Dynamical chaos in the integrable Toda chain induced by time discretization.

We use the Toda chain model to demonstrate that numerical simulation of integrable Hamiltonian dynamics using time discretization destroys integrability and induces dynamical chaos. Specifically, we integrate this model with various symplectic integrators parametrized by the time step τ and measure the Lyapunov time TΛ (inverse of the largest Lyapunov exponent Λ). A key observation is that TΛ is finite whenever τ is finite but diverges when τ→0. We compare the Toda chain results with the nonintegrable Fermi-Pasta-Ulam-Tsingou chain dynamics. In addition, we observe a breakdown of the simulations at times TB≫TΛ due to certain positions and momenta becoming extremely large ("Not a Number"). This phenomenon originates from the periodic driving introduced by symplectic integrators and we also identify the concrete mechanism of the breakdown in the case of the Toda chain.

In-Plane and Out-of-Plane Investigation of Resonant Tunneling Polaritons in Metal-Dielectric-Metal Cavities.

Polaritons can be generated by tuning the optical transitions of a light emitter to the resonances of a photonic cavity. We show that a dye-doped cavity generates resonant tunneling polaritons with Epsilon-Near-Zero (ENZ) effective permittivity. We studied the polariton spectral dispersion in dye-doped metal-dielectric-metal (MDM) cavities as a function of the in-plane (k||) and out-of-plane (k⊥) components of the incident wavevector. The dependence on k|| was investigated through ellipsometry, revealing the ENZ modes. The k⊥ dependence was measured by varying the cavity thickness under normal incidence using a Surface Force Apparatus (SFA). Both methods revealed a large Rabi splitting well exceeding 100 meV. The SFA-based investigation highlighted the collective nature of strong coupling by producing a splitting proportional to the square root of the involved photons. This study demonstrates the possibility of generating ENZ polaritons and introduces the SFA as a powerful tool for the characterization of strong light-matter interactions.

Enhanced dielectric, ferroelectric, energy storage and mechanical energy harvesting performance of ZnO-PVDF composites induced by MWCNTs as an additive third phase.

The present work highlights an attempt of fabricating a nanocomposite by the addition of multi-walled carbon nanotubes (MWCNTs) as a third phase into flexible ZnO-poly(vinylidene fluoride) (ZnO-PVDF) composites. MWCNTs played a very important role in distributing ZnO fillers in the PVDF matrix more homogeneously and increased the connection capability. Enhancement of the piezoelectric phase, dielectric permittivity, ferroelectric polarization, energy storage density and mechanical energy harvesting performance of ZnO-PVDF composites after the addition of MWCNTs was confirmed from the respective characterization studies. The sensing capability was demonstrated by the generation of ∼22 V ac output voltage through the application of human finger tapping on 15 wt% ZnO and a 0.1 wt% MWCNT-loaded PVDF (15PZNT) based composite film. The rectified voltage from the fabricated 15PZNT film was used to charge a 10-µF capacitor up to ∼3 V which was used for the illumination of 30 commercial LEDs. The maximum power density from the film was found to be 21.41 µW cm-2 at 4 MΩ load resistance. The effect of the addition of MWCNTs was also verified by simulation using COMSOL Multiphysics software.

Integrable Time-Dependent Quantum Hamiltonians.

We formulate a set of conditions under which the nonstationary Schrödinger equation with a time-dependent Hamiltonian is exactly solvable analytically. The main requirement is the existence of a non-Abelian gauge field with zero curvature in the space of system parameters. Known solvable multistate Landau-Zener models satisfy these conditions. Our method provides a strategy to incorporate time dependence into various quantum integrable models while maintaining their integrability. We also validate some prior conjectures, including the solution of the driven generalized Tavis-Cummings model.

Raman Scattering Enhancement through Pseudo-Cavity Modes.

