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We discuss the decoherence in a quantum system induced by interaction with gravitational degrees of freedom that are part of a higher derivative theory. The deformation of a mass distribution due to gravitational waves acquires naturally a mass quadrupole moment. This adds higher derivative dynamics of the quadrupole moment to the unitary evolution of the system, where the quadrupole moment oscillates with the gravitational frequencies following a higher derivative theory. The consequence of higher derivatives in the dynamics is that the system is described by four canonical variables. This departure from the usual particle position and momentum operators gives an entirely different interpretation of the decoherence basis. This model focuses on the open dynamics of the quadrupole moment, rather than on individual particles. As such, a short example is given to utilize quadrupole measurements to probe gravitational decoherence and noise. We first derive a Langevin equation for a lower derivative model and show how higher derivatives naturally emerge on the boundary. A quantum master equation is derived for the emerging quadrupole moment, considering that the environment is a higher derivative theory of gravity., Comment: 12 pages

We derive time reflection and transmission coefficients for 1D acoustic waves encountering a time boundary at which the properties of the medium change instantaneously. The time reflection and transmission coefficients are shown to be identical to so-called reverse-space reflection and transmission coefficients which appear in the recursive computation of focusing wavefields used in seismology. We establish a bijectivity between the focusing wavefields and the wavefields produced by time scattering and show how this can be used to construct a space-time medium where the time scattering anticipates the space scattering and "computes" the exact inverse for the space scattering. The construction is shown to be independent of the boundary conditions chosen to compute the reflection and transmission coefficients. We demonstrate the construction with a simple numerical example of a single pulse encountering a series of time boundaries before reaching a spatial inhomogeneity. The time boundaries scatter the single pulse into a focusing wavefield that subsequently focuses through the spatial inhomogeneity. Under certain conditions, the transmitted wave has both the same wave shape and amplitude as the original pulse, yielding a transmission coefficient of unity. The reflection coefficient of the space-time medium is always non-zero however., Comment: 23 pages, 5 figures, 2 tables

It has been known that the large-$q$ complex SYK model falls under the same universality class as that of van der Waals (mean-field) and saturates the Maldacena-Shenker-Stanford bound, both features shared by various black holes. This makes the SYK model a useful tool in probing the fundamental nature of quantum chaos and holographic duality. This work establishes the robustness of this shared universality class and chaotic properties for SYK-like models by extending to a system of coupled large-$q$ complex SYK models of different orders. We provide a detailed derivation of thermodynamic properties, specifically the critical exponents for an observed phase transition, as well as dynamical properties, in particular the Lyapunov exponent, via the out-of-time correlator calculations. Our analysis reveals that, despite the introduction of an additional scaling parameter through interaction strength ratios, the system undergoes a continuous phase transition at low temperatures, similar to that of the single SYK model. The critical exponents align with the Landau-Ginzburg (mean-field) universality class, shared with van der Waals gases and various AdS black holes. Furthermore, we demonstrate that the coupled SYK system remains maximally chaotic in the large-$q$ limit at low temperatures, adhering to the Maldacena-Shenker-Stanford bound, a feature consistent with the single SYK model. These findings establish robustness and open avenues for broader inquiries into the universality and chaos in complex quantum systems. We provide a detailed outlook for future work by considering the "very" low-temperature regime, where we discuss relations with the Hawking-Page phase transition observed in the holographic dual black holes. We present preliminary calculations and discuss the possible follow-ups that might be taken to make the connection robust., Comment: 20 pages, 10 figures, 1 table, same as published version but in a different formatting style

Waves in space-dependent and time-dependent materials obey similar wave equations, with interchanged time- and space-coordinates. However, since the causality conditions are the same in both types of material (i.e., without interchangement of coordinates), the solutions are dissimilar. We present a systematic treatment of wave propagation and scattering in 1D space-dependent and time-dependent materials. After formulating unified equations, we discuss Green's functions and simple wave field representations for both types of material. Next we discuss propagation invariants, i.e., quantities that are independent of the space coordinate in a space-dependent material (such as the net power-flux density) or of the time coordinate in a time-dependent material (such as the net field-momentum density). A discussion of reciprocity theorems leads to the well-known source-receiver reciprocity relation for the Green's function of a space-dependent material and a new source-receiver reciprocity relation for the Green's function of a time-dependent material. A discussion of general wave field representations leads to the well-known expression for Green's function retrieval from the correlation of passive measurements in a space-dependent material and a new expression for Green's function retrieval in a time-dependent material. After an introduction of a matrix-vector wave equation, we discuss propagator matrices for both types of material. Since the initial condition for a propagator matrix in a time-dependent material follows from the boundary condition for a propagator matrix in a space-dependent material by interchanging the time- and space-coordinates, the propagator matrices for both types of material are interrelated in the same way. This also applies to representations and reciprocity theorems involving propagator matrices., Comment: 46 pages, 5 figures

