Papers

We study connections between discrete probability distributions and the statistical mechanics of small systems. Using probability generating functions, we develop the theory of power series, infinitely divisible, and scalable distributions of non-negative integer-valued random variables, and introduce the class of Markovian distributions that arise naturally in stationary solutions of birth-death processes and in scalable infinitely divisible distributions. These results are applied to the grand canonical ensemble description in statistical mechanics: the infinite divisibility leads to a quasiparticle picture of an interacting gas, and the virial expansion is linked to the combinants of the distribution. A kinetic model of the liquid-vapor phase transition is presented, in which the particle-number distribution at the critical point converges to the Discrete Stable distribution - the fixed point of a renormalization semi-group transformation. We also show that the scalability of the particle-number distribution is preserved in Tsallis non-extensive thermodynamics, even though infinite divisibility fails. Moreover, deformed discrete distributions, including the negative binomial as a q-deformation of the Poisson, arise naturally in this setting.

Two-dimensional MXenes are promising materials for thermal management and spectral camouflage, combining low out-of-plane thermal conductivity with low infrared emissivity and mechanical robustness. Yet the near-order-of-magnitude spread in experimental out-of-plane thermal conductivity measurements (0.14-0.8 W/mK) and the systematic overestimation by simulations point to a fundamental gap in our understanding of heat transport in these materials. Here, we argue these differences originate in the overlooked role of heterogeneous surface terminations. Using Non-Equilibrium Molecular Dynamics simulations of Ti3C2Tx, we show that this discrepancy arises from a stereochemically induced vacuum gap between adjacent layers, formed when surface terminations of different sizes coexist. Even minor deviations from homogeneous terminations drastically suppress out-of-plane thermal conductivity, bringing simulated values into quantitative agreement with experiment. We also show that thermal conductivity scales strongly with the atomic density, and that introducing bulky surface terminations, including residual water, reduces the thermal conductivity to 0.3 W/mK, an order of magnitude below homogeneous termination values and below the minimum thermal conductivity limit predicted for disordered solids. Thus, we propose a chemistry-driven route to engineer thermal transport in MXenes.

We discuss some aspects of the uniqueness of analytically continuing Euclidean Green functions obtained by means of the Dyson-Schwinger equations (DSEs) and constrained by lattice data, back to Minkowski-space with physical $p^2$.

We investigate integrable exclusion Markov processes constructed from set-theoretical solutions of the Yang-Baxter Equation (YBE) that generalise the multi-species Symmetric Simple Exclusion Process (SSEP). We first introduce the process called the $ (p,1) $-SSEP that is analogous to the multi-species SSEP but with an extra particle species qualified as reactive. Reactive species are able to evaporate and condense by pairs or to transform by pairs depending on the interpretation. We provide a full combinatorial study of the sectors in the periodic case. We prove the integrability of the process in the periodic case and in the open case for two types of boundaries that we introduce using Baxterisations of solutions of the reflection equation. Next we move on to the process called $ (p,q) $-SSEP, i.e. the multi-species SSEP with an arbitrary number of reactive particle species. We prove its integrability in the periodic case and, for the open case, we introduce integrable boundaries generalising the ones considered for the $ (p,1) $-SSEP. Finally, we define physical quantities relevant to the models and we compute them in the non-equilibrium stationary state of the open $ (p,q) $-SSEP for one type of integrable boundaries.

Gelation is the transition from a fluid state into a system-spanning, out of equilibrim soft-solid network through a hierarchical process that couples local particle interactions to mesoscopic clustering and global connectivity. In time-resolved small-angle X-ray scattering (SAXS), isosbestic points – scattering wavevectors where scattering intensity remains invariant – emerge during this transformation, yet their physical meaning has remained unclear. Here, we show that two isosbestic points, $q_1$ and $q_2$, observed during salt-induced gelation of Ludox colloids, reflect fundamental structural constraints rather than a two-species interconversion. The high-$q$ point $q_2$ is a universal geometric marker, determined by particle contact distances, while the low-$q$ point $q_1$ arises from Porod invariant conservation and separates rapidly arrested local clusters from the growing mesoscopic network. By decomposing the Porod invariant across the reciprocal-space regions defined by these points, we define a dimensionless parameter, $\Phi(t/t_g)$, whose sigmoidal evolution provides a simple, model-free, scale-resolved fingerprint of gelation. Together with the combined evolution of $S(q_{\min},t)$ and $S(q \rightarrow 0,t)$, these results establish a quantitative model free framework linking local structuring, global connectivity, and scattering signatures, clarifying the role of isosbestic points in soft-matter transformations.

