Papers

The boson peak is a vibrational feature commonly found in glassy and disordered systems described as the deviation from the scaling of the Debye model ($g({E}){\propto}{E}^2$). Despite much interest, the microscopic nature of the vibrations is only anecdotally discussed. Here we report how the boson peak appears in conjunction with a crossover from localized to extended but non-wave-like and coincide with a maximum in phase coherence and spatial periodicity. Our analyses provide new insights into the microscopic origin of the boson peak across a wide range of glasses.

We reconsider the vacuum (Casimir) energy of a massive scalar field obeying Dirichlet boundary conditions inside a spherical cavity. Using zeta-function regularization, we carefully recalculate the analytic part of the zeta function via the uniform asymptotic expansion of the modified Bessel functions. We correct a sign error present in an earlier calculation (PR D56 (1997) 4896) that affected the large-mass behavior. The renormalized vacuum energy is shown to vanish for large mass, as required on physical grounds. Numerical results reveal that the energy changes sign several times as a function of the cavity radius.

While color centers in diamond and other three-dimensional crystals are nowadays key elements of several types of sensors, color centers in two-dimensional materials are rapidly developing and promise high-tech applications. One of the interesting centers in 2D materials is the negatively charged boron vacancy in hexagonal boron nitride (h-BN), which has already shown some potential for magnetometry, but the reliable creation of boron vacancies remains challenging. Here, we demonstrate the fabrication of negatively charged boron vacancy color centers in bulk h-BN via implantation of helium ions at ~1 MeV, as confirmed by characteristic photoluminescence and optically detected magnetic resonance. The resonance has a width of 180 MHz and exhibits the expected Zeeman shift of the resonance lines. The depth of the color center along the c-axis of the h-BN crystal was measured and compared with predictions from Stopping and Range of Ions in Matter modeling. The experimental value and the modeled prediction are consistent within the reported uncertainties, as their 1{\sigma} intervals overlap, although the experiment shows a greater depth and a wider distribution.

Radioactive iodine species, particularly I$_2$ and CH$_3$I, pose significant environmental and technological hazards owing to their high volatility, chemical stability, and relatively weak interaction with traditional substrate and sorption materials. In this work, we proposed a series of transition-metal (TM) (Fe, Ni, Cu, Zn) decorated boron-doped graphene (BDG) and 2D-MoTe2 substrates for efficient adsorptive capture and mitigation of such volatile Iodine species. Using systematic first-principles density functional theory (DFT) calculations, we elucidate the microscopic origin of the enhanced adsorption by analyzing the changes in the electronic structure upon adsorption. More importantly, we analyzed the thermodynamic and kinetic feasibility of adsorption on these newly designed substrates using Climbing-Image Nudged Elastic band (CI-NEB) calculations and found that TM decoration serves as an effective catalytic center, thereby making the reaction thermodynamically and kinetically feasible. Conversely, the reaction becomes thermodynamically and kinetically unfavorable on pristine substrates in the absence of a TM atom as a catalytic center. This work deepens our understanding of the electronic origin of the enhanced adsorption and reaction kinetics, and the predictions made will be useful for experimental realization.

The Lux-Zeplin collaboration recently reported one unusual event which was interpreted as first evidence for a WIMP (arXiv:2609.02823[hep-ex]). In this note we offer an alternative explanation of this event, following our earlier proposal that dark matter could consist of fractionally charged supermassive gravitinos. A main difference between the two interpretations is that one expects small cross sections and large flux rates for WIMPs, whereas it is the opposite for supermassive gravitinos, namely large (electromagnetic) cross sections and very low flux rates. The observed nuclear recoil energy of about 250 keV and the occurrence of one event in one year fit well with the estimates quoted in (K.A. Meissner, H.~Nicolai, Eur.Phys.J.C 84 (2024) 3, 269). A main characteristic of the new interpretation distinguishing it unequivocally from the WIMP hypothesis would be the sequential occurrence of two or more recoils within a few microseconds along the gravitino's straight trajectory, a prediction that remains to be checked. Such a measurement would also allow to overcome the `neutrino floor'. In this note we refine our previous estimates and propose some extra steps so as to enable the experiment to discriminate between the WIMP and gravitino hypotheses.

