Zeptonewton and attotesla per centimeter metrology with coupled oscillators.

We present the coupled oscillator: A new mechanism for signal amplification with widespread application in metrology. We introduce the mechanical theory of this framework and support it by way of simulations. We present a particular implementation of coupled oscillators: A microelectromechanical system (MEMS) that uses one large (∼100mm) N52 magnet coupled magnetically to a small (∼0.

The Metastable State of Fermi-Pasta-Ulam-Tsingou Models.

Classical statistical mechanics has long relied on assumptions such as the equipartition theorem to understand the behavior of the complicated systems of many particles. The successes of this approach are well known, but there are also many well-known issues with classical theories. For some of these, the introduction of quantum mechanics is necessary, e.

Modal engineering of electromagnetic circuits to achieve rapid settling times.

Inductive circuits and devices are ubiquitous and important design elements in many applications, such as magnetic drives, galvanometers, magnetic scanners, applying direct current (DC) magnetic fields to systems, radio frequency coils in nuclear magnetic resonance (NMR) systems, and a vast array of other applications. They are widely used to generate both DC and alternating current (AC) magnetic fields. Many of these applications require a rapid step and settling time, turning the DC or AC magnetic field on and off quickly.

Counterdiabatic driving in the classical β-Fermi-Pasta-Ulam-Tsingou chain.

Shortcuts to adiabaticity (STAs) have been used to make rapid changes to a system while eliminating or minimizing excitations in the system's state. In quantum systems, these shortcuts allow us to minimize inefficiencies and heating in experiments and quantum computing protocols, but the theory of STAs can also be generalized to classical systems. We focus on one such STA, approximate counterdiabatic (ACD) driving, and numerically compare its performance in two classical systems: a quartic anharmonic oscillator and the β Fermi-Pasta-Ulam-Tsingou lattice.

Analysis of a Casimir-driven parametric amplifier with resilience to Casimir pull-in for MEMS single-point magnetic gradiometry.

The Casimir force, a quantum mechanical effect, has been observed in several microelectromechanical system (MEMS) platforms. Due to its extreme sensitivity to the separation of two objects, the Casimir force has been proposed as an excellent avenue for quantum metrology. Practical application, however, is challenging due to attractive forces leading to stiction and device failure, called Casimir pull-in.

A system for probing Casimir energy corrections to the condensation energy.

In this article, we present a nanoelectromechanical system (NEMS) designed to detect changes in the Casimir energy. The Casimir effect is a result of the appearance of quantum fluctuations in an electromagnetic vacuum. Previous experiments have used nano- or microscale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces.

The β Fermi-Pasta-Ulam-Tsingou recurrence problem.

We perform a thorough investigation of the first Fermi-Pasta-Ulam-Tsingou (FPUT) recurrence in the β-FPUT chain for both positive and negative β. We show numerically that the rescaled FPUT recurrence time T=t/(N+1) depends, for large N, only on the parameter S≡Eβ(N+1). Our numerics also reveal that for small |S|, T is linear in S with positive slope for both positive and negative β.

Dynamical glass in weakly nonintegrable Klein-Gordon chains.

Integrable many-body systems are characterized by a complete set of preserved actions. Close to an integrable limit, a nonintegrable perturbation creates a coupling network in action space which can be short or long ranged. We analyze the dynamics of observables which become the conserved actions in the integrable limit.

Erratum: Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning [Phys. Rev. Lett. 121, 255304 (2018)].

This corrects the article DOI: 10.1103/PhysRevLett.121.

Behavior and breakdown of higher-order Fermi-Pasta-Ulam-Tsingou recurrences.

We numerically investigate the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the α and β Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences.

Accelerated Search and Design of Stretchable Graphene Kirigami Using Machine Learning.

Making kirigami-inspired cuts into a sheet has been shown to be an effective way of designing stretchable materials with metamorphic properties where the 2D shape can transform into complex 3D shapes. However, finding the optimal solutions is not straightforward as the number of possible cutting patterns grows exponentially with system size. Here, we report on how machine learning (ML) can be used to approximate the target properties, such as yield stress and yield strain, as a function of cutting pattern.

Kirigami actuators.

Thin elastic sheets bend easily and, if they are patterned with cuts, can deform in sophisticated ways. Here we show that carefully tuning the location and arrangement of cuts within thin sheets enables the design of mechanical actuators that scale down to atomically-thin 2D materials. We first show that by understanding the mechanics of a single non-propagating crack in a sheet, we can generate four fundamental forms of linear actuation: roll, pitch, yaw, and lift.

Highly stretchable MoS2 kirigami.

We report the results of classical molecular dynamics simulations focused on studying the mechanical properties of MoS2 kirigami. Several different kirigami structures were studied based upon two simple non-dimensional parameters, which are related to the density of cuts, as well as the ratio of the overlapping cut length to the nanoribbon length. Our key findings are significant enhancements in tensile yield (by a factor of four) and fracture strains (by a factor of six) as compared to pristine MoS2 nanoribbons.

Conductance signatures of electron confinement induced by strained nanobubbles in graphene.

We investigate the impact of strained nanobubbles on the conductance characteristics of graphene nanoribbons using a combined molecular dynamics - tight-binding simulation scheme. We describe in detail how the conductance, density of states, and current density of zigzag or armchair graphene nanoribbons are modified by the presence of a nanobubble. In particular, we establish that low-energy electrons can be confined in the vicinity of or within the nanobubbles by the delicate interplay among the pseudomagnetic field pattern created by the shape of the bubble, mode mixing, and substrate interaction.

Transport properties of pristine few-layer black phosphorus by van der Waals passivation in an inert atmosphere.

Ultrathin black phosphorus is a two-dimensional semiconductor with a sizeable band gap. Its excellent electronic properties make it attractive for applications in transistor, logic and optoelectronic devices. However, it is also the first widely investigated two-dimensional material to undergo degradation upon exposure to ambient air.

Functional renormalization group analysis of the half-filled one-dimensional extended Hubbard model.

We study the phase diagram of the half-filled one-dimensional extended Hubbard model at weak coupling using a novel functional renormalization group (FRG) approach. The FRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi points. Our results confirm the existence of a finite region of bond charge density wave, also known as a "bond order wave" near U=2V and clarify why earlier g-ology calculations have not found this phase.

Normal and anomalous heat transport in one-dimensional classical lattices.

We present analytic and numerical results on several models of one-dimensional (1D) classical lattices with the goal of determining the origins of anomalous heat transport and the conditions for normal transport in these systems. Some of the recent results in the literature are reviewed and several original "toy" models are added that provide key elements to determine which dynamical properties are necessary and which are sufficient for certain types of heat transport. We demonstrate with numerical examples that chaos in the sense of positivity of Lyapunov exponents is neither necessary nor sufficient to guarantee normal transport in 1D lattices.

Ground state phases of the half-filled one-dimensional extended hubbard model.

Using quantum Monte Carlo simulations, results of a strong-coupling expansion, and Luttinger liquid theory, we determine quantitatively the ground state phase diagram of the one-dimensional extended Hubbard model with on-site and nearest-neighbor repulsions U and V. We show that spin frustration stabilizes a bond-ordered (dimerized) state for U approximately V/2 up to U/t approximately 9, where t is the nearest-neighbor hopping. The transition from the dimerized state to the staggered charge-density-wave state for large V/U is continuous for U < or approximately 5.

Piecewise linear models for the quasiperiodic transition to chaos.

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode locking and the quasiperiodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps.