We study asymptotic properties of supercritical Galton-Watson (GW) branching processes in the asymptotic where the mean of the offspring distribution approaches 1 from above. We show that the population-size distribution of the GW branching processes at a sufficiently large generation in this asymptotic can be approximated by a compound Poisson-gamma distribution. Numerical experiments revealed that the compound Poisson-gamma models were in good agreement with the corresponding GW models for sufficiently large generations under a reasonable parameter regime. Our results can be regarded as supporting the use of the compound Poisson-gamma model as a model for cascaded multiplication processes.

The design and control of soft robots operating in fluid environments requires a careful understanding of the interplay between large elastic body deformations and hydrodynamic forces. Here, we show that this interplay leads to elastohydrodynamic instabilities in a clamped soft robotic arm driven terminally by a constant pressure in a viscous fluid. We model the arm as a Cosserat rod that can stretch, shear, and bend. We obtain invariant, geometrically exact, nonlinear equations of motion by using Cartan’s method of moving frames. Stability to small perturbations of a straight rod is governed by a non-Hermitian linear operator. Eigenanalysis shows that stability is lost through a Hopf bifurcation with the increase of pressure above a first threshold. A surprising return to stability is obtained with further increase of pressure beyond a second threshold. Numerical solutions of the nonlinear equations, using a geometrically exact spectral method, confirm stable limit-cycle oscillations between these two pressure thresholds. An asymptotic analysis in the beam limit rationalizes these results analytically. This counterintuitive sequence of bifurcations underscores the subtle nature of the elastohydrodynamic coupling in Cosserat rods and emphasizes their importance for the control of the viscous dynamics of soft robots.

Recent progress in manipulating individual quantum systems enables the exploration of engines exploiting nonclassical resources. One of the most appealing is the energy provided by the inherent backaction of quantum measurements. While a handful of experiments have investigated the inner dynamics of engines fueled by measurement backaction, powering a task by such an engine is missing. Here, we demonstrate the amplification of microwave signals by an engine fueled by repeated quantum measurements of a superconducting transmon qubit. Using feedback, the engine acts as a quantum Maxwell demon operating without a hot thermal source. Measuring the gain of this amplification constitutes a direct probing of the work output of the engine, in contrast to inferring the work by measuring the qubit state along its evolution. Observing a good agreement between both work estimation methods, our experiment validates the accuracy of the indirect method. We characterize the long-term stability of the engine as well as its robustness to transmon decoherence, loss, and drifts. Our experiment exemplifies the use of energy brought by quantum measurement backaction.

We present a general theoretical framework for group-resetting dynamics in a potential landscape. While traditional resetting models typically focus on a single particle, we consider a group of particles whose collective dynamics govern the resetting. We extend existing resetting theories to cover extreme-value group resetting. This has applications from bacterial evolution under antibiotic pressure to swarm-search optimization. Using renewal theory, we derive a Fokker-Planck equation for the spatial distribution of the group's center of mass, treated as an effective particle. This formalism yields analytical expressions for key observables such as the stationary mean position and variance. We also study a group avoidance problem, where the particles must avoid an undesirable region. Such problems have recently been studied in contexts such as preventing critically high water levels in dams and controlling excessive financial leverage. Our framework offers insights into how resetting can optimize group-level search and avoidance strategies.

To sustain bacterial growth, a fraction of active ribosomes must be allocated to synthesize ribosomal proteins. Two control parameters modulate the growth rate: the fraction of ribosomes allocated to ribosomal protein synthesis and the translation speed. At longer doubling times, which approach the active ribosome lifetime, the limited number of ribosomes poses a significant constraint in allocating ribosomes to ribosomal protein synthesis. We show that, to maintain slow growth while reducing the risk of depletion of the active cellular ribosome population, some bacteria must significantly reduce translation speed below its maximum, as previously observed. This change in the controls is due to a universal shot noise limitation that applies at slow growth rates in all kingdoms of life.