We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent $1/8$, preserved by arbitrary optimal control on any fixed spin set and, at the level of logarithmic exponents, on $o(\log N)$ spins. We derive the finite Cauchy product and its uniform strip asymptotics, and document exact two-spin optimization and an interferometric protocol for measuring the recovery. A separate finite-mediator theorem quantifies local compression and a decoder while retaining the rest of the environment exactly. We also give a ground-preparation Ramsey bound, counterexamples to stronger projected-state inferences, and independent full-Hamiltonian calculations.

Layer codes are three-dimensional local CSS codes of check weight at most six, obtained by quasi-concatenating a CSS input code with unrotated surface code patches. What is established about them describes the code, not the circuit that measures it. In this work, we evaluate them as active memories under circuit-level noise. Doing so first requires a syndrome extraction circuit, and the junction stabilizers that couple the patches rule out borrowing a surface code patch's CNOT schedule. We present a decoder-free scheduler that constrains hook propagation first and compresses depth afterwards, generate circuits for eighteen layer codes across four input codes, and compare them with surface codes of the same distance, simulated and decoded in the same way. The circuits lose no distance to hook errors on [[4,2,2]]-input codes wherever a circuit-distance proof is affordable, and reach a lower logical error rate than those of a general-purpose scheduler for CSS codes at roughly half its CNOT depth per round. Our primary family built from a [[4,2,2]] input code reaches a circuit-level threshold of $5.06(7)\times10^{-3}$. The layer code outperforms the surface code in terms of idle robustness: at the same distance it tolerates an interval between syndrome extraction rounds 1.7-3.0 times longer than the rotated surface code. This comes at the cost of 1.7-5.0 times more operations per unit time and approximately five times more physical qubits, both per logical qubit. Finally, we model the cost of the beyond-2D cross-plane CNOTs that the construction demands, and find that their speed matters far more than their fidelity.

The wide-bandgap compound semiconductor ZnSe is a promising host material for the realization of electron spin-qubits. Its non-degenerate conduction band and the potential for isotopic nuclear spin purification promise long spin coherence times. Key requirements for such devices include reliable electrostatic control of electrons in ZnSe and low-resistance ohmic contacts that remain functional at cryogenic temperatures. In this work, we utilize a novel Shadow Wall technique for molecular-beam epitaxy combined with in-situ deposition of Al ohmic contacts to realize normally-off ZnSe-based field-effect transistors. The devices exhibit linear output characteristics and effective gate control of the channel from room temperature down to 5 K, confirming low-resistance ohmic contacts to the undoped ZnSe channel. The drain current can be modulated by several orders of magnitude through electrostatic gating, with threshold voltages of approximately 3 V and field-effect mobilities exceeding 100 cm2/Vs over the investigated temperature range. Self-consistent Schrödinger-Poisson and drift-diffusion simulations reproduce the measured transfer characteristics and provide insight into the role of interface electrostatics in determining the channel formation and threshold voltage. These results demonstrate the potential of gated ZnSe heterostructures for future spin-qubit applications.

We discuss exclusive production of $\pi^+ \pi^-$ pairs in diffractive $\gamma p$ and in $pp$ collisions at high energies, considering resonant ($\rho(770)$, $\omega$, $f_2(1270)$) and non-resonant (Drell-Söding) contributions within the tensor-pomeron approach. For the $\gamma p \to \pi^+ \pi^- p$ reaction, the model describes well the H1 data in the region $M_{\pi \pi} \lesssim 1.2$ GeV. We discuss the important role of the Drell-Söding mechanism in shaping the resonance line. We also predict differential cross sections for the $pp \to pp \pi^+ \pi^-$ reaction at $\sqrt{s} = 13$ TeV where at least one proton emits a virtual photon. These findings are relevant for the central exclusive production of $\pi^+ \pi^-$ pairs in the context of ALICE, ATLAS, CMS, and LHCb measurements in hadron-hadron collisions at the LHC, especially under experimental selections using only rapidity-gap conditions. Additionally, our results are also applicable to $\pi^+ \pi^-$ production in ultraperipheral $p$A/AA collisions at the LHC and to photo- and electroproduction of $\pi^+ \pi^-$ at future electron-proton/ion colliders (EIC, LHeC).

