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In magnetic topological insulators, spontaneous time-reversal symmetry breaking by intrinsic magnetic order can open an energy gap in the topological surface spectrum. In the resulting state, exotic properties like axion electrodynamics, the quantum anomalous Hall effect, and other topological magnetoelectric responses are expected to emerge. A detailed understanding of the magnetic order and its coupling to the topological surface states is essential to harness and tune these properties. Here, we leverage near-resonant electric quadrupole optical second harmonic generation to probe magnetic fluctuations in the candidate axion insulator EuSn$_2$(As,P)$_2$ across its antiferromagnetic phase boundary. We observe a pronounced dimensional crossover in the quantum decoherence induced by magnetic fluctuations, where two-dimensional in-plane ferromagnetic correlations at high temperatures give way to three-dimensional long-range order at the N\'eel temperature. We also observe the breaking of rotational symmetry within the long-range-ordered antiferromagnetic state and map out the resulting spatial domain structure. More generally, we demonstrate the unique capabilities of nonlinear optical spectroscopy to study quantum coherence and fluctuations in magnetic quantum materials.

Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used, resulting in the iLQR approach. Neglecting the second-order terms often slows down the convergence rate compared to full DDP. Multi-Shooting is another popular technique to improve robustness, especially if the dynamics are highly non-linear. In this work, we consider Multi-Shooting DDP for trajectory optimization of a bounding gait for a simplified quadruped model. As the main contribution, we develop Second-Order analytical partial derivatives of the rigid-body contact dynamics, extending our previous results for fixed/floating base models with multi-DoF joints. Finally, we show the benefits of a novel Quasi-Newton method for approximating second-order derivatives of the dynamics, leading to order-of-magnitude speedups in the convergence compared to the full DDP method., Comment: https://www.youtube.com/watch?v=C0h6mEpcnAE

Despite significant achievements in characterizing the properties of Sr$_2$RuO$_4$ over the last three decades, the precise nature of its electronic ground state is still unresolved. In this work, we provide a missing piece of the puzzle by uncovering evidence of electronic nematic order in the normal state of Sr$_2$RuO$_4$, revealed by ultrafast time-resolved optical dichroism measurements of uniaxially strained thin films. This nematic order, whose domains are aligned by the strain, spontaneously breaks the four-fold rotational symmetry of the crystal. The temperature dependence of the dichroism resembles an Ising-like order parameter, and optical pumping induces a coherent oscillation of its amplitude mode. A microscopic model of intra-unit-cell nematic order is presented, highlighting the importance of Coulomb repulsion between neighboring oxygen $p$-orbitals. The existence of electronic nematic order in the normal state of Sr$_2$RuO$_4$ may have consequences for the form and mechanism of superconductivity in this material.

Technology moves towards ever faster switching between different electronic and magnetic states of matter. Manipulating properties at terahertz rates requires accessing the intrinsic timescales of electrons (femtoseconds) and associated phonons (10s of femtoseconds to few picoseconds), which is possible with short-pulse photoexcitation. Yet, in many Mott insulators, the electronic transition is accompanied by the nucleation and growth of percolating domains of the changed lattice structure, leading to empirical time scales dominated by slow coarsening dynamics. Here, we use time-resolved X-ray diffraction and reflectivity measurements to investigate the photoinduced insulator-to-metal transition in an epitaxially strained thin film Mott insulator Ca2RuO4. The dynamical transition occurs without observable domain formation and coarsening effects, allowing the study of the intrinsic electronic and lattice dynamics. Above a fluence threshold, the initial electronic excitation drives a fast lattice rearrangement, followed by a slower electronic evolution into a metastable non-equilibrium state. Microscopic calculations based on time-dependent dynamical mean-field theory and semiclassical lattice dynamics within a recently published equilibrium energy landscape picture explain the threshold-behavior and elucidate the delayed onset of the electronic phase transition in terms of kinematic constraints on recombination. Analysis of satellite scattering peaks indicates the persistence of a strain-induced nano-texture in the photoexcited film. This work highlights the importance of combined electronic and structural studies to unravel the physics of dynamic transitions and elucidates the role of strain in tuning the timescales of photoinduced processes.