Negative-parity medium- and high-spin structure of the nucleus 105Pd was studied through the 96Zr(13C,4n)105Pd reaction at incident energies of 51 and 58 MeV, using the EUROBALL IV gamma-ray spectrometer in conjunction with the DIAMANT charged particle array. New bands have been observed and the previously reported bands have been extended to higher energies and spins. Altogether six decoupled bands with E2 transitions and one strongly coupled band with M1 + E2 transitions have been observed. The observed energy spectra and B(M1)/B(E2) ratios are compared with results of quantum particle rotor model calculations. Based on these comparisons, quasiparticle configurations can be assigned to two newly observed decoupled bands as well as to the strongly coupled band. The previously emerged possible interpretation for the third decoupled band as a two-phonon wobbling excitation lacks support. The observations indicate possible gamma-band nature for this band. The strongly coupled band, consistently with the absence of another observed strongly coupled band in this experiment, does not exhibit chirality.

The quality of an image observed through a scattering layer, such as a shower curtain, depends strongly on the relative position of the scattering layer between the object and the observer. This well-known phenomenon is commonly referred to as the shower curtain effect. When the scattering layer is placed close to the observer, the image is strongly degraded, whereas if it is located close to the object, the object may still be observed with relatively high resolution. Previous analyses of the shower curtain effect have primarily modeled the scattering layer as a section of a random medium. In this work, we present a new analysis in which the scattering layer is modeled instead as a rough interface, a description that arises naturally in many physical configurations. Within this framework, we derive explicit characterizations of both the image resolution and the signal-to-noise ratio, and determine how these quantities depend on the statistical properties of the rough interface and on its relative location between the object and the observer.

We present analytical results for the macroscopic wave function of a Bose-Einstein condensate in a time dependent harmonic potential. The evolution of the spatial density is a dilatation, characterized by three scaling factors which allow a classical interpretation of the dynamics. This approach is an efficient tool for the analysis of recent experimental results on the expansion and collective excitation of a condensate.

While decoherence is known to erode classical hardness in quantum random sampling, the impact of coherent spatial disorder remains an open question. We study a square-lattice instantaneous quantum polynomial-time (IQP) architecture subject to two-qubit gate-angle disorder and single-qubit dephasing using exact tensor-network simulations up to 576 qubits. For finite systems without dephasing, increasing disorder drives two consecutive crossovers toward classical simulability: the output distribution first loses anticoncentration, and then the tensor-network simulation cost drops from exponential to polynomial as entanglement is suppressed. The finite-size scaling collapses are consistent with continuous transitions in the large-system limit. Dephasing further reduces the complexity. We characterize the computationally hard regime through scaling laws that provide quantitative error-budget bounds for realistic near-term devices.

The Stokes-Mueller description of tissue polarimetry is conventionally interpreted through local observables such as birefringence, depolarization, and helicity preservation. We show that tissue structure generates topology in the polarization field itself. Polarization-resolved measurements of unstained human breast tissue reveal polarization vortices and, where the tissue architecture provides coupled azimuthal and radial variation, Neel-type polarization skyrmions. These structures are quantified by the vortex winding number and skyrmion charge, integer-valued topological invariants that vanish for homogeneous media and therefore provide zero background readouts of tissue heterogeneity. Malignant ductal carcinoma exhibits non-trivial polarization topology, whereas adjacent healthy tissue remains topologically trivial. The results establish topological invariants of the polarization field as physically interpretable observables of tissue organization and motivate topological polarimetry as a field-based approach to tissue characterization.