We present B-GRASP (Bayesian GRAph inference with SPDE priors), a Bayesian framework for inferring uncertain edge weights in stochastic dynamical systems on graphs from noisy observations of nodal states. The unknown edge weights parameterize the graph differential operator and therefore directly govern the evolution of the graph process. Motivated by connections between differential operators in PDEs and SPDEs and their graph counterparts, we construct stochastic graph models incorporating diffusion, reaction dynamics, and stochastic forcing. The resulting hierarchical formulation jointly represents uncertainty in the graph structure and stochastic forcing. Latent graph variables determine positive edge weights and the corresponding graph Laplacian, while latent Brownian variables represent the stochastic forcing. Conditional on these variables, the graph dynamics define a deterministic forward map from which the likelihood and posterior distribution are constructed. We characterize the posterior using maximum a posteriori estimation and the No-U-Turn Sampler, enabling both point estimation and uncertainty quantification. We demonstrate the framework on a one-dimensional inverse heat-conduction problem, stationary and nonstationary graph reaction-diffusion systems with nonlinear dynamics, and state-level COVID-19 data in the United States. The numerical results show that posterior uncertainty provides information not captured by point estimates, particularly for weakly identifiable or highly conductive edges, and enables uncertainty in both graph connectivity and stochastic forcing to be quantified within a Bayesian framework.

Shape-morphing materials have the potential to realise simple, tunable telecommunication arrays without the need for complex circuitry. However, existing devices either lack individual cell control, or require an integrated power supply, reducing their beamsteering ability and increasing size, weight and power consumption. This paper presents a simple, photothermally activated 1-bit reflectarray unit cell requiring no integrated power sources. The unit cell consists of dimer elements, which are connected or disconnected via a photothermally activated electrical bridge to achieve modulation. The paper discusses the shape memory materials used for switching, and presents a design for a photothermal switching mechanism. The unit cell is validated by waveguide experiments, showing strong agreement with simulations at the working frequency of 3.7GHz. Finally, a 4-cell array is created. Each cell is activated sequentially, with good agreement between simulation and experiment, demonstrating the ability to control each cell exclusively. This study therefore demonstrates that a 1-bit unit cell can be photothermally configured without complicated electronics or an integrated power supply, opening the door to a new class of shape-morphing reflectarray.

A measurement of the correlation between the splitting angle $\theta_{\rm g}$ and the momentum-sharing fraction $z_{\rm g}$ of the first hard splitting in a parton shower in pp collisions and 0$-$10% central Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5 TeV with the ALICE detector is reported. Charged-particle jets are reconstructed using the anti-$k_{\rm T}$ algorithm with a jet resolution parameter $R$ = 0.2, in the transverse-momentum range $60 \leq p_{\rm T,ch\;jet} < 80$ GeV/$c$. The Soft Drop grooming algorithm is used to identify the first splitting in the parton shower. Jets observed in Pb$-$Pb collisions are narrower than in pp collisions. This effect is more pronounced for balanced than for unbalanced jets. No significant modification of the momentum-sharing fraction is observed for jets with small opening angles. In contrast, there is a hint that jets with a large opening angle may be less balanced in transverse momentum in Pb$-$Pb collisions compared to pp collisions. The correlations between $\theta_{\rm g}$ and $z_{\rm g}$ are well described in pp collisions by PYTHIA 8 and POWHEG while HERWIG shows too few jets with large opening angle. In Pb$-$Pb collisions the measurement is compared to a variety of models. The measurement is insensitive to the different implementations of medium response. Inclusion of elastic scatterings, as implemented in the HYBRID model is preferred to describe the unbalanced jets with large $\theta_{\rm g}$ in Pb$-$Pb collisions. The balanced jets, however, are less sensitive to elastic scatterings.

This study mathematically explores wave motion induced by earth-space forces specifically ground actions. Developing and solving governing differential equations provides insights into intricate propagation dynamics caused by these forces. Numerical simulation modeled wave behavior and results were analyzed to understand ground action impacts. Initial wave generation and subsequent propagation were simulated using COMSOL Multiphysics which models wave dynamics in physical media. Partial differential equations describing wave motion alongside Fourier transform techniques were applied to analyze the frequency components. Mathematical derivations yielded wave equations while COMSOL's built-in statistical analysis tool analyzed results. Data visualization employed plotting tools within the software to create detailed graphs. The wave amplitude relative to distance km varied at 0.001 at 0 km and 0.001 at 10 km over 10 km. Amplitudes were recorded at intervals 0.05 0.1 0.15 0.2 0.25 1.05 1.1 1.15 1.2 and 1.25 s. The impact of varying amplitude and frequency on the behavior ranges from 1 s at 0.1 amplitude in Case 1 (0.2, 200) to 1 s at 0.2 amplitude in Case 3 (0.2, 300). Outputs indicate: (1) initial energy input significantly influences the propagation characteristics aiding seismic prediction and mitigation design; (2) propagation details underscore the medium properties' importance in shaping behavior vital for earthquake engineering and accurate ground-motion prediction; (3) sensitivity to amplitude and frequency suggests tailoring parameters can optimize wave-based geophysical surveys and environmental monitoring. This study serves as a policy guide for understanding wave dynamics to inform building codes and disaster preparedness strategies for mitigating seismic impacts.

