Biomolecular machines operate as stochastic flows on networks. Here, we develop a principled approach to network design where local transition rates are systematically tuned to achieve global dynamical objectives. Based on the fluctuation-response duality in caliber force theory, our formalism unifies existing nonequilibrium response relations under a single conjugate structure. Topologically, a force-rate Jacobian yields response symmetries that establish a local orthogonal control protocol for network flows. Analytically, it parses covariance to diagnose noise mechanisms, revealing the transition from timing to branching fluctuations in a kinesin motor. With algebraic closure streamlining multiobjective gradient evaluations, this framework provides a unified blueprint for designing stochastic dynamics.

We derive the characteristic equation governing the linear stability of the incoherent state in delayed noisy Kuramoto-Daido oscillator ensembles with general periodic coupling. The calculation is formulated for arbitrary normalized delay kernels and natural-frequency distributions. For a Lorentzian frequency distribution and first-harmonic coupling, the characteristic equation reduces to a closed dispersion relation in which phase diffusion and frequency heterogeneity enter through the damping combination $D+\mathrm{\Delta }$, while the delay kernel enters through its Laplace transform. The neutral conditions recover the established fixed- and distributed-delay limits and are evaluated explicitly for Gamma-distributed delays. We then derive the reduced phase dynamics of an overdamped Josephson-junction array coupled through a delayed common load. A finite-dc-load admittance produces a uniform drift that corresponds to the constant Fourier component of the reduced coupling function. When the ac coupling and dc-induced drift vary with the same load parameter, the resulting effective-frequency shift displaces the neutral stability boundary. Finite-$N$ simulations of the reduced phase equations agree with the continuum prediction over the parameter range considered.

Microscopic heat engines operate in regimes where thermodynamic quantities fluctuate strongly, making stochastic effects an essential aspect of their performance. However, existing geometric formulations of finite-time thermodynamics primarily characterize average dissipation and do not systematically capture its fluctuations. Here, we develop a unified geometric framework that consistently describes both the mean dissipated availability and its fluctuations. In the linear-response regime, we show that these quantities are governed by metric tensors constructed from equilibrium correlation functions, providing a common geometric structure for dissipation and its fluctuations. This framework yields geometric bounds on both the mean and variance of the dissipated availability, and thereby on the efficiency and its fluctuations. The formalism applies broadly to stochastic systems, including Markov jump processes and overdamped and underdamped Brownian dynamics, establishing a unified geometric description across microscopic heat engines.

We investigate the performance of large language models (LLMs) on repetitive deterministic prediction tasks and study how the sequence accuracy rate (SAR) scales with output length. Each such task involves the repetition of the same operation $N$ times. Examples of such tasks include letter replacement in letter strings following a given rule, integer addition, and multiplication of string operators in many-body quantum mechanics. If the LLM performs the task by a simple repetition algorithm, the success rate would follow an exponential decay with sequence length. In contrast, our experiments on leading LLMs reveal a crossover that is sharper than exponential: $-log\mathrm{SAR}$ grows superlinearly with $N$, and accuracy collapses around a characteristic length $N_{*}$, the accuracy cliff that separates reliable from unreliable generation. The hypothesis of independent per-step errors is rejected for every model and task we studied. The crossover is well described by a double-exponential accumulation law, $\mathrm{SAR}=exp(-{\beta }_{0}N{\alpha }^{N-1})$, whose crossover scale $N_{*}$ does not depend on the functional form chosen to fit it. To interpret this behavior, we introduce a minimal effective model in which step-correctness variables interact through dense random couplings and compete with an external field set by the prompt. Solved by direct enumeration, the model reproduces the superlinear error accumulation and the accuracy cliff qualitatively, and it assigns to each model-task pair two interpretable parameters, an intrinsic error rate and an error-accumulation factor.

