The SS433 is a well-known binary system with an internal black hole, which is stripping mass from an orbiting companion of ten solar masses, at a hundred of light-seconds away. The black hole and its accretion disk fuel a thin precessing jet, whose spirals are well-observed. Surprisingly, disconnected gamma-ray tails have recently been discovered by H.E.S.S., HAWC and LHAASO, hundreds of light-years away and with energies of tens of TeV. We suggest that tens PeV neutron burst jets were ejected from the SS433 system over the past century. These beams of ultra high-energy PeVatron neutrons, by their in-flight beta decay and Inverse Compton scattering, could be the source of the enigmatic, distant and disconnected tens of TeV gamma-ray beams. These ultra-relativistic PeV neutron jets could have been formed during one of the system's rare and intense tidal eruptions, when tens of PeV protons collide CV October 2025 with thermal ultraviolet photons, creating delta resonances. Their decay into secondary neutron beams of tens of PeV is well consistent with observations. Alternative models appear uncompetitive.

We derive a generalized Beth-Uhlenbeck formula for the entropy of a dense fermion system with strong two-particle correlations, including scattering states and bound states. We work within the $Φ-$derivable approach to the thermodynamic potential. The formula takes the form of an energy-momentum integral over a statistical distribution function times a unique spectral density. In the near mass-shell limit, the spectral density reduces, contrary to naïve expectations, not to a Lorentzian but rather to a "squared Lorentzian" shape. The relation of the Beth-Uhlenbeck formula to the $Φ$-derivable approach is exact at the two-loop level for $Φ$. The formalism we develop, which extends the Beth-Uhlenbeck approach beyond the low-density limit, includes Mott dissociation of bound states, in accordance with Levinson's theorem, and the self-consistent back reaction of correlations in the fermion propagation. We discuss applications to further systems, such as quark matter and nuclear matter.

We develop a unified framework to analyze $d$-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity $F$ (how well a protocol works on average) and fidelity deviation $D$ (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for $F$ and $D$ in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair $(F, D)$ can be ported into a visibility estimate for isotropic channel resources, turning the $(F, D)$-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the $(F,D)$ plane: one line certifies that $F$ beats the classical benchmark $2/(d{+}1)$, while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.

Quantum computers based on cold-atom arrays offer long-lived qubits with programmable connectivity, yet their progress toward fault-tolerant operation is limited by the relatively low fidelity of site-selective local control. We introduce an artificial-intelligence (AI) framework that overcomes this limitation. Trained on atom-laser dynamics, a deep neural network autonomously designs composite pulses that improve local control fidelities tenfold while remaining compatible with existing control hardware. We further demonstrate the robustness of these pulses against optical aberrations and beam misalignment. This approach establishes AI-trained pulse compilation for high-fidelity qubit control and can be readily extended to other atom-like platforms, such as trapped ions and solid-state color centers.

The study of quantum reference frames has received renewed interest over the last years, leading to the parallel development of non-equivalent frameworks by different communities. We clarify the differences between these frameworks. At the mathematical level, they mainly differ in the kind of symmetry (either weak or strong) employed to constrain the system. We show that this mathematical difference corresponds to a fundamental physical question: whether the global charge associated to the symmetry group is accessible to symmetry-constrained observers. In this context, we formulate a definition of a perspective in terms of operational capacities, or lack thereof. Turning to consequences of adopting either approach, we discuss how adopting the weak approach induces an ambiguity in the momenta included in each perspective and bars from defining reversible QRF transformations. We then review and analyze the existing arguments motivating each approach, and show how they bear upon the problem of charge accessibility. Finally, we introduce a simple operational scenario in which upholding two reasonable physical postulates leads to the conclusion that internal observers could measure the global charge by 1/ performing a relativized interference measurement and 2/ classically communicating.