Even though one could already constrain different models in cosmology and Beyond Standard Model physics using CMB data, these models remained unconstrained at shorter wavelength scales, and knowledge of new physics at higher energy scales relied on theoretical assumptions and extrapolations to these scales. Recently, however, we have experienced the advent of gravitational-wave and multi-messenger astronomy, including the outstanding detections by the LIGO-Virgo collaboration over the past decade and the latest searches for Hellings-Downs correlations in pulsar timing data. Ongoing and future gravitational wave collaborations explore different frequency ranges of the gravitational wave spectrum. In these lecture notes, we focus on how we can probe cosmology and Beyond Standard Model physics with primordial gravitational waves. For this purpose, we review the formalism of gravitational waves in General Relativity, introduce stochastic gravitational waves, and derive the Hellings-Downs correlation for pulsar timing array searches. We comment on detection efforts and present some of the most important cosmological sources that could produce a background. Ultimately, one could compare model-dependent gravitational wave density spectra using gravitational wave data from ground-based, space-borne, and pulsar timing array searches. These lecture notes were inspired by the course "Gravitational Waves from the Early Universe" given at the 27th W.E. Heraeus "Saalburg" Summer School 2021 by Valerie Domcke., Comment: Submission to SciPost Physics Lecture Notes. v3: 60 pages, 26 figures, manuscript revised, discussion overall improved. Comments are welcome

Machine-matter, of which mechanical metamaterials and meta-devices are important sub-categories, is emerging as a major paradigm for designing advanced functional materials. Various exciting applications of these concepts have been recently demonstrated, ranging from exotic mechanical properties to device-like and adaptive functionalities. The vast majority of the studies published to date have, however, focused on the quasi-static behavior of such devices, neglecting their rich dynamic behavior. Recently, we proposed a new class of strain rate-dependent mechanical metamaterials that are made from bi-beams (i.e., viscoelastic bilayer beams). The buckling direction of such bi-beams can be controlled with the applied strain rate. The proposed approach, however, suffers from a major limitation: 3D printing of such bi-beams with such a 'strong' differential strain rate-dependent response is very challenging. Here, we propose an alternative approach that only requires a 'weak' differential response and a rationally designed geometric artifact to control the buckling direction of bi-beams. We present an analytical model that describes the landscape of all possible combinations of geometric designs and hyperelastic as well as viscoelastic properties that lead to the desired strain rate-dependent switching of the buckling direction. We also demonstrate how multi- and single-material 3D printing techniques can be used to fabricate the proposed bi-beams with microscale and submicron resolutions. More importantly, we show how the requirement for a weak differential response eliminates the need for multi-material 3D printing, as the change in the laser processing parameters is sufficient to achieve effective differential responses. Finally, we use the same 3D printing techniques to produce strain rate-dependent gripper mechanisms as showcases of potential applications.

Mitigating the energy requirements of artificial intelligence requires novel physical substrates for computation. Phononic metamaterials have a vanishingly low power dissipation and hence are a prime candidate for green, always-on computers. However, their use in machine learning applications has not been explored due to the complexity of their design process: Current phononic metamaterials are restricted to simple geometries (e.g. periodic, tapered), and hence do not possess sufficient expressivity to encode machine learning tasks. We design and fabricate a non-periodic phononic metamaterial, directly from data samples, that can distinguish between pairs of spoken words in the presence of a simple readout nonlinearity; hence demonstrating that phononic metamaterials are a viable avenue towards zero-power smart devices., Comment: 13 pages, 11 figures

Folding nanopatterned flat sheets into complex 3D structures enables the fabrication of meta-biomaterials that combine a rationally designed 3D architecture (e.g., to tune mechanical and mass transport properties) with nanoscale surface features (e.g., to guide the differentiation of stem cells). Self-folding is an attractive approach for realizing such materials. However, self-folded lattices are generally too compliant as there is an inherent competition between the ease-of-folding requirements and the final load-bearing characteristics. Inspired by sheet metal forming, we propose an alternative route for the fabrication of origami lattices. This automated folding approach allows for the introduction of sharp folds into thick metal sheets, thereby enhancing their stiffness. We then demonstrate the first time ever realization of automatically folded origami lattices with bone-mimicking mechanical properties (elastic modulus = 0.5 GPa). The proposed approach is highly scalable given that the unit cells making up the meta-biomaterial can be arbitrarily large in number and small in dimensions. To demonstrate the scalability and versatility of the proposed approach, we fabricated origami lattices with > 100 unit cells, lattices with unit cells as small as 1.25 mm, and auxetic lattices. We then used inductively coupled plasma reactive ion etching to nanopattern the surface of the sheets prior to folding. Protected by a thin layer of coating, these nanoscale features remained intact during the folding process. A cell culture assay was then used to assess the bone tissue regeneration performance of the folded origami. We found that the nanopatterned folded specimens exhibit significantly increased mineralization as compared to their non-patterned counterparts.