We investigate how quantum correlations in squeezed driving fields determine scaling laws in dissipative multiphoton quantum sensing. Independently squeezed fields yield factorized scaling, with separate absorption and emission contributions and nonlinear thresholds that suppress exponential scaling in linear processes. In contrast, jointly squeezed fields generate collective scaling governed by the total nonlinear photon order of the dissipative interaction. Remarkably, we show that normally ordered observables do not inherit the full nonlinear scaling of the underlying multiphoton fluctuations. Instead, they exhibit asymptotic behavior with an effective nonlinear order reduced by one. This arises because normally ordered observables probe only part of the underlying multiphoton fluctuation structure. These findings reveal how multiphoton fluctuations, quantum correlations, and measurement structure jointly determine the experimentally accessible sensitivity of nonlinear dissipative quantum sensors and establish design principles for quantum sensing protocols based on structured squeezed light.

Using both simulation and experiment, we investigate the robustness of dynamical decoupling sequences to pulse errors: rotation errors and detuning errors. Whereas prior work examined the effect of errors on coherence times, here we show that quantum sensing can be affected by pulse errors in dramatically different ways than coherence times alone. We also explore the effects of qubit leakage: off-resonant coupling to other quantum levels. We find order-of-magnitude differences between commonly used dynamical decoupling sequences in both their sensitivity to pulse errors and leakage.

Scattering theory has long established that wave packets can experience time delays and advances, while developments in attosecond interferometry have made such temporal shifts experimentally accessible. They are encoded in the spectral phase of the emitted electron wave packet and are commonly accessed through interferometric techniques. Here, we report an intensity-driven reversal of the angular phase of a threshold photoelectron sideband in helium. By varying the intensity of an infrared dressing field, we control the direction of the phase change at large emission angles, which is associated with interference between partial waves near angular nodes. Solving the time-dependent Schrödinger equation within the single-active-electron approximation confirms the existence of an angular phase inversion. Our results reveal a mechanism for manipulating the angular phase structure of photoelectron wave packets over a large range via laser-induced interference.

We investigate the low-Reynolds-number propulsion of a slender elastic filament with a dipolar magnetic head actuated by an oscillating magnetic field in a viscous fluid by studying its strokes and net forward motion. To capture these dynamics, we employ an elastohydrodynamic (EH) framework that couples Euler-Bernoulli beam mechanics with resistive force theory. Unlike prescribed-kinematics models, filament shapes here emerge self-consistently from the actuation and the force and torque boundary conditions (BCs). We demonstrate that viscous boundary contributions are crucial for quantitative agreement and show that the swimming dynamics are governed by the EH length and a magneto-viscous-elastic stroke amplitude introduced here. The swimming speed is nonmonotonic with increasing ratio of the swimmer length to the EH length and is shown to reach a maximum when the swimmer length is on the order of the EH length. We further discuss the analytical limit in which the tail BCs can be described as free, and the limitations that arise when viscous contributions to the BCs are ignored.

We present a theoretical approach for computing and analyzing two-dimensional spectroscopy of bosonic collective excitations in disordered many-body systems. Specifically, we employ the Keldysh formalism to derive, within a nonperturbative treatment of disorder effects, the third-order nonlinear response and obtain two-dimensional spectroscopy maps. In the weak nonlinear regime of our formalism, we demonstrate the ability of the echo peak to distinguish between elastic and inelastic scattering processes, in perfect agreement with the intuition developed in isolated two-level systems. Furthermore, we discuss unique many-body effects on the echo peak signature arising from interaction-induced quantum fluctuations. In particular, we show that these quantum fluctuations induce a finite nonrephasable broadening and examine how the echo peak is influenced by the attractive or repulsive nature of the collective excitations.