We report a fully kinetic, quantum study of Kinetic Electrostatic Electron Nonlinear (KEEN) waves, showing that quantum diffraction systematically erodes the classical trapping mechanism, narrow harmonic locking to the fundamental, and hasten post-drive decay. Electrons are evolved with a second-order Strang-split 1D1V Wigner-Poisson solver that couples conservative semi-Lagrangian WENO advection to an analytic Fourier space update for the non-local Wigner term, while ions remain classical. Short, frequency-tuned ponderomotive pulses drive KEEN formation in a uniform Maxwellian plasma; as the dimensionless quantum parameter H rises from the classical limit to values relevant to warm-dense matter, doped semiconductors, and 2D electron systems, the drive threshold increases, higher harmonics are damped, trapped electron vortices diffuse, and the subplasma electrostatic energy relaxes to a lower stationary level, as confirmed by continuous wavelet analysis. These microscopic changes carry macroscopic weight. Ignition-scale capsules now compress matter to regimes where the electron de Broglie wavelength rivals the Debye length, making classical kinetic descriptions insufficient. By extending KEEN physics into this quantum domain, our results offer a potential diagnostic of nonequilibrium electron dynamics for next-generation inertial-confinement designs and high-energy-density platforms, indicating that predictive fusion modeling may benefit from the integration of kinetic fidelity with quantum effects.

The Richards equation, a nonlinear elliptic parabolic equation, is widely used to model infiltration in porous media. We develop a finite element method for solving the Richards equation by introducing a new bounded auxiliary variable to eliminate unbounded terms in the weak formulation of the method. This formulation is discretized using a semi-implicit scheme and the resulting nonlinear system is solved using Newton's method. Our approach eliminates the need of regularization techniques and offers advantages in handling both dry and fully saturated zones. In the proposed techniques, a non-overlapping Schwarz domain decomposition method is used for modeling infiltration in layered soils. We apply the proposed method to solve the Richards equation using the Havercamp and van Genuchten models for the capillary pressure. Numerical experiments are performed to validate the proposed approach, including tests such as modeling flows in fibrous sheets where the initial medium is totally dry, two cases with fully saturated and dry regions, and an infiltration problem in layered soils. The numerical results demonstrate the stability and accuracy of the proposed numerical method. The numerical solutions remain positive in the presence of totally dry zones. The numerical investigations clearly demonstrated the capability of the proposed method to effectively predict the dynamics of flows in unsaturated soils.

The rapid decay of target signal strength with distance from the sensor presents a key challenge in nanoscale magnetic sensing with nitrogen-vacancy (NV) centers in diamond, limiting both sensitivity and spatial resolution. Here we introduce a strategy to overcome this limitation by using radical anions formed from rhodamine-derived dyes as reporter spins localized to the diamond surface. These radicals, generated through photoreduction, are optically identifiable and stable on timescales exceeding an hour. We experimentally demonstrate their coherent manipulation and detection using single, shallow NV centers for readout. We observe heterogeneity in the local magnetic environments of the photoactivated spins from site to site, likely due to variations in inter-radical couplings across our measurements. Looking forward, our approach enables correlative nanoscale magnetic and optical imaging, and opens new pathways toward single-molecule magnetic resonance studies.

Electrons bound to the surface of superfluid helium have been proposed for scalable charge and spin-based quantum computing. However single electron quantum measurement in this system has remained elusive. Here we use a hybrid circuit quantum electrodynamic (cQED) device that comprises a quantum dot and a high-impedance superconducting resonator to demonstrate, for the first time, strong coupling between the resonator microwave field and the motional quantum state of the electron. We find a coupling strength between the electron motion and a resonator photon of $g/2π=118$ MHz, exceeding both the electron motional state decoherence and the resonator loss. These experiments open new avenues for investigating light-matter interaction at the single electron level, and are a key step towards measurement and control of electrons on helium-based spin qubits.

