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A bstract We implement a bootstrap method that combines stationary state conditions, thermal inequalities, and semidefinite relaxations of matrix logarithm in the ungauged one-matrix quantum mechanics, at finite rank N as well as in the large N limit, and determine finite temperature observables that interpolate between available analytic results in the low and high temperature limits respectively. We also obtain bootstrap bounds on thermal phase transition as well as preliminary results in the ungauged two-matrix quantum mechanics.

Capturing the structural changes that molecules undergo during chemical reactions in real space and time is a long-standing dream and an essential prerequisite for understanding and ultimately controlling femtochemistry. A key approach to tackle this challenging task is Coulomb explosion imaging, which has benefited decisively from recently emerging high-repetition-rate X-ray free-electron laser sources. With this technique, information on the molecular structure is inferred from the momentum distributions of the ions produced by the rapid Coulomb explosion of molecules. Retrieving molecular structures from these distributions poses a highly nonlinear inverse problem that remains unsolved for molecules consisting of more than a few atoms. Here, we address this challenge using a diffusion-based Transformer neural network. We show that the network reconstructs unknown molecular geometries from ion-momentum distributions with a mean absolute error below one Bohr radius, which is half the length of a typical chemical bond. Coulomb explosion imaging provides real space/time resolution of molecular processes. Here the authors develop a generative model to reconstruct molecular geometries from ion momentum measurements which extends the system size accessible with this technique.

We establish an equivalence between non-isometry of quantum codes and state dependence of operator reconstruction, and discuss implications of this equivalence for holographic duality. Specifically, we define quantitative measures of non-isometry and state dependence and describe bounds relating these quantities. In the context of holography we show that, assuming known gravitational path integral results for overlaps between semiclassical states, non-isometric bulk-to-boundary maps with a trivial kernel are approximately isometric and bulk reconstruction approximately state-independent. In contrast, non-isometric maps with a non-empty kernel always lead to state-dependent reconstruction. We also show that if a global bulk-to-boundary map is non-isometric, then there exists a region in the bulk which is causally disconnected from the boundary. Finally, we conjecture that, under certain physical assumptions for the definition of the Hilbert space of effective field theory in AdS space, the presence of a global horizon implies a non-isometric global bulk-to-boundary map.

The entanglement negativity 𝓔(A : B) is a useful measure of quantum entanglement in bipartite mixed states. In random tensor networks (RTNs), which are related to fixed-area states, it was found in ref. [1] that the dominant saddles computing the even Rényi negativity 𝓔(2k) generically break the ℤ2k replica symmetry. This calls into question previous calculations of holographic negativity using 2D CFT techniques that assumed ℤ2k replica symmetry and proposed that the negativity was related to the entanglement wedge cross section. In this paper, we resolve this issue by showing that in general holographic states, the saddles computing 𝓔(2k) indeed break the ℤ2k replica symmetry.

We present the tightest cosmic microwave background (CMB) lensing constraints to date on the growth of structure by combining CMB lensing measurements from the Atacama Cosmology Telescope (ACT), the South Pole Telescope (SPT) and Planck. Each of these surveys individually provides lensing measurements with similarly high statistical power, achieving signal-to-noise ratios of approximately 40. The combined lensing bandpowers represent the most precise CMB lensing power spectrum measurement to date with a signal-to-noise ratio of 61 and an amplitude of \\(A_lens^recon = 1.025 0.017\\) with respect to the theory prediction from the best-fit CMB Planck-ACT cosmology. The bandpowers from all three lensing datasets, analyzed jointly, yield a \\(1.6\\%\\) measurement of the parameter combination \\(S_8^CMBL _8\\,(_m/0.3)^0.25 = 0.825^+0.015_-0.013\\). Including Dark Energy Spectroscopic Instrument (DESI) Baryon Acoustic Oscillation (BAO) data improves the constraint on the amplitude of matter fluctuations to \\(_8 = 0.829 0.009\\) (a \\(1.1\\%\\) determination). When combining with uncalibrated supernovae from Pantheon+, we present a \\(4\\%\\) sound-horizon-independent estimate of \\(H_0=66.42.5\\,km\\,s^-1\\,Mpc^-1 \\). The joint lensing constraints on structure growth and present-day Hubble rate are fully consistent with a \\(\\)CDM model fit to the primary CMB data from Planck and ACT. While the precise upper limit is sensitive to the choice of data and underlying model assumptions, when varying the neutrino mass sum within the \\(\\) cosmological model, the combination of primary CMB, BAO and CMB lensing drives the probable upper limit for the mass sum towards lower values, comparable to the minimum mass prior required by neutrino oscillation experiments.