We develop a theoretical framework to elucidate the mechanics and morphogenesis of open vesicles coupled to boundary filaments, capturing their geometric, energetic, and mechanical interplay. Using a spherical harmonics parametrization and constrained energy minimization, we systematically explore equilibrium morphologies as functions of filament length, stiffness, and topology, as well as membrane spontaneous curvature, uncovering a rich spectrum of shapes and transitions. For open vesicles bounded by flexible closed filaments, increasing filament length or spontaneous curvature drives transitions from cuplike to stomatocyte and budded morphologies, both axisymmetric and nonaxisymmetric, with continuous and discontinuous regimes mapped in a phase diagram. For open vesicles partially bounded by open filaments, the coupled filament-membrane system exhibits more complex morphological evolution, including free edge stretching or contraction, localized filament bending, and opening expansion with increasing filament length. The derived force and moment balances at the vesicle edge connect local geometric quantities, such as filament and membrane curvatures, to filament internal forces and membrane tension, providing a direct mechanical interpretation of shape equilibria. Our results reveal how filament geometry, topology, and bending stiffness govern membrane shape transformations and establish a general mechanical framework for coupled filament-membrane systems, such as DNA-vesicle complexes and other filament-mediated membrane structures.

The elastic response of mechanical, chemical, and biological systems is often modeled using a discrete arrangement of Hookean springs, representing either finite material elements or even the molecular bonds of a system. However, to date, there is no direct derivation of the relation between a general discrete spring network, with arbitrary geometry, and its corresponding elastic continuum. Furthermore, understanding the network’s mechanical response requires simulations that may be expensive computationally. Here, we report a method to derive the exact elastic continuum model of any discrete network of springs, requiring network geometry and topology only. We identify and calculate the so-called “nonaffine” displacements. Explicit comparison of our calculations to simulations of different crystalline and disordered configurations shows that we successfully capture the mechanics even of auxetic materials. Our method is valid for residually stressed systems with nontrivial geometries, and is an important step in generalizing active stresses on such discrete systems. It is easily generalizable to other discrete models, and opens the possibility of a rational design of elastic systems.

We detail experimental results inferring ionization and temperature for warm dense copper plasmas at several times solid density (15–25 ${\mathrm{g}/\mathrm{cm}}^3$) and temperatures of 10–21 eV. Experiments performed at the OMEGA Laser Facility generate uniform warm dense matter conditions via symmetric shock compression of a buried copper layer. The plasma is probed with a laser-generated x-ray source to collect the K-shell x-ray absorption spectrum. Fitting bound-bound absorption contributions from constituent charge states of copper provides an estimated $\overline{Z}$ of approximately 4–7 for these warm dense copper plasmas. We find that these partially ionized plasmas have K-edge shifts of 12–30 eV and bound-bound resonance $1s\to 3p$ absorption shifts of 4–26 eV with respect to the cold K edge. This study provides necessary experimental data to improve ionization and opacity models in the warm dense matter regime.

The Magnus expansion underpins average Hamiltonian theory (AHT), a central tool in quantum control and sensing that is used to generate efficient approximations of system dynamics. Here, we demonstrate that the conditions for Magnus expansion convergence are violated under typical operating regimes for sensing using solid-state spin systems. We also establish that certain symmetries, such as those found in rapid echo pulse sequences, cancel all higher-order Magnus terms outside standard convergence frameworks. We introduce an exact method to compute the sensor response beyond the AHT regime, and apply it to both broadband and narrow-band magnetometry protocols. Our results clarify AHT limits and enable opportunities in pulse sequence design through symmetry-driven convergence, with implications for entanglement-enhanced sensing and quantum Fisher information estimation in control protocols.