4D printing of flat sheets that self-fold into architected 3D structures is a powerful origami-inspired approach for the fabrication of multi-functional devices and metamaterials. The possibility to endow the initially flat sheet with a variety of surface-related functionalities provides the means to simultaneously achieve multi-functional performance and a complex 3D architecture. One intrinsic limitation of such a production strategy is the contradictory stiffness requirements for the folding and for subsequent load-bearing steps: while a low stiffness is required to allow for the successful completion of the intended self-folding process, a high stiffness is needed for the subsequent application of the folded structure as a load-bearing mechanical metamaterial. The competition between these two requirements determines the theoretical limits of 4D printed self-folding mechanical metamaterials, which have not been determined before. Here, we present a nonlinear analytical model of self-folding bilayer constructs composed of an active and a passive layer. This finite deformation theoretical model predicts the curvature of activated bilayers, establishes their stability limits, and estimates the stiffness of folded bilayers. Combining the three abovementioned aspects allows for establishing the theoretical stiffness limits of self-folding bilayers. The optimal combinations of geometrical and mechanical properties that result in the highest possible stiffness of folded constructs can then be determined. We compare the predictions of our analytical models with computational as well as experimental results. Finally, we evaluate the theoretical stiffness limits of bilayer constructs made using the most common types of stimuli-responsive materials. Our analysis shows that a maximum effective modulus of ~1.5 GPa can be achieved using the currently available shape-memory polymers.

Rendering objects invisible to impinging acoustic waves (cloaking) and creating acoustic illusions (holography) has been attempted using active and passive approaches. While passive methods are applicable only to narrow frequency bands, active approaches attempt to respond dynamically, interfering with broadband incident or scattered wavefields by emitting secondary waves. Without prior knowledge of the primary wavefield, the signals for the secondary sources need to be estimated and adapted in real-time. This has thus far impeded active cloaking and holography for broadband wavefields. We present experimental results of active acoustic cloaking and holography without prior knowledge of the wavefield so that objects remain invisible and illusions intact even for broadband moving sources. This opens novel research directions and facilitates practical applications including architectural acoustics, and stealth.

In 2011-2012, the Georgia legislature funded a series of ongoing studies to evaluate Georgia's Pre-K Program. The 2016-2017 Georgia's Pre-K Program Evaluation focuses on the results of the fourth year of this longitudinal study, through second grade. The purpose of the current evaluation study was to examine longitudinal outcomes for children related to key academic and social skills as well as the quality of their classrooms from pre-k through second grade. The primary evaluation questions included: (1) What are the learning outcomes through second grade for children who attended Georgia's Pre-K Program?; (2) What factors predict better learning outcomes for children?; and (3) What is the quality of children's instructional experiences from pre-k through second grade? To address these questions, the evaluation study included a sample of 1,169 children (139 Spanish-speaking dual language learners/DLLs) attending a random sample of 199 Georgia's Pre-K classrooms in year 1. Of the original sample of children, 1,034 were followed into kindergarten in year 2 (118 Spanish-speaking DLLs), 969 (119 Spanish-speaking DLLs) were followed into first grade in year 3, and 951 (116 Spanish-speaking DLLs) were followed into second grade in year 4. Researchers conducted individual child assessments near the beginning and end of each year to examine growth in children's skills. The assessment measures covered multiple domains of learning, including language, literacy, math, executive function, and teacher ratings of behavior skills. For the DLL subsample, parallel assessments were conducted in both English and Spanish. Researchers also conducted observations in children's classrooms each year from pre-k through second grade to gather data on the quality of teacher-child instructional interactions using the Classroom Assessment Scoring System (CLASS). In addition, information about characteristics of the classrooms, teachers, and children was gathered from teacher and parent surveys and from existing statewide pre-k program data. Child/family characteristics, classroom/teacher characteristics, and classroom quality were examined as predictors of children's growth in skills. Overall, this large, representative sample of children who attended Georgia's Pre-K continued to perform near the mean on most standardized measures based on national norms by the end of second grade. Although children continued to learn and develop throughout this period, their growth was greater than expected from pre-k through kindergarten, but decreased during first and second grades for most measures. [For the executive summary of this report, see ED598161.]