We present a real-time quantum Monte Carlo algorithm that simulates the dynamics of open quantum systems by stochastically compressing and evolving the density matrix under both Markovian and non-Markovian master equations. Our algorithm uses population dynamics to continuously suppress the sign problem, preventing its accumulation throughout the evolution. We apply it to a variety of quantum circuits and demonstrate significant speedups over state-of-art quantum trajectory methods and convergence to exact solutions even in non-Markovian regimes where trajectory methods fail. Our approach improves the efficiency of classical simulation of gate-based quantum computing, quantum annealing, and general open system dynamics.

The present work concerns the detailed construction of a holographic model for a type-II s-wave superconductor defined on a 5-dimensional anisotropic rotating black hole. We examine the role of rotation and anisotropy on the properties of the superconductor model focusing on the condensate and the AC conductivity, for which we obtain closed formulas, using both analytical and numerical methods. The results reveal that the rotation is responsible for the appearance of a peak and for introducing an exponentially vanishing behavior in the high-frequency limit of the real component of the AC conductivity. Such a behavior aligns with that observed in high-temperature superconductor models and experiments, where the peak and vanishing behavior result from quasiparticle damping, suggesting a relation between the {\it rotation of a black hole} and {\it quasiparticle damping effects} due to impurities or defects in a superconducting material. This relation supplements the holographic dictionary of the gravity/Condensed Matter Theory correspondence. In addition, we provide a detailed construction of the vortex lattice presented in arXiv:2208.05988 and study its behavior as a function of an external uniform magnetic field. Once again, it is shown that the vortex lattice can be continuously deformed along with a change in the vortex population by virtue of the magnetic field, providing a promising avenue for holographically modeling the vortex lattice deformations observed in experimental studies with superconducting materials. As a concrete example, we describe both the vortex lattice deformation and the increment of the vortex population under the action of an external magnetic field in the LiFeAs type-II superconductor. These effects supplement those previously found for the FeSe type-II superconductor studied in arXiv:2208.05988.

Recent observations have revealed star-forming regions as possible origin sites of very-high-energy (TeV) cosmic rays, not associated with supernova remnants. Colliding-wind binaries (CWBs) are strong X-ray and radio synchrotron emitters and have been proposed as potential accelerators of such particles. We perform high-resolution three-dimensional magnetohydrodynamic simulations coupled with test-particle integration to investigate how local plasma conditions affect particle acceleration in CWBs. We find that the maximum particle energies and the hardness of the energy distributions depend on the shock magnetization and cooling efficiency. For moderate magnetization ($\gt$1 G), CWBs can accelerate hadronic particles up to hundreds of TeV or even PeV energies, with more than 1\% of particles reaching the very-high-energy range. By correlating the local acceleration rate with plasma quantities - \textit{magnetic field strength, current density, vorticity, and velocity divergence} - we show that turbulence and magnetic field complexity dominate the acceleration, while classical diffusive shock acceleration plays a limited role. These results suggest that turbulent, magnetically driven processes are key to producing relativistic particles in CWBs, with implications for future high sensitivity $γ$-ray observations (e.g. LACT and CTAO).

The nitrogen-vacancy (NV) center in diamond is emerging as a powerful tool for imaging magnetic and electric signals at the microscale and below. However, most imaging demonstrations thus far have relied on costly, millimeter-sized bulk diamond substrates, which cannot be easily scaled or integrated with other materials. Here, we report a scalable method for fabricating NV-containing dense and homogenous fluorescent nanodiamond (FND) layers through electrostatic self-assembly and demonstrate the utility of the FND layers for magnetic imaging. We investigate the effect of FND concentration in suspension, substrate immersion time, and solvent pH on the FND density on the substrate. We identify optimized self-assembly conditions that maximize the FND density while minimizing aggregation. Using FND layers on a quartz substrate, we demonstrate magnetic field and magnetic noise imaging at the microscale, based on NV optically detected magnetic resonance magnetometry and T$_1$ relaxometry, respectively. Our results provide a direction for the development of cost-effective and scalable FND layers and surface coatings. This paves the way for on-demand quantum sensing and imaging on a broad range of surfaces based on NV centers and other diamond quantum emitters.