As a sister compound of the antiferromagnetic topological insulator MnBi2Te4, MnSb2Te4 is also a candidate for exotic magnetic topological phases. On the other hand, the structurally analogous but nonmagnetic phase-change material GeSb2Te4 is also known to exhibit nontrivial band topology. Motivated by their shared crystal structure, the similar ionic radii of Mn2+ and Ge2+, and the opportunity to explore the interplay between magnetism and topology, here we investigate the effects of Ge substitution at Mn sites in MnSb2Te4. The Mn1-xGexSb2Te4 solid solutions were synthesized via high-temperature solid-state reaction and characterized for composition, structure, phase behavior, and magnetism using SEM-EDS, PXRD, DTA, and SQUID. Ge substitution was successful across the full composition range, producing homogeneous, single-phase samples that melt via peritectic reactions, as confirmed by the MnSb2Te4GeS-b2Te4 phase diagram. Ge substitution strengthens the sample's paramagnetism, but with ferrimagnetic ordering up to x = 0.75, with both effective moment and saturation magnetization decreasing with increasing Ge content. Two distinct magnetic transitions - high-temperature paramagnetic to ferrimagnetic and low-temperature ferrimagnetic to ferromagnetic - were identified, with a dome-like shape dependence of the low-temperature magnetic transition on Ge substitution. A negative magnetization was observed in the pristine MnSb2Te4 and x = 0.12 substituted samples, while two distinct spin-flop transitions appeared in the samples with x = 0.32 and x = 0.55 Ge substitutions as a result of competing magnetic orderings. These findings facilitate future selective single-crystal growth of homogeneous, magnetic phases, paving the way for magneto-transport and topological surface states investigations.

We study the finite-time accretion of complex massive scalar wave packets by a Schwarzschild black hole in the test-field regime, with parameters motivated by ultralight fuzzy dark matter around supermassive black holes. Our goal is to determine how the scalar content of a localized configuration is redistributed after interacting with the black hole, and which spectral and multipolar components are more efficiently absorbed. We decompose the Klein–Gordon field into independent multipolar sectors and evolve nearly monochromatic Gaussian packets mode by mode, reducing the problem to a set of 1+1 dimensional evolutions. Accretion is quantified with the flux of the conserved Noether current through the horizon surface, providing a direct measure of the scalar charge absorbed by the black hole. For a carrier radial wavenumber $k_0$ and multipole index $\ell$, we construct accretion-efficiency maps in the $(k_0,\ell)$ plane that contain the fraction of accreted modal charge. These maps exhibit a transition between inefficient, partial, and efficient accretion regimes, which we relate to the structure of an effective potential. We show that the process is controlled by the ratio between the Schwarzschild radius $R_s$ and the reduced Compton wavelength $\lambdabar_C$. For $R_s \lesssim \lambdabar_C$, the transition is broad and dominated by the angular momentum barrier, while for $R_s > \lambdabar_C$ it sharpens across a narrower range of $k_0$ and a partial-accretion floor emerges at low $k_0$. These results provide a time-domain, Noether-charge-based classification of black hole accretion for massive scalar wave packets.

Exotic compact objects (ECOs) may produce late-time gravitational-wave (GW) echoes, but sufficiently compact ECOs undergoing realistic accretion may eventually form an event horizon. We investigate the evolution of quasinormal modes and GW echoes during this transition. Modeling the exterior spacetime with the ingoing Vaidya solution, we numerically evolve scalar perturbations on the resulting dynamical background. We show that the echo signal is progressively compressed and suppressed during accretion and disappears once the growing event horizon engulfs the reflecting surface, after which the waveform smoothly approaches the standard black hole ringdown. Our results identify the disappearance of GW echoes as a characteristic signature of horizon formation and provide a framework for studying dynamical compact objects with future GW observations.

We introduce an architecture where mesoscopic quantum matter distributed over spatially separated nodes can be correlated in equilibrium, creating an unprecedented form of many-body quantum system. Central to the design is a multi-gap split-ring resonator (SRR) where the cavity photon has multiple hot spots – each with deep-subwavelength volume at a split gap and separated by millimeter-scale distances. The cavity's vacuum fluctuations can then mediate a many-body interaction that bridges the distributed quantum materials embedded in the multiple gaps, coupling them into a single correlated mesoscopic system in equilibrium. As an example, we consider a THz SRR with two split gaps, each proximitized to a metallic moiré superlattice, where virtual exchange of a photon in the cavity vacuum mediates a current-current interaction across the gaps. The inherent attractive interaction channels lead to remote Cooper pairing reminiscent of mesoscopic superconductivity, demonstrated with density matrix renormalization group and exact diagonalization calculations. With the two constituents of a Cooper pair now paired across a millimeter-scale separation, a hole incident at one split gap can be converted into an outgoing electron at the remote gap, a process we term Andreev teleportation. The entanglement entropy between the two mesoscopic superlattices is shown to scale linearly with the area (total number of sites) of the mesoscopic lattice. Our results suggest an intriguing paradigm for equilibrium quantum networks of mesoscopic matter that enable emergent nonlocal functionalities and distributed quantum resources.