We consider a procedure for nonperturbative quantization based on an infinite system of nonperturbative Dyson–Schwinger equations. We propose a first approximation for truncating this infinite system of equations in the static case. The main ideas underlying this approximation are as follows: (a) the two-point Green's functions of vacuum gauge fields are factorized by introducing scalar fields; (b) in the non-vacuum case, the degrees of freedom of the $SU(3)$ gauge field can be divided into “almost classical” and “almost quantum” degrees of freedom; (c) the four-point Green's functions of the gauge fields are represented as bilinear combinations of two-point Green's functions; (d) an approximation for the three-point Green's function describing the interaction between quarks and gauge fields is proposed, which leads to the splitting of the original Dirac equation for the quark-field operators into two equations, one describing the expectation value of the fermion field and the other acquiring a nonlinear term and serving to describe a condensate composed of sea quarks bound by the vacuum gauge field. We consider the choice of gauge appropriate for this approximation to nonperturbative quantization. We point out that the emergence of a nonlinear Dirac equation within this approximation may lead to a mass gap in the energy spectrum of solutions of the corresponding systems of equations. The issue of the emergence of “dimensional transmutation” within this approximation is also discussed. We provide arguments in favor of the statement that the “closure constants” appearing in the finite truncation and giving rise to “dimensional transmutation” should survive in the transition to the infinite system of Dyson–Schwinger equations. An analogy between nonperturbative quantization and the stochastic theory of turbulence is also discussed.

We discuss central exclusive production (CEP) of $\eta$ and $\eta'(958)$ mesons in high-energy proton-proton collisions using the tensor-pomeron approach, incorporating absorption effects at the amplitude level. Model parameters are constrained using WA102 experimental data measured at $\sqrt{s} = 29.1$ GeV. We present cross sections and differential distributions for the LHC energy of $\sqrt{s} = 13$ TeV. For $pp \to pp \eta$, the upper limit of the total cross section is 2.5 $\mu$b for $|\eta_{M}| < 1$ and 5.6 $\mu$b for $2 < \eta_{M} < 5$. For $pp \to pp \eta'$, the predicted cross sections are 0.3–0.7 $\mu$b and 0.9–2.1 $\mu$b in the respective pseudorapidity regions. These results demonstrate the feasibility of studying diffractive flavour singlet pseudoscalar meson production to probe the nature of the pomeron at the LHC.

The interaction between flame dynamics & hydrodynamic instabilities plays a fundamental role in determining the stability of swirl-stabilized combustors. In the present study, we investigate the hypothesis that spatial overlap between flame & wavemaker region is a necessary prerequisite for combustion stability in flows characterized by a wavemaker region. To test the hypothesis, a low-momentum secondary methane injection was introduced through circumferential holes located on the centerbody of a swirl-stabilized burner. The injection velocity was maintained below 5% of bulk flow velocity to minimize momentum-induced modifications of flow field while selectively redistributing heat release. In addition, an equivalent amount of fuel was diverted from primary fuel supply to secondary injection ports, known as fuel-staging, to isolate the effects of flame relocation from those of the total fuel flow rate. The introduction of secondary injection produced a transition of the flame from M-shaped to V-shaped structure, while fuel-staging yielded a similar flame response, demonstrating that observed behavior results primarily from redistribution of heat release. Linear stability analysis revealed that wavemaker region remains near inlet of the combustion chamber. Moreover, flame root transitions from a lifted M-flame to attached V-flame and consistently stabilizes at radial position corresponding to the identified wavemaker region. The coincidence of flame attachment & wavemaker location under stable operating conditions provides strong experimental evidence that flame stabilization is governed by their spatial overlap rather than by a modification of the underlying hydrodynamic instability. The proposed framework provides new insight into the coupling between flame stabilization & hydrodynamic instability & offers practical guidance for the design of stable, low-emission combustion systems.