We develop a real-space first-principles method based on density functional theory to investigate orbitronic phenomena in complex materials. Using the Real-Space Linear Muffin-Tin Orbital method within the Atomic Sphere Approximation (RS-LMTO-ASA) combined with a Chebyshev polynomial expansion of the Green's functions, we compute orbital (spin) Hall transport and orbital (spin) accumulation directly in real space. The approach scales linearly with system size and naturally incorporates disorder, finite-size effects, and interface roughness. We apply the method to transition-metal-based heterostructures and demonstrate the emergence of substantial orbital (spin) accumulation, even in centrosymmetric systems. Our methodology provides a scalable and flexible framework for realistic simulations of orbital transport phenomena in complex heterostructures.

Granular creep is the slow, sub-yield movement of constituents in a granular packing due to the disordered nature of its grain-scale interactions. Despite the ubiquity of creep in disordered materials, it is still not understood how to best predict the creep-to-failure regime based on the forces and interactions among constituents. To address this gap, we perform experiments to explore creep and failure in quasi two-dimensional piles of photoelastic disks, allowing the quantification of both grain movements and grain-scale contact force networks. Through controlled external disturbances, we investigate the emergence and evolution of grain rearrangements, force networks, and voids to illuminate signatures of creep and failure. Surprisingly, the force chain structure remains dynamic even in the absence of observable particle motion. We find that shifts in force chains provide an indication to larger, avalanche-scale disruptions. We connect these force signatures with the geometry of the voids in the pile. Overall, our novel experiments and analyses deepen our mechanical and geometric understanding of the creep-to-failure transition in granular systems.

The free energy, or equivalently the ground state energy in finite volume, may be calculated from forward scattering amplitudes using a formula due to Dashen, Ma, and Bernstein. However a naive treatment leads to singularities when considering the scattering of three or more particles. It is shown in detail how the approach can be applied to multi-particle scattering in various massive scalar theories in 1+1d, with or without integrability. The results for the sinh-Gordon, Lieb-Liniger, and $O(N)$ non-linear sigma models are compared to exact results. It is shown how bound states can be considered in this approach by considering the attractive Lieb-Liniger model.

The Kolmogorov-Zakharov stationary states for weak wave turbulence involve solving a leading-order kinetic equation. Recent calculations of higher-order corrections to this kinetic equation using the Martin-Siggia-Rose path integral are reconsidered in terms of stationary states of a Fokker-Planck Hamiltonian. A non-perturbative relation closely related to the quantum mechanical Ehrenfest theorem is introduced and used to express the kinetic equation in terms of divergences of two-point expectation values in the limit of zero dissipation. Similar equations are associated to divergences in higher-order cumulants. It is additionally shown that the ordinary thermal equilibrium state is not actually a stationary state of the Fokker-Planck Hamiltonian, and a non-linear modification of dissipation is considered to remedy this.

Metastable atomic qubits are a highly promising platform for the realization of quantum computers, owing to their scalability and the possibility of converting leakage errors to erasure errors mid-circuit. Here, we demonstrate and characterize a universal gate set for the metastable fine-structure qubit encoded between the $^3\text{P}_0$ and $^3\text{P}_2$ states in bosonic strontium-88. We find single-qubit gate fidelities of 0.993(1), and two-qubit gate fidelities of 0.9945(6) after correcting for losses during the gate operation. Furthermore, we present a novel state-resolved detection scheme for the two fine-structure states that enables high-fidelity detection of qubit loss. Finally, we leverage the existence of a stable ground state outside the qubit subspace to perform mid-circuit erasure conversion using fast destructive imaging. Our results establish the strontium fine-structure qubit as a promising candidate for near-term error-corrected quantum computers, offering unique scaling perspectives.