Fock-space fragmentation, as it is currently investigated, primarily originates from specific kinematic constraints or emergent conservation laws in many-body systems with translation invariance. It leads to nonergodic dynamics and possible breakdown of the eigenstate thermalization hypothesis. Here, we demonstrate that also in disordered systems, such as the XXZ model with random on-site fields, fragmentation appears as a natural concept offering fresh perspectives, for example, on many-body localization. Specifically, for a given quenched initial state, we identify a potential-energy shell in Fock space, defined by its energy and energy uncertainty, which represents the energetically accessible part of the many-body configuration space. For example, the drastic sample-to-sample fluctuations observed in the weak disorder regime, $W<W_{\text{frag}}$, represent fluctuations of the mass of the shell. Upon increasing disorder, the potential-energy shell becomes increasingly fragmented. Its finite-size evolution exhibits a turnaround flow; extrapolating this flow to the disorder at which the turnaround vanishes provides a heuristic estimate of the strong-fragmentation scale $W_{\text{frag}}$. We conjecture that the fragmentation identified here provides a geometric mechanism contributing to the finite-time slowing down of relaxation observed in studies of disordered interacting systems.

The circular Unruh effect is the excitation of a detector moving along a planar circular trajectory within an electromagnetic vacuum. We demonstrate that the magnetic dipole transitions in an atom, acting as the detector, dominate the electric dipole transitions. Our analysis of both free-space and cavity schemes shows that the sensitivity to the circular Unruh effect can be maximized by balancing the minimization of mode volume against the resulting decrease in mode density. Moreover, we propose a measurement scheme that uses the atom's multilevel structure to suppress the spontaneous emission rate, thereby enabling the experimental detection of the circular Unruh effect.

We introduce a framework for remotely tunable dynamical metamaterials based on interacting nodes embedded in an elastic matrix, effectively forming meta-atoms governed by a programmable nonlinear landscape. Using secondary acoustic radiation forces between microbubble arrays, we predict and experimentally realize an acoustically actuated linear unit cell exhibiting geometric reconfiguration, discontinuous switching, and memory. Building on these results, we introduce a general numerical model for the system that predicts diverse behaviors in larger lattices, including a remote stiffness softening up to 60% and auxeticity up to $\nu =-0.22$. The theory applies to other modes of actuation (e.g., optical or magnetic) and reveals universal behavior in these systems arising purely from the interplay of local $r^{-n}$ forces and elastic interactions in the lattice.

A recent proposal suggested that neutron orbital angular momentum (OAM) states could be detected via spin-polarized absorption in polarized ${}^3\mathrm{He}$, with predicted cross-section variations linked to the neutron’s OAM. We experimentally tested this hypothesis using spin-polarized neutron beams with OAM $=-2$ to 2, generated by fork-dislocation phase gratings and transmitted through a polarized ${}^3\mathrm{He}$ cell. Within statistical precision, no OAM-dependent change in the absorption cross section was observed. This null result places stringent constraints on polarized ${}^3\mathrm{He}$-based OAM detection schemes. The absence of an effect in the given regime is traced to the proposal’s disregard of the spatial character of neutron OAM: Unlike spin, OAM arises from the transverse phase structure of the wavefunction and couples only through spatial gradients and overlap. The transverse extent of neutron OAM modes expands rapidly, producing a doughnut-shaped intensity profile with negligible overlap with on-axis ${}^3\mathrm{He}$ nuclei, while off-axis capture samples only a locally uniform phase and reduces the interaction to the known spin dependence. These results establish the limits of absorptive nuclear methods for probing neutron OAM and emphasize the necessity of spatially resolved interactions in any viable detection scheme.

Understanding equilibration and universality after sudden quantum quenches remains a central challenge in isolated many-body systems. Persistent oscillations and anomalous scaling reported in lattice models appear to challenge the standard picture based on integrability and quantum-to-classical correspondence. Focusing on the quantum $O\left(n\right)$ model in the large-$n$ limit, we show that these apparent anomalies originate from lattice effects and an underlying integrable structure. In particular, we map the postquench dynamics onto an integrable Neumann system and we derive an exact action-angle description valid in the thermodynamic limit. This framework explains both the convergence of long-time averages to the generalized Gibbs ensemble and the emergence of persistent oscillations associated with an isolated mode at the upper edge of the phonon spectrum. We further show that the expected thermal universality class is recovered in the appropriate scaling regime, while the oscillations disappear in the quantum-field-theory limit.