Theoretical descriptions of proton radioactivity near the drip lines are often challenged by parametric uncertainties in nuclear potential models. To address this, a robust Bayesian uncertainty quantification (UQ) framework is established to calibrate the deformed Woods–Saxon potential coupled with the semi-classical WKB approximation for odd-$A$ proton emitters across the $Z=50$–$82$ region. Constrained by experimental half-lives, the joint and marginal posteriors and covariance topologies are extracted for the potential geometry, multipole deformations, and spectroscopic factors. Using a signed relative sensitivity index, a dynamic, mass-dependent re-ordering of parameter hierarchies is unraveled. Crucially, propagating these parametric uncertainties yields posterior predictive medians and differentiated $\sigma$ bands that tightly encompass experimental half-lives across multiple orders of magnitude without systematic bias. Furthermore, near the $Z=82$ shell closure, the structural softening of the nuclear potential manifests as a systematic expansion and volatility of the $\sigma$ bands in the deformation profiles. This correlation suggests that the macroscopic behavior of parametric error distributions can potentially be mapped onto potential energy configurations, underscoring that the Bayesian UQ methodology may serve as a sensitive probe to extract reliable nuclear structure information directly from deformed proton decay systematics.

Kinesin is a molecular motor that transports intracellular cargoes along microtubules. Recent studies have quantified kinesin performance using various efficiencies within the framework of stochastic thermodynamics; however, quantitative comparisons remain difficult because different models and assumptions have been employed. As a result, it remains unclear which aspect of kinesin performance, if any, is thermodynamically optimized. Here, we systematically compare multiple thermodynamic efficiencies within a single kinesin-cargo model. To this end, we construct a thermodynamically consistent two-state kinesin-cargo model that retains both the discrete stepping of kinesin and its coupling to the cargo. Assuming a separation of time scales between the motor and the cargo, we derive analytical expressions for the thermodynamic efficiency, the information-thermodynamic efficiency, the thermodynamic uncertainty relation (TUR) efficiency, and the bipartite TUR efficiency, and compare them with numerical simulation results. We find that these efficiencies generally remain low, suggesting that kinesin is not optimized for maximizing the thermodynamic efficiencies considered here. Our results suggest that thermodynamic efficiencies alone may not fully characterize kinesin performance and motivate further investigation of complementary kinetic perspectives for assessing molecular motor function.

Coherent perfect absorption (CPA) has emerged as a powerful paradigm for controlling classical and quantum light, and has been demonstrated across a broad range of physical platforms. CPA realized in optomechanics relies on interference between the input field and the mechanically scattered field, but is intrinsically confined to the weak-cooperativity regime, resulting in a narrow absorption bandwidth and the mechanical mode remains thermally occupied. Here, we experimentally demonstrate collective interference-induced CPA in a synthetic photon–phonon lattice. By harnessing cavity-reservoir-mediated interactions among Floquet lattice sites, collective interference shifts the CPA condition deep into the high-cooperativity regime. This enables CPA to coexist with ground-state cooling of the mechanical oscillator, together with a broadened non-Lorentzian absorption lineshape and a singular group-delay response. Our results identify collective interference as a route to quantum-compatible perfect absorption and long-lived quantum storage.

We design a reflective scatterer that operates only in the backscatter direction using modulation of the Kerker effect. This being a phenomena where the resonant modes of a scattering object produce total destructive interference in the backscatter direction. Our design consists of a dielectric shell and an interior metal element that provide the required dipolar contributions for Kerker interference with angular stability. By incorporating a PIN diode, we obtain a scatterer that exhibits strong amplitude modulation in the backscattering direction that is weaker at other bistatic angles. Backscatter modulation is a key technology to connect everyday objects but can be vulnerable to eavesdropping, the device presented in this work may help guard against such flaws.