Raman spectroscopy plays a pivotal role in spectroscopic investigations. The small Raman scattering cross-section of numerous analytes, however, requires enhancement of the signal through specific structuring of the electromagnetic and morphological properties of the underlying surface. This enhancement technique is known as surface-enhanced Raman spectroscopy (SERS). Despite the existence of various proposed alternatives, the approach involving Fabry-Pérot cavities, which constitutes a straightforward method to enhance the electromagnetic field around the analyte, has not been extensively utilized. This is because, for the analyte to experience the maximum electric field, it needs to be embedded within the cavity. Consequently, the top mirror of the cavity will eventually shield it from the external laser source. Recently, an open-cavity configuration has been demonstrated to exhibit properties similar to the classic Fabry-Pérot configuration, with the added advantage of maintaining direct accessibility for the laser source. This paper showcases how such a simple yet innovative configuration can be effectively utilized to achieve remarkable Raman enhancement. The simple structure, coupled with its inexpensive nature and versatility in material selection and scalability, makes it an ideal choice for various analytes and integration into diverse Raman apparatus setups.

Understanding and Controlling Mode Hybridization in Multicavity Optical Resonators Using Quantum Theory and the Surface Forces Apparatus.

Optical fields in metal-dielectric multilayers display typical features of quantum systems, such as energy level quantization and avoided crossing, underpinned by an isomorphism between the Helmholtz and Schrödinger wave equations. This article builds on the fundamental concepts and methods of quantum theory to facilitate the understanding and design of multicavity resonators. It also introduces the surface forces apparatus (SFA) as a powerful tool for rapid, continuous, and extensive characterization of mode dispersion and hybridization. Instead of fabricating many different resonators, two equal metal-dielectric-metal microcavities were created on glass lenses and displaced relative to each other in a transparent silicone oil using the SFA. The fluid thickness was controlled in real time with nanometer accuracy from more than 50 µm to less than 20 nm, reaching mechanical contact between the outer cavities in a few minutes. The fluid gap acted as a third microcavity providing optical coupling and producing a complex pattern of resonance splitting as a function of the variable thickness. An optical wave in this symmetric three-cavity resonator emulated a quantum particle with nonzero mass in a potential comprising three square wells. Interference between the wells produced a 3-fold splitting of degenerate energy levels due to hybridization. The experimental results could be explained using the standard methods and formalism of quantum mechanics, including symmetry operators and the variational method. Notably, the interaction between square wells produced bonding, antibonding, and nonbonding states that are analogous to hybridized molecular orbitals and are relevant to the design of "epsilon-near-zero" devices with vanishing dielectric permittivity.

Hydroxylated BiFeO3 as efficient fillers in poly(vinylidene fluoride) for flexible dielectric, ferroelectric, energy storage and mechanical energy harvesting application.

Here we report the effect of surface hydroxylation of BiFeO3 fillers on the dielectric, ferroelectric, energy storage and mechanical energy harvesting performance of poly(vinylidene fluoride). Surface hydroxylation helped to improve the interfacial interaction between the filler and PVDF matrix by introducing a strong hydrogen bonding between the -OH group of the hydroxylated BiFeO3 filler surface and the -CF2 dipole of PVDF in place of electrostatic interfacial interaction between non-hydroxylated BiFeO3 and the -CH2 dipole of PVDF. The amount of polar phase increased to around 91% for a 7 wt% hydroxylated BiFeO3 loaded PVDF film (7BFOH) by this new type of interfacial interaction. The dielectric, ferroelectric, energy storage and mechanical energy harvesting performance of the PVDF based composite films also improved by the above said technique. Upon repeated human finger tapping, the 7BFOH film delivered ∼18 V output peak to peak open circuit ac voltage (VOC). After rectification, the VOC of the 7BFOH film was able to charge a 10 µF capacitor up to ∼3 V which was able to light up some LEDs (connected in parallel) together instantaneously, which proved the real life applicability of the composite films in low power consuming self-powered electronic devices.

Hybrid Plasmonic/Photonic Nanoscale Strategy for Multilevel Anticounterfeit Labels.