We present a novel approach to implementing all-optical Rectified Linear Unit (ReLU) activation functions using compact doubly-resonant cavities with dimensions of approximately $10\,μ\mathrm{m}$. Our design leverages $χ^{(2)}$ nonlinear processes within carefully engineered photonic structures that simultaneously resonate at both fundamental and second-harmonic frequencies. By exploiting the phase-sensitive nature of second-harmonic generation, we demonstrate an optical analog to the ReLU function, achieving femtojoule-level activation energy-comparable to state-of-the-art approaches-while reducing device footprint by two orders of magnitude compared to previous implementations. We develop the theoretical framework using coupled-mode theory and validate it through rigorous finite-difference time-domain simulations. Beyond ReLU, we show that the same physical structure can implement alternative activation functions such as ELU and GELU through simple adjustments to input conditions. Neural network simulations demonstrate that our proposed optical activation functions achieve classification accuracy within $0.4\%$ of ideal electronic implementations while offering significant advantages in energy efficiency and processing speed. This work represents a significant advancement toward realizing energy-efficient, high-density optical neural networks for next-generation artificial intelligence hardware.

In this work, we report the recent progress in obtaining new curvature-squared invariants in 5D, N=1 gauged minimal supergravity. We exhibit the structure of various composite multiplets that are pivotal in the construction. We also present the form of the gauged Riemann-squared and Gauss-Bonnet superinvariants in a dilaton-Weyl multiplet. As a first application of the new curvature squared invariants, we compute their corrections to holographic central charges and the Euclidean action of supersymmetric charged rotating black holes, exhibiting exact matching between the gravity and CFT results.

In the context of planar conformal gauge theory, we study five-point correlation functions between the interaction Lagrangian and four of the lightest single-trace, gauge-invariant scalar primaries. After performing two light-cone OPEs, we express this correlator in terms of the three-point functions between two leading-twist spinning operators and the Lagrangian. For finite values of spin, we compute these structure constants in perturbation theory up to two loops in N=4 super Yang-Mills theory. Large values of spin are captured by null polygon kinematics, where we use dualities with null polygon Wilson loops as well as factorization properties to bootstrap the universal behavior of the structure constants at all loops. We find explicit maps that relate the Lagrangian structure constants with the leading-twist anomalous dimension. From the large-spin map, we recover the cusp anomalous dimension at strong and weak coupling, including genus-one terms.

Soft and active condensed matter represent a class of fascinating materials that we encounter in our everyday lives -- and constitute life itself. Control signals interact with the dynamics of these systems, and this influence is formalized in control theory and optimal control. Recent advances have employed various control-theoretical methods to design desired dynamics, properties, and functionality. Here we provide an introduction to optimal control aimed at physicists working with soft and active matter. We describe two main categories of control, feedforward control and feedback control, and their corresponding optimal control methods. We emphasize their parallels to Lagrangian and Hamiltonian mechanics, and provide a worked example problem. Finally, we review recent studies of control in soft, active, and related systems. Applying control theory to soft, active, and living systems will lead to an improved understanding of the signal processing, information flows, and actuation that underlie the physics of life.

Creating superior lanthanide-activated inorganic phosphors is pivotal for advancing energy-efficient LED lighting and backlit flat panel displays. The most fundamental property these luminescent materials must possess is effective absorption/excitation by a blue InGaN LED for practical conversion into white light. The 5$d_1$ excited state energy level of lanthanides, which determines the excitation peak position, is influenced by the inorganic host structure, including the local environment, crystal structure, and composition, making it challenging to predict in advance. This study introduces a new extreme gradient boosting machine learning method that quantitatively determines a phosphor's longest (lowest energy) excitation wavelength. We focus on the Ce$^{3+}$ 4$f$ $\rightarrow$ 5$d$ transition due to its well-defined 5$d_1$ energy level observed in excitation and diffuse reflectance spectra. The model was trained on experimental data for 357 Ce$^{3+}$ cation substitution sites sourced from literature and in-house measurements and ultimately experimentally validated through the successful synthesis of a novel, blue-excited, green-emitting phosphor: Ca$_2$SrSc$_6$O$_{12}$:Ce$^{3+}$. This compound's excitation under commercial blue LED wavelength aligned remarkably well with the model's predictions. These results highlight the transformative potential of data-driven approaches in expediting the discovery of blue-absorbing phosphors for next-generation LED lighting.