How and when dust settles in young protostellar disks is a key open question for the dust concentration needed to form planetesimals and, ultimately, planets. However, directly measuring the vertical dust distribution in embedded (Class 0/I) systems remains challenging. We show that brightness asymmetry along the minor axis of highly inclined disks provides a simple, powerful geometric diagnostic of vertical dust structure. Using radiative transfer modeling with RADMC-3D, we generate synthetic continuum images showing that the observed asymmetry arises naturally from disk inclination, optical depth, and dust scale height. We apply this framework to nine Class 0 and I disks from the ALMA Large Program, Early Planet Formation in Embedded Disks (eDisk), using Markov Chain Monte Carlo (MCMC) fitting. Outflow observations independently validate the inferred near- and far-side geometries: all eight sources with useful outflow constraints agree with the orientations predicted by the dust continuum modeling. Our results indicate that most embedded disks show no strong evidence of significant dust settling, with dust scale heights comparable to the gas scale height. Given that the literature indicates Class II disks tend to be well settled, our results reinforce the notion that significant dust settling occurs during the Class I phase, when deeply embedded Class 0 disks transition to their more revealed Class II counterparts. Intriguingly, the timing of dust settling appears to broadly coincide with the development of widespread dust substructures, suggesting that gravitationally driven vertical dust concentration may have triggered substructure formation.

In graphene and other two-dimensional materials, periodic modulations of the electron density can significantly alter the energy spectrum and transport properties. Here, we report magnetotransport measurements in encapsulated monolayer graphene with ultra-high-quality patterned periodic antidot lattices that preserve the intrinsic electronic properties of the material. This lithographically defined platform enables controlled access to commensurability and superlattice phenomena at length scales otherwise difficult to achieve. By systematically tuning the lattice dimensions, we reveal a hierarchy of classical commensurability features arising from cyclotron orbits with comparable radii that follow multiple classical trajectories, resulting in broadened resistance peaks beyond the conventional single-orbit picture. Superimposed on these features, we observe pronounced Brown-Zak oscillations arising from the quantum commensurability between the magnetic flux quantum and the unit cell of the engineered Bravais lattices. We demonstrate that the intrinsic geometric phase of our system is directly measurable and show a precise matching of the magnetic field periodicity to the lithographic periodic patterning, where moiré-like electronic spectra can be geometrically generated in single-layer graphene without the need for twist, lattice mismatch, or multilayer stacking. Our results establish nanopatterned graphene as a clean, tunable, and scalable platform for realizing and exploring moiré physics through on-demand real-space design

High-precision measurement of oscillating signal is a ubiquitous issue in fundamental science and a critical task in practical technologies. In quantum metrology, quantum lock-in detection provide an efficient method for measuring such signal. In general, when the initial phase of the oscillating signal is unknown,quantum double lock-in detection can effectively extract complete information about the signal's amplitude, frequency, and initial phase. Conventional quantum double lock-in detection requires two individual quantum interferometry, each of which must undergo state preparation and readout. However, the time for state preparation and readout need not be negligible in practical experiments. In particular, the time for state preparation is longer than the time for sensing. To save experimental resources, it is challenging to achieve quantum double lock-in detection just via a single quantum interferometry while still extracting complete information about the signal's amplitude, frequency, and initial phase. Here, we present a general protocol for achieving a quantum double lock-in detection just via a single quantum interferometry under a sequential orthogonal periodic multipulse sequences. In particular, if the input state is a Greenberger-Horne-Zeilinger state and two interaction-based operations are applied during interferometry, the measurement precisions for frequency, amplitude, and initial phase can both approach the Heisenberg limit. Our study paves a new way for measuring oscillating signals with a single quantum interferometry, and provides a feasible method for achieving Heisenberg-limited detection of alternating signals.