Membrane remodeling into vesicles is essential for processes such as receptor transport and viral budding. In many cases, this remodeling is driven by the assembly of multivalent protein lattices that stochastically grow while coupled to bending the membrane. Here, we ask how membrane mechanics can bias the structural pathways sampled during lattice growth. Using a continuum membrane model coupled to growing human immunodeficiency virus Gag lattice intermediates, we show that radially symmetric lattice growth is energetically favored over eccentric growth because it induces membrane bending at lower cost per protein. For rigid lattices, the penalty for asymmetric growth is controlled primarily by the shape of the lattice perimeter rather than by the density of protein-membrane links, with all membrane deformations retaining strong radial symmetry. Reevaluating the energy relative to the circumscribing radius of the lattice thus collapses all growth pathways to a similar curve. When the lattice is flexible, asymmetric growth introduces another cost, as these intermediates also generate weaker curvature. Analytical spherical-cap estimates support the trends in our numerical energy minimization calculations, and our results remain robust across a range of tested modeling assumptions including membrane spontaneous curvature. Although kinetic barriers along growth pathways are not assessed, our results show that membrane bending can strongly select for symmetric assembly pathways, providing a mechanical bias against irregular lattice growth during membrane remodeling.

Triple-layer cuprate superconductor ${\mathrm{HgBa}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_8$ (Hg1223) keeps the record of the highest superconducting (SC) critical temperature $T_{\mathrm{c}}\sim 134\mathrm{K}$ among all the existing materials at ambient pressure. $T_{\mathrm{c}}$ further increases under pressure up to $T_{\mathrm{c}}\sim 160\mathrm{K}$, thereby holding the key to the realistic and comprehensive understanding of the cuprate superconductors, which is one of the grand challenges in physics. However, the microscopic mechanism of high $T_{\mathrm{c}}$ of Hg1223 remains to be elucidated. Here, we perform first-principles calculations of Hg1223 both at ambient and applied pressures by solving ab initio Hamiltonians with an accurate variational solver supplemented by a neural network. The pressure dependence of the calculated $d$-wave SC order parameter and estimated $T_{\mathrm{c}}$ shows a structure supporting a $T_{\mathrm{c}}$ peak around 30 GPa in quantitative agreement with the reported experimental indications. The origin of the strong SC amplitude of Hg1223 at ambient pressure compared to other cuprates is identified as strong local Coulomb repulsion $U$ attributed to poorer screening of the Coulomb interaction in multilayer compounds. The origin of the further increase in $T_{\mathrm{c}}$ under pressure is ascribed to a unique interplay of three elements, namely, increased electron hopping $t$, decreased $U$, and more importantly, strongly reduced nonlocal Coulomb repulsion $V$ with increasing pressure. The origin of Cooper pairing is identified as the emergent local attraction counterintuitively arising from the strong bare local repulsion $U$ for Hg1223. It explains why Hg1223 shows the highest $T_{\mathrm{c}}$ among other cuprates, while the pairing mechanism is common in other cuprates as well. The emergent attraction is interpreted from “attraction from reduced repulsion,” originating from the release of the fluctuating doubly occupied sites characterized from the “false vacuum” in the Mott insulator to the double-occupation-free $d$-wave SC states caused by the carrier doping. This instantaneous and local attraction is in marked contrast with the case of the conventional BCS SC mediated by bosonic glues. The local attraction is consistent with the electron fractionalization supported in experimental analyses. The coexistence of SC and antiferromagnetic orders is also demonstrated as a characteristic feature of the multilayer system with self-doping in the underdoped region. The quantitative and microscopic understanding of the high $T_{\mathrm{c}}$ in Hg1223 provides a new perspective on the origin of the cuprate superconductivity and offers a new route explicitly using this channel of the emergent attraction for future superconductivity research aiming at designing and optimizing SC materials.