Recent studies have shown that a soliton can be {\it fractionally} transported by slowly varying a system parameter over one period in a nonlinear system. This phenomenon is attributed to the nontrivial topology of the corresponding energy bands of a linear Hamiltonian. Here we find the occurrence of fractional Thouless pumping of solitons in a nonlinear off-diagonal Aubry-André-Harper model. Surprisingly, this happens despite the fact that all the energy bands of the linear Hamiltonian are topologically trivial, indicating that nonlinearity can induce fractional Thouless pumping of solitons. Specifically, our results show that a soliton can be pumped across one unit cell over one, two, three or four pump periods, implying an average displacement of $1$, $1/2$, $1/3$ or $1/4$ unit cells per cycle, respectively. We attribute these behaviors to changes in on-site potentials induced by a soliton solution, leading to the nontrivial topology for the modified linear Hamiltonian. Given that our model relies solely on varying nearest-neighbor hoppings, it is readily implementable on existing state-of-the-art photonic platforms.

The $\frac12$-BPS indices of $\mathcal{N}=4$ Super Yang-Mills theory with unitary, orthogonal, and symplectic groups all admit $q$-expansions suggesting an interpretation in terms of D-branes in the dual bulk AdS$_5$ string theories. We present a derivation of these expansions in the corresponding bulk duals by quantizing the moduli space of $\frac12$-BPS giant gravitons using supersymmetric localization, extending and clarifying our study in arxiv:2312.14921. We perform a detailed analysis of the one-loop fluctuations around the maximal giants (the fixed points), and show how the Hamiltonian analysis is recovered from the functional integral for the equivariant index. We show that the analytic continuation for these giant graviton expansions observed in the literature maps precisely to a wall-crossing phenomenon for the index. In the case of orthogonal and symplectic gauge groups, the $\mathbb{Z}_2$ quotient in the bulk leads to a corresponding projection in the $q$-expansion. Additional terms in the expansion related to the Pfaffian operator arise from topologically stable branes in the bulk dual on AdS$_5 \times \mathbb{RP}^5$.

We report the experimental super-resolution of pairs of point-like fluorescent sources using a modified image inversion interferometer microscope. The technique is inspired by recent developments in the application of quantum parameter estimation theory to semiclassical imaging problems. We find that the image inversion technique requires special polarization filtering to account for the dipolar nature of the emission. Using an azimuthal polarizer, we obtain improvements in the Fisher information of point-source separation by over an order of magnitude relative to direct imaging. Unlike established super-resolution fluorescence techniques, the method does not require sequential photoswitching/blinking of the fluorophores, and thus could facilitate significant speed-ups for certain biological imaging/tracking tasks.

The Galactic disk is one of the main components of the Milky Way, which contributes most of the luminosity. Its structure is essential for understanding the formation and evolution of the Milky Way. Using 174,443 K-type dwarf stars observed by both LAMOST and Gaia DR3, we study the disk density profile in the local volume within 1,200 pc. In the azimuthal dimension, we find strong asymmetric signal of the thin disk. The surface density and the scale height of the southern disk significantly change versus the azimuthal angle at the same galactocentric distance $R$. Meanwhile, in the vertical dimension, the scale height of the northern disk has quite different trend than that of the southern one. The scale height of the southern disk shows a decreasing trend with $ϕ\sim-2.5^\circ$, and change to an increasing one with $ϕ\sim5.0^°$. Meanwhile, the scale height of the northern disk has a consistently smaller increase. Finally, we divide the entire sample into three subsamples based on metallicity and all three subsamples show significant non-axisymmetric and north-south asymmetric signals in the Galactic disk. Furthermore, we find that the scale height of the metal-poor ([Fe/H] $<$ -0.4 dex) subsample in the northern disk is greater than that of the metal-rich ([Fe/H] $>$ -0.1 dex) subsample. However, in the southern disk, the scale height exhibits varying relationships across different metallicity slices.