Two-dimensional semiconductors such as monolayer MoS2 combine a useful band gap with a thickness of three atomic planes, which places the entire carrier density within a few angstroms of the surface and makes them attractive both as transistor channels and as chemical sensors. We present a self-consistent ensemble Monte Carlo (EMC) framework for monolayer MoS2 built on the ViennaEMC solver, which couples a Boltzmann transport model to Poisson's equation with degenerate free-carrier statistics. The transport model carries wavevector-dependent acoustic, polar-optical, homopolar and intervalley phonon scattering within and between the K valleys and the spin-orbit-split Q valleys, together with remote substrate phonons, screened charged impurities and surface roughness. Every intrinsic input is computed from first principles for this work, the band structure of the K and Q valleys, the phonon energies, the sound velocities and the dielectric response, and the electron-phonon couplings from density-functional perturbation theory matrix elements at 34 explicit phonon wavevectors and from Wannier interpolation with the two-dimensional long-range treatment. The model therefore contains no fitted transport parameter and no coupling taken from another calculation, and its scattering rates are checked against an independent solution of the linearised Boltzmann equation with the same couplings. The EMC velocity-field characteristic feeds a one-dimensional channel model, verified against a direct self-consistent three-dimensional EMC simulation of the gated channel, which reproduces the measured transfer characteristics of a CVD monolayer device in air and vacuum. An ambient and adsorbate extension reproduces the measured conductivity response to oxygen partial pressure and the concentration dependence of NO2 and NH3 sensing of independent monolayer devices.

We investigate deterministic coarsening dynamics in a spatially extended bistable gene toggle model with diffusive coupling. Unlike classical curvature-driven coarsening, where domain walls move continuously and annihilate gradually, the present system exhibits a qualitatively different mechanism. The domain walls remain pinned for long intervals and disappear abruptly through collective cascade events. The density of domain walls decays approximately as $\rho(t)\sim t^{-\delta}$, but the coarsening exhibits clear log-periodic oscillations superimposed on the power-law behavior. For all values of the promoter strength $\alpha$ considered, the measured exponent satisfies $\delta<0.5$, indicating a systematic deviation from the classical Allen–Cahn prediction $\delta=1/2$ for curvature-driven coarsening. We show that log-periodic oscillations are not controlled by the density of domain walls, but by the domains that disappear in each cascade. The average size of disappearing domains grows roughly linearly with cascade index, producing a constant geometric spacing of cascade times, consistent with discrete scale invariance.

We investigate the role of large separation, rotational correction order, structural resolution, and non-adiabatic effects in modelling the rotating $\delta$ Scuti star V1790 Ori. From TESS data, we extract 69 frequencies and determine $\Delta\nu \simeq 82$ $\mu$Hz. Rotating MESA models are computed at low and high resolution; their pulsation frequencies are calculated with GYRE (adiabatic/non-adiabatic, first-order rotation) and FILOU (adiabatic, second-order rotation). Using $\Delta\nu$ as a structural constraint is necessary to reduce model degeneracy. For the selected minimum-misfit reference model, considering only the 40 modes with consistent $(n,\ell,m)$ labels, the RMS$_{40}$ theoretical frequency differences are 0.442 $\mu$Hz (resolution), 0.062 $\mu$Hz (non-adiabatic), and 2.962 $\mu$Hz (GYRE vs FILOU); including all 48 frequencies gives RMS$_{48}$ values of 1.033, 2.326, and 3.931 $\mu$Hz. Relative to observations, higher resolution reduces residuals from 4.457 to 4.387 $\mu$Hz (RMS$_{40}$) and from 4.715 to 4.682 $\mu$Hz (RMS$_{48}$); non-adiabatic effects change them marginally to 4.381 and 4.673 $\mu$Hz. FILOU gives the largest residuals: 5.331 $\mu$Hz (RMS$_{40}$) and 5.270 $\mu$Hz (RMS$_{48}$). Second-order rotation produces the largest frequency shifts, but improving agreement with observations requires denser grids and self-consistent FILOU optimisation. The 260.672 $\mu$Hz peak – previously identified as the fundamental radial mode – shows uncertain identification. The results should be interpreted as diagnostics of modelling systematics and mode-identification robustness.