The primary purpose of the 2017-2018 NC Pre-Kindergarten (NC Pre-K) Evaluation was to examine the effectiveness of the NC Pre-K Program using a randomized controlled trial (RCT) design. The major issue addressed by this type of study is around the benefits of offering children access to enrollment in NC Pre-K. An RCT is considered the gold-standard design for addressing such a question because children are randomly assigned to either receive the program (treatment) or not (control). Therefore, differences in outcomes can be causally attributed to whether or not they received treatment rather than to other differences between the children and families in the two different groups. This study is designed to follow children longitudinally from pre-k into elementary school in order to examine the short- and longer-term effects. The current study (2017-2018) provided baseline data about children's outcomes during their pre-k year. This small-scale study compared 582 children who were randomly assigned to either NC Pre-K (Treatment=473) or the waitlist (Control=109) in two selected counties with substantially large waitlists. Because children in both groups had applied to and were eligible for NC Pre-K, they had similar characteristics. However, because not everyone could be served with the available number of program slots, random assignment was used to select children for NC Pre-K or the waitlist (with very few crossovers between groups). The study considered factors that might affect the impact of receiving the treatment -- specifically, children's level of oral language proficiency and classroom quality for children in preschool settings. In addition, the study also included a sample of children who were Spanish-speaking dual language learners and gathered data in both Spanish and English to examine the effects of treatment in both their first and second languages. [For the executive summary of this report, see ED598159.]

The primary purpose of the 2016-2017 North Carolina (NC) Pre-Kindergarten (NC Pre-K) Evaluation study was to examine variability in enrollment practices within the statewide Pre-K Program. Four major categories of enrollment practices were examined: recruitment, application, placement, and waitlist. The study involved all 91 local NC Pre-K Program contracts, with data gathered through both surveys and phone interviews. The results provided information about local variations in implementation of the NC Pre-K Program and how these variations impacted who was served and not served by the program; how placement decisions were made; who was on the waitlist (i.e., those who applied to the NC Pre-K Program but were not selected); and the extent of collaboration and coordination of NC Pre-K with other programs and agencies. Second, these data also were used to inform the feasibility and design of the subsequent year's evaluation utilizing a randomized controlled trial (RCT) design. These data provided information about how children were recruited and placed, which populations of children were served by the program, where there were sufficient waitlists to conduct random assignment into the program, and the likely make-up of the control group to help guide sample selection, study recruitment, and the development of procedures for collaborating with local Pre-K administrators and programs on the study. In addition, key characteristics of the NC Pre-K Program during the 2016-2017 year, along with trends over time (2003-2004 to 2016-2017), were examined based on statewide administrative data (NC Pre-K Kids and NC Pre-K Plan). Information examined included characteristics of the local NC Pre-K settings, the children served, the qualifications of teachers, and the distributions and counts of program participants and service providers. Since the inception of the statewide Pre-K program in North Carolina in 2001-2002, the evaluation has been conducted by the FPG Child Development Institute at the University of North Carolina-Chapel Hill.

We study Morse theory of the (power) distance function to a set of points in $\mathbb{R}^n$. We describe the topology of the union of the corresponding set of growing balls by a Morse poset. The Morse poset is related to the power tesselation of $\mathbb{R}^n$. We remark that the power diagrams from computer science are the spines of amoebas in algebraic geometry, or the hypersurfaces in tropical geometry. We show that there exists a discrete Morse function on the coherent triangulation, dual to the power diagram, such that its critical set equals the Morse poset of the power diagram., Comment: 37 pages, 24 figures. In this updated version we have added an extra section about the 2-dimensional case. Moreover added more details, update of proofs and extra pictures in order to improve the exposition. Section about medial axis removed, since this is published separately. Former title was: "Power Diagrams and their applications"

From computational geometry comes the notion of a Gabriel graph of a point set in the plane. The Gabriel graph consists of those edges connecting two points of the point set such that the circle whose diameter is the edge does not contain any point of the point set in its interior. We define a generalization of the Gabriel graph to $n$ dimensions: the Morse poset. Using Morse theory we prove that for a generic set of 4 points in $\bR^3$ there are nine different Morse posets, up to combinatorial equivalence. At the end we mention some open questions and report on the results of computer experiments concerning these. We also compare our shape classification to another criterion widely used in computer science., Comment: 14 pages, 4 figures

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in $\R^n$ occur when $0 \leq n-l \leq 4$. Other related sets, such as kite curves and centre sets are also defined and discussed. Throughout canonical relations are used as an essential tool to carry out several of these geometrical constructions., Comment: 20 pages, 12 figures