Attosecond pulse trains (APTs) are indispensable for probing electron dynamics at their intrinsic timescales. High-harmonic generation (HHG) has long been a successful and widely used technique in producing extreme ultraviolet APTs. However, in the soft x-ray regime, HHG suffers from low conversion efficiency and lacking flexibility in the waveform and spectrum control. Here in this study, based on the waveform synthesis of the echo-enabled harmonic generation (EEHG) free-electron laser (FEL), we propose a method that can generate soft x-ray APTs with high temporal and spectral tunability. EEHG scheme is well-known in forming phase-locked high-harmonic bunching combs down to the soft x-ray regime. Here, the EEHG scheme is employed to facilitate successive FEL lasing in several different harmonic numbers and then perform the coherent waveform synthesis to generate soft x-ray APTs. Three-dimensional simulation results indicate that reproducible generation of coherent APTs in the soft x-ray regime with peak power of 3.5 GW and micropulse duration of 160 as can be achieved by five-harmonic synthesis. The micropulse duration together with the spectral components of the APTs can be adjusted easily according to the programmable high-harmonic bunching combs in the EEHG scheme. This method has the potential to establish a robust platform for attosecond sciences in the soft x-ray regime, which can enable unprecedented studies of electron dynamics in physical and chemical reactions, biological systems, and quantum materials.

Lanthanides are nowadays extensively used to investigate the properties of strongly correlated matter. Nevertheless, exploiting the Zeeman manifold of a lanthanide atom ground state is challenging due to the unavoidable presence of depolarization collisions. Here, we demonstrate that in the case of the thulium atom, it is possible to suppress this depolarization by a factor of 1000 with a carefully tuned magnetic field, thus opening the way for the efficient use of the Zeeman manifold in quantum simulations.

Mode switching in exciton-polariton condensates represents a significant phenomenon that illustrates the non-Hermitian properties and out-of-equilibrium dynamics of exciton-polaritons. In this research, we experimentally demonstrate controllable mode switching in a tunable ZnO microrod cavity at room temperature, where increasing pump power drives the condensate from one lower polariton branch to another of higher energy. This unconventional up-switching is explained by an imbalance in the densities of the active excitonic reservoirs, governed by both loss and relaxation efficiency. Ultrafast spectroscopy reveals a several-picosecond delay between the condensates, providing direct evidence for this mechanism. Our results provide important insights into the fundamental physics of Bose-Einstein condensation in dissipative systems, enable control of polariton condensation through reservoir engineering, and open routes to room-temperature polaritonic devices exploiting nonlinear switching.

Schrödinger cat states play an important role for applications in continuous variable quantum information technologies. As macroscopic superpositions, they are inherently protected against certain types of noise making cat qubits a promising candidate for quantum computing. It has been shown recently that cat states occur naturally in driven Kerr parametric oscillators as degenerate ground states with even and odd parity that are adiabatically connected to the respective lowest two Fock states by switching off the drive. To perform operations with several cat qubits, one crucial task is to create entanglement between them. Here, we demonstrate efficient transformations of multimode cat states through adiabatic and diabatic switching between Kerr-type Hamiltonians with degenerate ground-state manifolds. These transformations can be used to directly initialize the cats as entangled Bell states in contrast to initializing them from entangled Fock states.

We investigate the dynamics of nonstabilizerness—also known as “magic”—in monitored quantum circuits composed of random Clifford unitaries and local measurements. For measurements in the computational basis, we derive an analytical model for dynamics of the stabilizer nullity, showing that it decays in quantized steps and requires exponentially many measurements to vanish, which reveals the strong protection through Clifford scrambling. On the other hand, for measurements performed in rotated non-Clifford bases, measurements can both create and destroy nonstabilizerness. Here, the dynamics leads to a steady state with nontrivial nonstabilizerness, independent of the initial state. We find that Haar-random states equilibrate in constant time, whereas stabilizer states exhibit linear-in-size relaxation time. While the stabilizer nullity is insensitive to the rotation angle, stabilizer Rényi entropies expose a richer structure in their dynamics. Our results uncover sharp distinctions between coarse and fine-grained nonstabilizerness diagnostics and demonstrate how measurements can both suppress and sustain quantum computational resources.