Current quantum computers do not yet have the required qubit resources to meet the demands of most practical quantum algorithms. To circumvent this constraint, the practice of dividing these algorithms into parts through quantum circuit cutting has been explored. Many of these works either show exponential scaling or are far from optimal solutions. In this paper, MosaiQC is presented as a novel framework to improve upon existing circuit cutting frameworks. A hybrid warmstart with refinement optimization is used to find cutting solutions, allowing the combination of both wire and gate cuts. Additionally, MosaiQC enables hardware partitions of mixed sizes. Furthermore, the refinement stage incorporates a fast approximate quadratic assignment solver to better place hardware partitions, demonstrating a mean local fidelity improvement of $19.56 \% \pm 6.17\%$ over the baseline algorithm. In runtime and sampling overhead costs, improvements of $2.88 \times$ and an average of $16.84\%$ cut reduction (resulting in an average $5.83 \cdot 10^{11} \times$ overhead reduction) are observed. MosaiQC demonstrates a superior trade-off for run speed and solution quality, while adding fundamental features excluded by most competitors. With this, MosaiQC demonstrates that scalable heuristic optimization can substantially reduce the computational overhead of circuit-cut placement for increasingly large quantum circuits.

With infrared Fourier-transform spectroscopy and spectroscopic ellipsometry we investigated the in-plane reflectance of the superconducting Na$_{0.27}$K$_{0.27}$Rb$_{0.27}$Fe$_{1.7}$Se$_2$ single crystals with a critical temperature $T_c\approx 34.3$ K over a broad frequency range at temperatures of 4–300 K. The normal-state response of Na$_{0.27}$K$_{0.27}$Rb$_{0.27}$Fe$_{1.7}$Se$_2$ is analyzed by a Drude-Lorentz model with one Drude component. The temperature dependences of the plasma frequency, optical conductivity, scattering rate, and dc resistivity of the Drude component in the normal state are presented. We report a Fano-shaped mode at 1430~cm$^{-1}$ indicating a coupling of the discrete mode presumably related to some electronic transition to a two-magnon continuum as well as a low-frequency broad band assigned to the acoustic magnon branch of the antiferromagnetic superstructure. These features persist in the reflectance in both the normal and superconducting states suggesting a mesoscopic coexistence of superconductivity and magnetism in Na$_{0.27}$K$_{0.27}$Rb$_{0.27}$Fe$_{1.7}$Se$_2$.

The monolithic integration of compact laser sources onto silicon remains a critical bottleneck for the scalable development of silicon photonics. In particular, the direct epitaxial growth of near-infrared vertical-cavity surface-emitting lasers (VCSELs) on silicon has long been hindered by the simultaneous requirements of low crystalline defect density in the active region and smooth interfaces in the distributed Bragg reflector (DBR) mirrors, both essential to achieving high cavity quality factors and low lasing thresholds. Here, we report the direct epitaxial integration of near-infrared VCSELs on silicon substrates using a two-step growth strategy specifically designed to suppress defect propagation while preserving mirror interface abruptness. This approach enables effective confinement of threading dislocations away from the active region and ensures high-reflectivity DBRs with excellent structural uniformity. Structural and optical characterizations reveal an epitaxial stack of high crystalline quality, leading to laser performance comparable to VCSELs commonly grown on GaAs substrates. We demonstrate, for the first time, directly grown VCSELs on silicon wafers exhibiting threshold currents of only a few milliamperes. These results establish a decisive proof of concept for the monolithic integration of good-performance VCSELs onto silicon platforms and open a viable pathway toward fully integrated, low-cost silicon-based photonic systems.

Systems of hard rods of equal length in a one-dimensional harmonic trap have been observed to exhibit peculiar non-ergodic behavior that might suggest the existence of a novel hidden conserved quantity beyond the two well known ones, i.e., the total energy and the center-of-mass energy. In this work, we investigate this possibility by systematically constraining the forms of the conserved quantities, and we rigorously rule out the existence of any extra hidden conserved quantity that is analytic in the positions and momenta of the rods involved. We do so by showing two key results: conservation during free motion demands the $U(1)$ invariance of these quantities under rotations of the position and momenta of each rod, and conservation during collisions demand an $S_N$ invariance under the permutation of the momenta of the rods as long as one of the rods have non-zero length. We then show that these conditions imply that any conserved quantity is functionally dependent on the two known conserved quantities. In addition, we show that in the special case where all rods have zero length (i.e., when they are point particles), conservation under collisions only requires invariance under a smaller $S_N$ group of permutations of the labels of the rods, which leads to a much larger set of analytic conserved quantities that we explicitly write down. In all, this rigorously clarifies the structure of conserved quantities in the hard rod problem, and motivates the application of such systematic methods to other classical systems.