Very long baseline radio interferometry (VLBI) with ground-based observatories is limited by the size of Earth, the geographic distribution of antennas, and the transparency of the atmosphere. In this whitepaper, we present a design for a space-to-space VLBI program composed of two missions: Mimosa, a pathfinder, and Capella, a science-grade VLBI observatory. Mimosa is a two-element space-to-space radio interferometer composed of two small (250 kg) satellites on co-planar polar circular low Earth orbits. Using single-band, single-circular polarization heterodyne HEMT receivers operating at frequencies around 100 GHz, the interferometer is able to achieve a near-perfect visibility plane coverage and an angular resolution of approximately 35 microarcsec. Capella comprises four small (500 kg) satellites in two orthogonal polar low-Earth orbit planes. With single-band heterodyne receivers operating at frequencies around 690 GHz, the interferometer is able to achieve angular resolutions of approximately 7 microarcsec. Within a total observing time of three days, a near-complete uv plane coverage can be reached. The technology for all key components required - radio telescope, receiver, sampler, recorder, frequency standard, positioning system, data downlink, and pointing control system - is already available, partially off-the-shelf. Capella will be able to address a range of science cases, including: the shadows of supermassive black holes; the acceleration and collimation zones of plasma jets emitted from the vicinity of supermassive black holes; the chemical composition of accretion flows into active galactic nuclei through observations of molecular absorption lines; mapping supermassive binary black holes; the magnetic activity of stars; and nova eruptions of symbiotic binary stars -- and, like any substantially new observing technique, has the potential for unexpected discoveries.

The excess work performed in a heat-engine process with given finite operation time τis bounded by the thermodynamic length, which measures the distance during the relaxation along a path in the space of the thermodynamic state. Unfortunately, the thermodynamic length, as a guidance for the heat engine optimization, is beyond the experimental measurement. We propose to measure the thermodynamic length \mathcal{L} through the extrapolation of finite-time measurements \mathcal{L}(τ)=\int_{0}^τ[P_{\mathrm{ex}}(t)]^{1/2}dt via the excess power P_{\mathrm{ex}}(t). The current proposal allows to measure the thermodynamic length for a single control parameter without requiring extra effort to find the optimal control scheme. We illustrate the measurement strategy via examples of the quantum harmonic oscillator with tuning frequency and the classical ideal gas with changing volume.

The Schur index of a $4$ dimensional $\mathcal{N}=2$ superconformal field theory counts (with sign) bosonic and fermionic states that preserve $4$ supercharges. We consider the Schur indices of $4$d $\mathcal{N}=4$ super Yang-Mills and $\mathcal{N}=2$ circular quiver gauge theories with gauge groups $U(N)$ or $SU(N)$. We calculate the exponentially dominant part of their asymptotic expansions as the index parameter $q$ approaches any root of unity. We find that some of the indices exhibit ``small" ($\mathcal{O}(N^0)$ as $N \rightarrow \infty$) exponential growth, which is much smaller than an $\mathcal{O}(N^2)$ exponential growth of states that is indicative of a black hole. This implies that the indices do not capture a growth of states that would correspond to a supersymmetric black hole that preserves 4 supercharges in the holographic dual AdS theory. Interestingly, the exponentially dominant part in the Schur asymptotics we consider, depends on the parity of the rank $N$.