Interactive proof systems with a laconic prover, studied by Goldreich, Vadhan, and Wigderson (CC, 2002), capture problems verifiable with logarithmic prover communication in the classical setting. For two-message quantum analogs, even a single-bit prover response contains quantum statistical zero-knowledge ($\sf QSZK$), introduced by Watrous (FOCS 2002). However, restricting the verifier's question to classical public coins collapses the corresponding class to $\sf BQP$, as shown by Beigi, Shor, and Watrous (ToC, 2011). We further study two-message quantum interactive proof systems with a laconic prover. To this end, we introduce the class ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, where $\ell$ is the length of the prover's response, and establish: 1. A natural complete characterization of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ by Multi-State Distinguishability. In particular, Quantum State Distinguishability (QSD) is ${\sf QIP}_{\rm bit}$-complete. Since QSD is $\sf QSZK$-hard, our result places ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$, for $\ell\geq 2$, in a landscape "just above" $\sf QSZK$. 2. Easy regimes for ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ collapsing to $\sf QSZK$. We prove that QSD$[a,b]$ (and thus ${\sf QIP}_{\rm bit}[a,b]$) is in $\sf QSZK$ when $a(n)-b(n)\geq 1/O(\log n)$, and combine this with an answer compression from ${\sf QIP}_{\ell\text{-}{\rm bit}}[2,c,s]$ to ${\sf QIP}_{\rm bit}$ to obtain another easy regime when $2c>(1+2^{\ell/2})s$. Remarkably, our improved polarization applies to SD and $\sf SZK$, resolving an open problem in Sahai and Vadhan (JACM, 2003). 3. Quantum public coins also make the interaction useless: ${\sf qc}\text{-}{\sf QAM}[O(\sqrt{\log{n}})]$ with constant gap is in $\sf BQP$, where ${\sf qc}\text{-}{\sf QAM}[\ell]$ is a subclass of ${\sf QIP}_{\ell\text{-}{\rm bit}}(2)$ in which the verifier's question is exactly halves of EPR pairs.

Spintronic terahertz emitters (STEs) are versatile sources of terahertz (THz) frequency radiation that offer high electric field strengths and gap-free bandwidths covering the THz (0.1-30 THz) band. In addition, they are low-cost to produce and easy to use in a variety of optical setups. However, an obstacle to their wider applicability is the recently reported decrease in optical fluence damage threshold when driven with high-repetition-rate lasers. Here, we use an asynchronous optical sampling (ASOPS) THz time-domain spectrometer (THz-TDS) to observe the degradation of the THz signal in real-time when driven by a 1 GHz repetition-rate laser. We demonstrate that the loss of THz emission is permanent and is likely the result of thermal damage to the STE structure. However, by utilizing substrates with high thermal conductivities, an increase of the damage threshold of over three orders of magnitude is observed enabling stable emission from a STE for the first time when driven by a high-repetition-rate laser.

The Gottesman-Kitaev-Preskill encoding has emerged as a leading candidate for fault-tolerant quantum computation with continuous variables. For photonic architectures, the major challenge is preparing high-quality resource states, which can be deterministically synthesised from many large-amplitude cat states. Thus far, only modest-sized optical cat states have been prepared experimentally, and the implemented methods are highly probabilistic. We propose an all-optical scheme utilising quantum non-demolition interactions and photon-number measurements to prepare large-amplitude cat states with near-unity probability. Importantly, no particular photon-number outcome is postselected: all outcomes contribute to the accumulated photon number, with the protocol repeated until a required threshold is reached. We demonstrate that the scheme is robust to realistic levels of photon-loss, the dominant source of error in optical systems. Our results highlight the power of active Gaussian operations for state preparation and pave the way for efficient quantum error correction using bosonic codes.

Extending a previous work on the energy-momentum tensor of the linearized gravitational field in Minkowski background, conserved currents in linearized gravity associated with Lorentz transformations, dilatations and special conformal transformations are explored in the framework of Lagrangian field theory. Both outstanding special cases and general parametric families of currents are considered. Regarding the former, the distinguished energy-momentum tensor $T_{\mathrm{lg}}^{ab}$ we found earlier, guided by similarities between linearized gravity and electrodynamics, is supplemented with an angular momentum tensor $M_{\mathrm{lg}}^{abc}$ and a dilatation current $D_{\mathrm{lg}}^a$, associated with Lorentz and dilatation symmetries. Concerning special conformal transformations, a generalization of Noether's theorem that is useful if additional conditions (such as gauge fixing conditions) are imposed is formulated, it is shown that special conformal transformations are Noether symmetries of linearized gravity in the generalized harmonic gauges, and a special conformal tensor $C_{\mathrm{lg}}^{ab}$, accompanying $T_{\mathrm{lg}}^{ab}$, is obtained using the generalized Noether's theorem. The angular momentum tensor, dilatation current and special conformal tensor accompanying two other notable energy-momentum tensors are discussed as well. General multi-parameter families of $M^{abc}$, $D^a$ and $C^{ab}$ tensors accompanying a general family of energy-momentum tensors, which was found earlier and includes canonical energy-momentum tensors, are also determined, and local balance equations that are relevant if matter is present are derived for them. Their members do not depend on higher than first derivatives of the linearized metric.