When focusing on a few essential bands in an effective description of a material to calculate observable quantities, the respective operators have to be adjusted accordingly. Ignoring contributions arising from integrating out remote bands can lead to qualitatively wrong results. We present a detailed analysis of the interband mixing effects on spin currents. Specifically, we calculate the intrinsic spin current in a time-reversal invariant noncentrosymmetric crystal in the presence of electron-lattice spin-orbit coupling. Starting from formally exact microscopic expressions, we derive the spin-current operator restricted to one or more essential bands by iterative elimination of the contributions from distant bands. We show that the standard definition of the spin-current operator in terms of the group velocity obtained from an effective band Hamiltonian cannot be justified using a microscopic theory. The modified expression for the spin-current operator contains additional terms, which dominate the equilibrium spin current in a uniform crystal. We show that the magnitude of these additional terms can considerably exceed the spin current obtained using the standard definition.

The magnetic Weyl semimetal ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ has garnered significant experimental and theoretical interest, particularly regarding its electronic structure and transport properties. In this study, we comprehensively investigated the effects of Fe and Ni substitution in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. The temperature-dependent Seebeck coefficient ($S$) implies that the reduction of the band gap and the shift in the Fermi level ($E_{\mathrm{F}}$) due to Fe and Ni substitution, which was supported by angle-resolved photoemission spectroscopy results. These band-structure modifications influence not only thermoelectric (TE) performance but also the anomalous Hall conductivity (${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$). Specifically, Fe substitution increases ${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$ via skew scattering, while Ni substitution increases ${\sigma }_{\mathrm{xy}}^{\mathrm{A}}$ via intrinsic deflection with minor skew scattering. Additionally, the Fe and Ni dopant-induced changes in the $c/a$ ratio were demonstrated using high-resolution powder synchrotron x-ray diffraction, which explains the different modulation in the magnetic anisotropy of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$ due to the magnetostriction effect. Notably, the oxidation states of Co, Fe, and Ni in each single crystal were confirmed as 0 using x-ray absorption near-edge structure analysis, further explaining the dopant-induced suppression in ferromagnetism of ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$. These findings provide deeper insight into the band-filling effects on both TE and anomalous Hall transport in ${\mathrm{Co}}_3{\mathrm{Sn}}_2{\mathrm{S}}_2$, offering perspectives for topological spintronics and TE applications.

Quantum key distribution (QKD) theoretically provides unconditional security between remote parties. However, guaranteeing practical security through device characterization alone is challenging in real-world implementations due to the multidimensional spaces in which the devices may be operated. The side channel secure (SCS) QKD protocol, which only requires bounding the upper limits of the intensities for the two states, theoretically provides a rigorous solution to the challenge and achieves measurement-device-independent security in detection and security for whatever multidimensional side channel attack in the source. Here, we demonstrate a practical implementation of SCS-QKD, achieving a secure key rate of 6.67 kbps through a 50.5 km fiber and a maximum distribution distance of 101.1 km while accounting for finite-size effects. Our experiment also represents an approximately 40 times improvement over the previous experiment.

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of ${10}^2–{10}^4$.

The ability to physically move qubits within a register allows the design of hardware-specific error correction codes, which can achieve fault tolerance while respecting other constraints. In particular, recent advancements have demonstrated the shuttling of electron and hole spin qubits through a quantum dot array with high fidelity. It is therefore timely to explore error correction architectures consisting merely of two parallel quantum dot arrays, an experimentally validated architecture compatible with classical wiring and control constraints. Upon such an architecture, we develop a suite of heuristic methods for compiling any Calderbank-Shor-Steane (CSS) error-correcting code's syndrome-extraction circuit to run with a reduced number of shuttling operations. We demonstrate how column-regular qLDPC codes can be compiled in a provably minimal number of shuttles that is exactly equal to the column weight of the code when Shor-style syndrome extraction is used. We provide tables stating the number of required shuttles for many contemporary codes of interest. In addition, we provide a proof of the NP hardness of minimizing the number of shuttle operations for general codes, even when using Shor-syndrome extraction. We also discuss how one could get around this by placing blanks in the ancilla array to achieve minimal shuttles with Shor-syndrome extraction on any CSS code, at the cost of longer ancilla arrays.