We study higher-rank generalized Killing tensors with mixed symmetries, providing a couple of examples and applications. It is shown that such objects naturally exist in higher-dimensional rotating black hole spacetimes, where they arise as partially contracted "squares" of Killing-Yano tensors and display interesting algebraic and differential properties. Motivated by conformal Killing tensors, a generalization of these objects that gives rise to parallel-transported tensors along null geodesics is proposed and shown to exist in higher-dimensional rotating black hole spacetimes.

To investigate the origins of the high abundance of UV-bright galaxies at z > 10, we present a new semi-analytic model that bridges the gap between small-scale star formation physics and large-scale galaxy evolution by explicitly tracking discrete star-forming clouds within smoothly evolving dark matter potentials. Unlike conventional semi-analytic models, our approach naturally captures the stochasticity of star formation, allowing us to isolate how cloud properties, star formation efficiencies (SFEs), and stellar initial mass functions (IMFs) shape the star-formation burstiness of early galaxies. Clouds are drawn sequentially from a cloud mass distribution, assigned an SFE and IMF depending on cloud mass, metallicity, and redshift, and evolve under the influence of short-timescale stellar feedback. We identify three distinct star formation regimes arising from the interplay between cloud masses, densities, and feedback timescales: a stochastic, feedback-limited regime in low-mass halos with long quiescent phases; a bursty regime regulated by the cloud mass distribution; and a smooth, continuous regime in massive halos. Our fiducial model adopts a dynamic IMF, an SFE linked to cloud properties and the IMF, and massive, moderately dense clouds. Varying assumptions reveals that top-heavy IMFs and enhanced SFEs in massive clouds amplify burstiness, while altering the upper cloud mass or density normalisation is secondary. Among model ingredients, the IMF most strongly impacts the UV luminosity function (LF), while switching to a constant SFE boosts the faint end, and reducing the maximum cloud mass decreases the bright end. These results demonstrate that cloud-scale physics critically shape early galaxy UV luminosity distributions.

Neural quantum states offer expressive representations of quantum many-body wave functions, yet their practical accuracy can be limited by stochastic optimization rather than representational capacity. Here we identify a finite-sample instability, termed subspace trapping, in which physically important configurations become strongly underestimated, remain absent from successive sampling batches and receive insufficient gradient feedback. This self-reinforcing loss of sampled support can confine optimization to an effective subspace and produce apparently stationary states above the true ground state energy. To address this problem, we introduce annealed gradient descent (AGD), a sampling-aware update with annealing factor that temporarily increases the relative contribution of sampled low-probability configurations while limiting the dominance of high-probability ones. We establish the connection between finite-sample support loss and effective subspace optimization, and then evaluate the method across molecular systems, one and two-dimensional $J_1$-$J_2$ models. Annealed gradient descent suppresses metastable trapping, preserves physically relevant configurations and enables compact neural quantum states to attain chemical accuracy and competitive state-of-the-art performance. These results establish AGD as a lightweight complement to expressive neural architectures, improved sampling strategies for scalable quantum many-body optimization.

We address the existence, stability, and propagation dynamics of multipole solitons and vortex clusters in cubicquintic media subject to a harmonic trapping potential.We found that vortex clusters comprising N off centered vortices with alternating topological charges m equal to +(-)1, evenly distributed on a ring, can bifurcate from a multipole soliton for N less than or equal to 4 and from a second-order ring soliton for N greater than 4. Rigorous linear stability analysis, corroborated by direct numerical simulations, shows that upper branch vortex clusters with N equal to 2 and 4 remain stable over a wide range of the propagation constant. Thus, we reveal the formation mechanism of vortex clusters.

Within the framework of strong-field quantum electrodynamics, we study the creation of muon-antimuon pairs in laser-assisted collisions of electrons with positrons, whose center-of-mass energy is close to the threshold of the process. Our focus lies on incident collision energies slightly below the threshold, where the associated energy gap has to be overcome by multiphoton absorption from the applied high-intensity laser field while the collision occurs. We calculate the cross section of the process and discuss its nonperturbative dependencies on the energy gap and the laser parameters. Three qualitatively different interaction regimes are identified, where the influence of the laser field either has a classical or fully quantum nature. In the latter case, an exponential dependence of the cross section on the collision parameters is found, which resembles the Schwinger effect.