation that can accomplish both OAM multiplication and division by arbitrary rational factors in a single stage.

Optical frequency combs are revolutionizing modern time and frequency metrology. In the past years, their range of applications has increased substantially, driven by their miniaturization through microresonator-based solutions. The combs in such devices are typically generated using the third-order ${\chi }^{(3)}$ nonlinearity of the resonator material. An alternative approach is making use of second-order ${\chi }^{(2)}$ nonlinearities. While the idea of generating combs this way has been around for almost two decades, so far only few demonstrations are known, based either on bulky bow-tie cavities or on relatively low-$Q$ waveguide resonators. Here, we present the first such comb that is based on a millimeter-sized microresonator made of lithium niobate, that allows for cascaded second-order nonlinearities. This proof-of-concept device comes already with pump powers as low as 2 mW, generating repetition-rate-locked combs around 1064 and 532 nm. From the nonlinear dynamics point of view, the observed combs correspond to Turing roll patterns.

High harmonic generation (HHG) from gases and solids has been studied extensively. Whereas for liquids, it is far more challenging to understand the ultrafast dynamics with conventional methods. From a statistical perspective, we investigate the liquid-phase HHG theoretically by using a disordered linear chain. Our results reveal that (i) the harmonic spectra are characterized by a transition energy that separates the spectra into a low-energy region containing only odd harmonics and a high-energy region containing both even and odd harmonics with low yields; (ii) the transition energy depends on the fluctuation of structure and the field strength, but independent of the laser wavelength; (iii) the occurrence of dephasing is a natural result of the electron dynamics modulated by the long-range disorder. Furthermore, a simple formula is proposed to identify the transition energy, from which we correctly reproduce the experimental cutoff energies of HHG from liquid ethanol. Our results pave the way to better understand and control the HHG in liquids as another compact HHG source.

We study experimentally the interaction of nonlinear internal waves in a stratified fluid confined in a trapezoidal tank. The setup has been designed to produce internal wave turbulence from monochromatic and polychromatic forcing through three processes. The first is a linear transfer in wavelength obtained by wave reflection on inclined slopes, leading to an internal wave attractor which has a broad wave number spectrum. Second is the broadbanded time-frequency spectrum of the trapezoidal geometry, as shown by the impulse response of the system. The third one is a nonlinear transfer in frequencies and wave vectors via triadic interactions, which results at large forcing amplitudes in a power law decay of the wave number power spectrum. This first experimental spectrum of internal wave turbulence displays a $k^{-3}$ behavior.

In addition to surface tension lowering and Marangoni stresses, surfactants also induce surface rheological effects when they deform against themselves at fluid interfaces. Because surface viscosities are functions of surfactant concentration, surface rheological stresses can compete with capillary, Marangoni, and bulk stresses in surfactant-laden free surface flows with breakup. To elucidate the effects of surface rheology, we examine the breakup of a Stokes thread covered with a monolayer of insoluble surfactant when either surfactants are convected away from the space-time singularity or diffusion is dominant. Surprisingly, in both limits, surface rheological effects always enter the dominant balance of forces and alter the thread’s thinning rate. Moreover, if surfactants are convected away from the singularity, we provide an analytical expression for thinning rate that explicitly depends on surface rheological parameters, providing a simple route for measuring surface viscosity.

Parity-time ($PT$) symmetry has recently been opening exciting directions in photonics, yet the required careful balance of loss and gain has been hindering its widespread applicability. Here, we propose a gain-free route to $PT$ symmetry by extending it to complex-frequency excitations that can mimic gain in passive systems. Based on the concept of virtual absorption, extended here to implement also virtual gain, we implement $PT$ symmetry in the complex-frequency plane and realize its landmark effects, such as broken phase transitions, anisotropic transmission resonances, and laser-absorber pairs, in a fully passive, hence inherently stable, system. These results open a path to establish $PT$ symmetry and non-Hermitian physics in passive platforms.

A basic feature of liquid drops is that they can merge upon contact to form a larger drop. In spite of its importance to various applications, drop coalescence on prewetted substrates has received little attention. Here, we experimentally and theoretically reveal the dynamics of drop coalescence on a thick layer of a low viscosity liquid. It is shown that these so-called “liquid lenses” merge by the self-similar vertical growth of a bridge connecting the two lenses. Using a slender analysis, we derive similarity solutions corresponding to the viscous and inertial limits. Excellent agreement is found with the experiments without any adjustable parameters, capturing both the spatial and temporal structures of the flow during coalescence. Finally, we consider the crossover between the two regimes and show that all data of different lens viscosities collapse on a single curve capturing the full range of the coalescence dynamics.