Innovative goods authentication strategies are of fundamental importance considering the increasing counterfeiting levels. Such a task has been effectively addressed with the so-called physical unclonable functions (PUFs), being physical properties of a system that characterize it univocally. PUFs are commonly implemented by exploiting naturally occurring non-idealities in clean-room fabrication processes. The broad availability of classic paradigm PUFs, however, makes them vulnerable. Here, we propose a hybrid plasmonic/photonic multilayered structure working as a three-level strong PUF. Our approach leverages on the combination of a functional nanostructured surface, a resonant response, and a unique chromatic signature all together in one single device. The structure consists of a resonant cavity, where the top mirror is replaced with a layer of plasmonic Ag nanoislands. The naturally random spatial distribution of clusters and nanoparticles formed by this deposition technique constitutes the manufacturer-resistant nanoscale morphological fingerprint of the proposed PUF. The presence of Ag nanoislands allows us to tailor the interplay between the photonic and plasmonic modes to achieve two additional security levels. The first one is constituted by the chromatic response and broad iridescence of our structures, while the second by their rich spectral response, accessible even through a common smartphone light-emitting diode. We demonstrate that the proposed architectures could also be used as an irreversible and quantitative temperature exposure label. The proposed PUFs are inexpensive, chip-to-wafer-size scalable, and can be deposited over a variety of substrates. They also hold a great promise as an encryption framework envisioning morpho-cryptography applications.

Optically Controlled Electron-Transfer Reaction Kinetics and Solvation Dynamics: Effect of Franck-Condon States.

Experimental results for optically controlled electron-transfer reaction kinetics (ETRK) and nonequilibrium solvation dynamics (NESD) of Coumarin 480 in DMPC vesicle show their dependence on excitation wavelength λex. However, the celebrated Marcus theory and linear-response-theory-based approaches for ETRK and NESD, respectively, predict both of the processes to be independent of λex. The above said lacuna in these theories prompted us to develop a novel theory in 1D space, where the effect of innumerable Franck-Condon states is included through λex. The present theory not only sheds light on the origin of failure of the existing theories but also gives the correct trend for the effect of λex on ETRK and NESD. More importantly, the calculated results of NESD are in excellent agreement with the experimental results for different values of λex. The new theory will therefore advance the knowledge of scientific community on the dynamics of photoinduced nonequilibrium processes.

Projection of the Dynamics of Electron Transfer Reaction in Dual Space onto the One-Dimensional Slower Reaction Coordinate Axis.

We have derived here for the first time an exact dynamical equation within the domain of classical mechanics for the time dependent density distribution function of one-dimensional reaction coordinate (RC) in the condensed phase for electron transfer reaction by projecting the dynamics of slower modes in multidimensional Liouville space starting with a given set of coordinates of the faster modes. After the faster modes were ensemble averaged, the dynamics of the whole system solely depends on the slower RC. To simplify the complicated equation into a tractable form, benchmark approximations are employed to reduce the formally exact equation into an equation similar to the Smoluchowski equation with a delocalized sink term. As a test case, a Hamiltonian for the solute-solvent system modeled by quadratic functions for fast-relaxing vibrational and slow-relaxing polarization modes, respectively, has been considered. Interestingly, our simplified kinetic equation corresponding to this model Hamiltonian is transformed into the well-known phenomenological Sumi-Marcus equation.

Mapping the reaction dynamics in Liouville space onto a reaction coordinate space: a first-principle- based theory.

We have derived here an exact kinetic equation for the time evolution of the probability distribution for a general reaction coordinate space, starting from a multidimensional Liouville equation based on first-principles theory. To make the equation tractable we use two standard approximations, which reduce the exact equation into a Fokker-Planck-type equation with a sink term. As illustrative examples, we consider its application to two important classes of reactions, viz., the electron transfer and diffusion-controlled reactions. The kinetic equations for the reaction coordinates corresponding to these reactions become one dimensional. We also provide a scheme to find the critical value of the reaction coordinate at which the reaction takes place, and also to obtain the initial distribution function in the same space for different experimental situations. In the case of photoinduced electron transfer, we introduce the effect of excitation frequency through the use of suitable initial distribution functions.