Space-charge compensation is routinely used to mitigate emittance growth in linear accelerator beam transport lines. Severe space-charge effects and incomplete compensation within low-energy beam transport sections universally induce beam divergence and emittance degradation, constituting a key bottleneck for low-energy, high-intensity beams. This work investigates the evolution of residual-gas-generated secondary-ion clouds under applied electric fields and their impact on primary beam emittance growth. By implementing barrier electrodes to confine the secondary-ion cloud, we achieve substantial reductions in both the emittance and beam radius of an ${\mathrm{H}}^{-}$ beam while preserving full beam intensity. The proposed ion cloud trap scheme also has important implications for neutral beam injection in magnetic confinement fusion and high-current ion implanters, providing insights into low-energy charged particle transport across diverse ion-beam platforms.

Motivated by the prospect of chiral-mode control in compact photonic systems, we analyze discrete coupled single-mode resonators. Using the minimal three-resonator model, we show that an infinitesimal complex on-site perturbation near a Hermitian diabolic point (DP) induces chiral-mode selection, governed by what we term an asymptotic exceptional point (AEP). Here, an AEP denotes a Hermitian DP equipped with a non-Hermitian perturbation that induces an asymptotically defective effective Hamiltonian. The eigenvectors coalesce in the asymptotic limit toward the DP, although the Hamiltonian at the point itself remains diagonalizable. Operationally, this AEP response realizes chirality switching from an achiral state to a chiral state. The associated eigenvalue response exhibits the anomalous fractional-power scaling $\mathrm{\Delta }\lambda \propto {\varepsilon }^{3/2}$, distinct from the square-root response of an ordinary exceptional point (EP). We further show that, in a broader two-parameter perturbation space, ordinary EPs lie on exceptional-line branches that meet at the AEP. A finite-bias control sweep crosses these branches at an EP pair, enabling chirality reversal between opposite chiral states. The central message is therefore that the AEP organizes two related routes for chirality switching: direct switching from an achiral state to a chiral state via the AEP and switching between opposite chiral states via an EP2 pair in the vicinity of the AEP. Within a finite-resolution averaging model, these two operating points exhibit different practical performance characteristics, and under sufficiently high control resolution, the AEP operating point can become more favorable than the EP-pair operating point, suggesting a route toward compact and low-energy chiral photonic devices.

Fixation probabilities are essential for characterizing stochastic evolutionary dynamics, but analytical results remain limited mainly to systems with two competing types. We develop a perturbative framework to compute fixation probabilities in multiallele Moran processes under weak selection. Exploiting the general structure of the backward Fokker-Planck operator in this regime, we show that fixation probabilities admit a systematic expansion around their neutral solution. We first introduce the framework for $M$ competing alleles with multivariate polynomial fitness functions. We then apply it to three biologically motivated examples: a constant-fitness model, which we solve for an arbitrary number of alleles; a three-allele coordination game in which allele fitness increases with its frequency in the population; and a three-allele model of clonal interference between mutualistic alleles. These results extend the analytical understanding of fixation probabilities beyond pairwise interactions, establishing a framework for investigating multistrategy stochastic evolutionary dynamics.

An active research line within the broader field of network science is the one concerning link prediction. Close in scope to network reconstruction, link prediction targets specific connections with the aim of uncovering the missing ones, as well as predicting those most likely to emerge in the future, from the available information. In this paper, we consider two families of methods, i.e., those rooted in statistical physics and those based upon machine learning: the members of the first family identify missing links as the most probable nonobserved ones, the probability coefficients being determined by solving maximum-entropy benchmarks over the accessible network structure; the members of the second family, instead, associate the presence of single edges with explanatory node-specific variables. Running likelihood-based models such as the configuration model, or one of its many fitness-based variants, in parallel with the gradient boosting decision tree algorithm reveals that the accuracy of the former is comparable to the accuracy of the latter. Such a result confirms that white-box algorithms are viable competitors to the currently available black-box ones, being more interpretable and computationally faster.