Model-based control for robots has increasingly been dependent on optimization-based methods like Differential Dynamic Programming and iterative LQR (iLQR). These methods can form the basis of Model-Predictive Control (MPC), which is commonly used for controlling legged robots. Computing the partial derivatives of the dynamics is often the most expensive part of these algorithms, regardless of whether analytical methods, Finite Difference, Automatic Differentiation (AD), or Chain-Rule accumulation is used. Since the second-order derivatives of dynamics result in tensor computations, they are often ignored, leading to the use of iLQR, instead of the full second-order DDP method. In this paper, we present analytical methods to compute the second-order derivatives of inverse and forward dynamics for open-chain rigid-body systems with multi-DoF joints and fixed/floating bases. An extensive comparison of accuracy and run-time performance with AD and other methods is provided, including the consideration of code-generation techniques in C/C++ to speed up the computations. For the 36 DoF ATLAS humanoid, the second-order Inverse, and the Forward dynamics derivatives take approx 200 mu s, and approx 2.1 ms respectively, resulting in a 3x speedup over the AD approach., Comment: Evolved work from https://ieeexplore.ieee.org/document/9981356. arXiv admin note: text overlap with arXiv:2203.01497

Optimization-based robot control strategies often rely on first-order dynamics approximation methods, as in iLQR. Using second-order approximations of the dynamics is expensive due to the costly second-order partial derivatives of the dynamics with respect to the state and control. Current approaches for calculating these derivatives typically use automatic differentiation (AD) and chain-rule accumulation or finite-difference. In this paper, for the first time, we present analytical expressions for the second-order partial derivatives of inverse dynamics for open-chain rigid-body systems with floating base and multi-DoF joints. A new extension of spatial vector algebra is proposed that enables the analysis. A recursive algorithm with complexity of $\mathcal{O}(Nd^2)$ is also provided where $N$ is the number of bodies and $d$ is the depth of the kinematic tree. A comparison with AD in CasADi shows speedups of 1.5-3$\times$ for serial kinematic trees with $N> 5$, and a C++ implementation shows runtimes of $\approx$51$\mu s$ for a quadruped., Comment: Accepted for IROS 2022 (Oct 23-27, 2022 Kyoto)

The details of second-order partial derivatives of rigid-body Inverse/Forward dynamics are provided. Several properties and identities using Spatial Vector Algebra are listed, along with their detailed derivations. The expressions build upon previous work by the author on first-order partial derivatives of inverse dynamics. The first/second-order derivatives are also extended for systems with external forces. Finally, the KKT Forward dynamics and Impact dynamics derivatives are derived.

An essential need for many model-based robot control algorithms is the ability to quickly and accurately compute partial derivatives of the equations of motion. State of the art approaches to this problem often use analytical methods based on the chain rule applied to existing dynamics algorithms. Although these methods are an improvement over finite differences in terms of accuracy, they are not always the most efficient. In this paper, we contribute new closed-form expressions for the first-order partial derivatives of inverse dynamics, leading to a recursive algorithm. The algorithm is benchmarked against chain-rule approaches in Fortran and against an existing algorithm from the Pinocchio library in C++. Tests consider computing the partial derivatives of inverse and forward dynamics for robots ranging from kinematic chains to humanoids and quadrupeds. Compared to the previous open-source Pinocchio implementation, our new analytical results uncover a key computational restructuring that enables efficiency gains. Speedups of up to 1.4x are reported for calculating the partial derivatives of inverse dynamics for the 50-dof Talos humanoid.

Talagrand observed that finiteness of $\mathbb{E}\, e^{\frac{1}{2}|\nabla f(X)|^{2}}$ implies finiteness of $\mathbb{E}\, e^{\, f(X)}$ where $X$ is the standard Gaussian vector in $\mathbb{R}^{n}$ and $f$ is a smooth function with zero average. However, in this paper we show that finiteness of $ \mathbb{E}\, e^{\frac{1}{2}|\nabla f|^{2}} (1+|\nabla f|)^{-1}$ implies finiteness of $\mathbb{E}\, e^{\, f(X)}$, and we also obtain quantitative bounds \begin{align*} \log\, \mathbb{E}\, e^{\, f} \leq 10\, \mathbb{E}\, e^{\frac{1}{2}|\nabla f|^{2}} (1+|\nabla f|)^{-1}. \end{align*} Moreover, the extra factor $(1+|\nabla f|)^{-1}$ is the best possible in the sense that there is smooth $f$ with $\mathbb{E}\, e^{\,f} =\infty$ but $\mathbb{E}\, e^{\frac{1}{2}|\nabla f|^{2}} (1+|\nabla f|)^{-c}<\infty$ for all $c>1$. As an application we show corresponding dual inequalities for the discrete time dyadic martingales and its quadratic variations., Comment: We included an application showing what is the corresponding dual inequality for the dyadic square function