Mathematically rigorous statements on the spectral gap of quantum many-body systems in the thermodynamic limit are notoriously difficult to prove – yet they are of fundamental importance for classifying quantum phases of matter. Here we prove the existence of a finite excitation gap for a particular Hamiltonian which was proposed in [T. F. Maier et al., PRX Quantum 6, 030340 (2025)] and is motivated by the Rydberg platform. The Hamiltonian exhibits only two-body blockade interactions between two-level systems and has a topologically ordered ground state in the toric code phase. We show that our result also applies to a broader class of blockade Hamiltonians which realize non-Abelian quantum double phases and were proposed in [H. P. Büchler et al., Phys. Rev. B 114, 065113 (2026)]. The proof builds on known gap stability results and exploits the local symmetry of the studied models.

Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis $\Lambda=1/4$, $\omega^+=\omega^-=1$ makes one collision eliminate all non-hydrodynamic perturbations; $\eta(\nu)=|6\nu-1|/(6\nu+1)$ vanishes at $\nu=1/6$, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at $N=256$, $\mathrm{Re}=1$ under matched-accuracy and $1\%$ gates. The matched speedup rises monotonically to 122.02 at $N=1024$, with gains persisting across $\mathrm{Re}=10^{-4}$–$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at $N=128$, $\mathrm{Re}=1$. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at $\mathrm{Re}=10$ and 3.84 at $\mathrm{Re}=100$ for $N=128$. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.

We investigate the propagation properties and canonical gauge structure of Generalised Non-Linear Electrodynamics (GNLED) in the presence of a non-dynamical background field. Starting from the quadratic photon sector of the theory, we perform a field redefinition that converts the background-induced derivative coupling into a mass-like contribution characterized by the vector \(V_\mu=\partial_\mu\alpha/\alpha\) where $\alpha= \sqrt{\left.\frac{\partial\mathcal{L}}{\partial \mathcal{F}}\right|_B}$. For a constant background, we derive the corresponding dispersion relation and show that, for a purely space-like \(V_\mu\), the propagating mode obeys \(\omega^2=\|\vec k\|^2+\|\vec V\|^2\), defining an effective mass scale \(m_{\rm eff}=|\vec{V}|\) and a finite rest frequency. The resulting phase and group velocities exhibit the characteristic dispersive behaviour of a gapped mode, with subluminal group velocity and superluminal phase velocity. We then construct the propagator and show that the massive pole resides in the transverse sector, while the longitudinal singularity is associated with gauge fixing. A complete Hamiltonian analysis yields two first-class constraints and only two physical degrees of freedom, demonstrating that the effective mass does not introduce an additional polarisation. The associated gauge transformation is a deformed Abelian \(U(1)\) symmetry. Finally, we show that the Hamiltonian is positive definite for purely space-like backgrounds.

We argue that the local violation of null energy condition at the throat of a traversable wormhole does not necessarily indicate that the total volume integrated null energy contribution is negative. It is already known that it can be arbitrarily close to zero. We show that it can even be positive and use this argument to reconstruct a family of wormhole geometries. We also propose a novel classification of traversable wormholes based on the global volume integrated measure of null energy condition.

These notes are based on a mini-course delivered at the Les Houches Summer School, Quantum Theory on All Scales, in August 2026. They introduce many-body localization to mathematicians, emphasizing the physical mechanisms that support or destabilize it. The mathematical discussion deals with how perturbative rotations, renormalization, and probabilistic estimates are used in a rigorous approach to many-body localization.

Topology and geometry are inseparable in physical networks. Here we show that, after factoring out the topology-dependent number of eligible edge pairs, exchangeability makes the mean crossing propensity of those pairs exactly graph independent while preserving topology in fluctuations. We derive a microscopic, parameter-free theory for the response when topology and geometry are coupled. Synthetic and real three-dimensional networks confirm that structure hidden from the normalized mean survives in correlations that determine response.

We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz $\phi=F(X\cdot\xi)$, via embeding coordinate $X_\alpha$ of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector $\xi$. For time-like $\xi$, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like $\xi$, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions $D \le 5$. We show that the $D=4$ global vacuum transition solution has the radiation equation of state $w=1/3$. In $D=4$ global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.