The discovery of topological phases has introduced a new dimension to materials science. Three-dimensional (3D) topological insulators (TIs) are a remarkable class of matter that is insulating in the bulk while hosting conductive topological surface states (TSSs) with unique charge and spin properties. High-order harmonic generation (HHG) has emerged as a powerful tool to probe condensed matter systems by providing insights into their electronic structure and dynamic behavior. Here, we investigate HHG in the prototype 3D-TI Bi₂Se₃. We demonstrate that the contributions of bulk and surface states to the harmonic emission can be controlled by tuning the thickness of thin film samples. An ultrathin (6 nm) film substantially enhances HHG from the surface states, while the bulk states dominate HHG in a thicker (50 nm) film. By applying a quasi-static terahertz perturbing field, we disentangle the bulk and surface responses and reveal the significant impact of the surface states' shift vector and Berry curvature on HHG. Our study provides effective methods for isolating the optical responses of TSSs from those of the bulk, which opens the door to resolving an ongoing debate regarding whether it is possible to reliably extract topological signatures in HHG.

Jet flavour tagging enables the identification of jets originating from heavy-flavour quarks in proton–proton collisions at the Large Hadron Collider, playing a critical role in its physics programmes. This paper presents GN2, a transformer-based flavour tagging algorithm deployed by the ATLAS Collaboration that represents a different methodology compared to previous approaches. Designed to classify jets based on the flavour of their constituent particles, GN2 processes low-level tracking information in an end-to-end architecture and incorporates physics-informed auxiliary training objectives to enhance both interpretability and performance. Its performance is validated in both simulation and collision data. The measured c -jet (light-jet) rejection in data is improved by a factor of 3.5 (1.8) for a 70% b -jet tagging efficiency, compared to the previous algorithm. GN2 provides substantial benefits for physics analyses involving heavy-flavour jets, such as measurements of Higgs boson pair production and the couplings of bottom and charm quarks to the Higgs boson, and demonstrates the impact of advanced machine learning methods in experimental particle physics. Identifying jets originating from heavy quarks plays a fundamental role in hadronic collider experiments. In this work, the ATLAS Collaboration describes and tests a transformer-based neural network architecture for jet flavour tagging based on low-level input and physics-inspired constraints.

The electric monopole (\\(E0\\)) transition strength \\(^2\\) for the transition connecting the third 0\\(^+\\) level, a \"superdeformed\" band head, to the \"spherical\" 0\\(^+\\) ground state in doubly magic \\(^40\\)Ca has been determined via \\(e^+e^-\\) pair-conversion spectroscopy. The measured value, \\(^2(E0; 0^+_3 0^+_1)~=~2.3(5)10^-3\\), is the smallest \\(^2(E0; 0^+ 0^+)\\) found in \\(A<50\\) nuclei. In contrast, the \\(E0\\) transition strength to the ground state observed from the second 0\\(^+\\) state, a band head of \"normal\" deformation, is an order of magnitude larger, \\(^2(E0; 0^+_2 0^+_1)~=~25.9(16)~10^-3\\), which shows significant mixing between these two states. Large-Scale Shell Model (LSSM) calculations were performed to understand the microscopic structure of the excited states, and the configuration mixing between them; experimental \\(^2\\) values in \\(^40\\)Ca and neighboring isotopes were well reproduced by the LSSM calculations. The unusually small \\(^2(E0; 0^+_3 0^+_1)\\) value is due to destructive interference in the mixing of shape-coexisting structures, which are based on several different multiparticle-multihole excitations. This observation goes beyond the usual treatment of \\(E0\\) strengths, where two-state shape mixing cannot result in destructive interference.