SrTiO$_3$ is an incipient ferroelectric on the verge of a polar instability, which is avoided at low temperatures by quantum fluctuations. Within this unusual quantum paraelectric phase, superconductivity persists despite extremely dilute carrier densities. Ferroelectric fluctuations have been suspected to play a role in the origin of superconductivity by contributing to electron pairing. To investigate this possibility, we used optical second harmonic generation to measure the doping and temperature dependence of the ferroelectric order parameter in compressively strained SrTiO$_3$ thin films. At low temperatures, we uncover a spontaneous out-of-plane ferroelectric polarization with an onset that correlates perfectly with normal-state electrical resistivity anomalies. These anomalies have previously been associated with an enhancement of the superconducting critical temperature in doped SrTiO$_3$ films, directly linking the ferroelectric and superconducting phases. We develop a long-range mean-field Ising model of the ferroelectric phase transition to interpret the data and extract the relevant energy scales in the system. Our results support a long-suspected connection between ferroelectricity and superconductivity in SrTiO$_3$, but call into question the role played by ferroelectric fluctuations.

We present the first results from the HST Archival Legacy project "SKYSURF." As described in Windhorst et al., SKYSURF utilizes the large HST archive to study the diffuse UV, optical, and near-IR backgrounds and foregrounds in detail. Here, we utilize SKYSURF's first sky-surface-brightness measurements to constrain the level of near-IR diffuse Extragalactic Background Light (EBL) in three near-IR filters (F125W, F140W, and F160W). This is done by comparing our preliminary sky measurements of >30,000 images to zodiacal light models, carefully selecting the darkest images to avoid contamination from stray light. Our sky-surface-brightness measurements have been verified to an accuracy of better than 1%, which when combined with systematic errors associated with HST, results in sky-brightness uncertainties of ∼ 2%–4% ≃ 0.005 MJy sr−1 in each image. When compared to the Kelsall et al. zodiacal model, an isotropic diffuse background of ∼30 nW m−2 sr−1 remains, whereas using the Wright zodiacal model results in no discernible diffuse background. Based primarily on uncertainties in the foreground model subtraction, we present limits on the amount of diffuse EBL of 29, 40, and 29 nW m−2 sr−1, for F125W, F140W, and F160W, respectively. While this light is generally isotropic, our modeling at this point does not distinguish between a cosmological origin or a solar system origin (such as a dim, diffuse, spherical cloud of cometary dust).

We give an overview and describe the rationale, methods, and testing of the Hubble Space Telescope (HST) Archival Legacy project "SKYSURF." SKYSURF uses HST's unique capability as an absolute photometer to measure the ∼0.2–1.7 μm sky-surface brightness (sky-SB) from 249,861 WFPC2, ACS, and WFC3 exposures in ∼1400 independent HST fields. SKYSURF's panchromatic data set is designed to constrain the discrete and diffuse UV to near-IR sky components: Zodiacal Light (ZL), Kuiper Belt Objects (KBOs), Diffuse Galactic Light (DGL), and the discrete plus diffuse Extragalactic Background Light (EBL). We outline SKYSURF's methods to: (1) measure sky-SB levels between detected objects; (2) measure the discrete EBL, most of which comes from AB≃17–22 mag galaxies; and (3) estimate how much truly diffuse light may exist. Simulations of HST WFC3/IR images with known sky values and gradients, realistic cosmic ray (CR) distributions, and star plus galaxy counts were processed with nine different algorithms to measure the "Lowest Estimated Sky-SB" (LES) in each image between the discrete objects. The best algorithms recover the LES values within 0.2% when there are no image gradients, and within 0.2%–0.4% when there are 5%–10% gradients. We provide a proof of concept of our methods from the WFC3/IR F125W images, where any residual diffuse light that HST sees in excess of zodiacal model predictions does not depend on the total object flux that each image contains. This enables us to present our first SKYSURF results on diffuse light in Carleton et al.