Papers

A density-functional theory developed for equilibrium freezing also produces a high-density endpoint close to terminal packing. We revisit the nonlinear Ramakrishnan–Yussouff bifurcation framework and distinguish the first crystalline fold, thermodynamic coexistence, and terminal marginality. At the terminal point, the grand-potential curvature vanishes along the principal finite-wavevector density mode, exactly when the nonlinear self-consistency equation loses stiffness. The construction gives exact close packing for one-dimensional hard rods, a terminal hard-disk packing fraction near 0.8407, and a hard-sphere value near 0.629, close to random close packing. These results identify a finite-wavevector thermodynamic marginality of a metastable liquid continuation, rather than equilibrium freezing or mechanical jamming, and expose a persistent puzzle: why should liquid-state correlations encode the approach to terminal disordered packing across different physical dimensions and systems?

The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law “long-time tails.” In this paper, we apply the recently proposed hyperstatistics framework to the problem of quantum decay in such complex environments. By considering a $\gamma$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\langle t\rangle = \int_0^\infty P(t)\,dt= [\langle\Gamma\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$. These results provide a refined physical interpretation: for $1<q<3/2$ both the mean lifetime and its variance are finite; for $3/2\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for $q\ge2$ the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.

Quantum optomechanics (QOM) explores the interaction between a quantum field, often confined in a cavity, and the quantum motion of mirrors, membranes or material media, usually assumed slow enough with negligible particle production, which is the central concern of dynamical Casimir effects, and a drive laser field for effective control. This rapidly developing field has a wide range of applications, from quantum sensing to the detection of gravitational waves. Because the opto-mechanical coupling is nonlinear, most theoretical investigations assume that the amplitude of mirror motion $x$ remains small. Recent years saw several papers treating $x^2, x^3$ orders in the mirror displacement. In our work we take a different route, deploying the functional perturbative method presented in [1] and enriched in [2], applicable for sufficiently weak opto-mechanical couplings. With this we can treat arbitrary displacement of the mirror, not just at a higher order in a power series expansion in $x$. We first derive the influence action of the quantum field and its non-Markovian noises back-reacting on the moving mirror with self-consistency. From it we derive a nonlinear Langevin equation driven by these back-action noises from the quantum field. We then show how results from our general modeling and treatment can be linked with the models and the Langevin equations presented in the literature, starting with the popular radiation pressure $Nx$ coupling, with $N$ the photon number, up to the recent $x^3$ order results. We hope this new approach and the results presented here can provide useful theoretical support for high precision QOM experimentation in the future.

Information can be converted into work, but in quantum mechanics information about a state is not freely available: it must be inferred statistically from measurements on a finite number of copies. We study work extraction in this finite-resource setting by introducing a partial-information and finite-resources (PIFR) quantum Maxwell's demon. Given $N$ identical copies of a state with known Hamiltonian, the demon measures $M$ copies to estimate the state and the corresponding ergotropic unitary, which is then applied to the remaining $N-M$ copies. This protocol induces a trade-off between information acquisition, reconstruction accuracy, and thermodynamic yield, making the total extracted work normalized to the ideal ergotropic benchmark the relevant figure of merit. As our central result, we derive a universal closed-form trade-off bound that places this ergotropic efficiency between a Carnot-type ceiling $1-M/N$ and a floor controlled by a reconstruction precision rooted in finite-sample quantum estimation theory; optimizing the copy allocation yields $M^*\propto N^{2/3}$ and an $N^{-1/3}$ approach to the ideal limit, set by a conservative, worst-case reconstruction precision. By considering standard quantum state tomography, we numerically verify the presence of an optimal resource distribution, which also depends on the purity of the state under consideration. Our results identify finite-copy work extraction as a genuinely task-dependent inference problem, in which estimation strategies should be judged by thermodynamic performance rather than reconstruction fidelity alone.

On the space of density matrices $D(H)$, Kadison's theorem establishes that all invertible convex transformations $K:D(H)\to D(H)$ are unitarity or antiunitary. For a finite Hilbert space, we propose a similar theorem which replaces the invertibility requirement with that of entropy conservation. Thus, we argue, the supposition of reversibility in quantum mechanics may be replaced with a principle of entropy conservation.

We study a generalized Ornstein-Uhlenbeck process driven by a superposition of $K$ independent dichotomous noises with arbitrary fixed amplitudes and switching rates. Unlike the classical Ornstein-Uhlenbeck process driven by equilibrium Gaussian white noise, the present system is governed by bounded nonequilibrium fluctuations with finite correlation times. We obtain exact expressions for the stationary position distribution and all cumulants, and show that the stationary state possesses an unexpectedly rich structure, including compact support, algebraic branch-point singularities, edge divergences, and multiple extrema. We establish a mapping onto a heterogeneous random-flight process with bounded jumps, yielding a transparent probabilistic interpretation of the stationary measure. We further analyze several limiting regimes, including the crossover to Gaussian statistics for large numbers of noise sources. For ensembles with exponentially-distributed quenched amplitudes, we derive exact disorder-averaged stationary distributions and show that disorder fundamentally alters the stationary state, producing exponential tails decorated by algebraic prefactors with non-trivial exponents.

Liquid-state theory provides a fundamental connection between microscopic structure and macroscopic thermodynamic behaviour. Here, we develop a framework for predicting thermodynamics and phase behaviour directly from structural correlations, using either radial distribution functions or static structure factors as input. The approach constructs a free-energy functional from structural information obtained at a single thermodynamic state point, without requiring explicit knowledge of the underlying interaction potentials. This circumvents a central difficulty in modelling complex fluids, for which effective interactions are often unknown or rely on approximations. We demonstrate the framework for a range of model fluids, including colloidal and colloid–polymer systems, with predictions in good agreement with molecular simulation data. The results show that structural information at a single state point can provide sufficient information to predict the broader thermodynamic response of a system. This establishes a route toward inferring phase behaviour directly from experimentally measured structure, even when the microscopic interactions are not known a priori.

In a quantum many-body system, a periodic drive can often generate effective static forces on the slow collective degrees of freedom. We study the static forces generated by light on electronic order parameters in solid-state systems. We show that the forces can have nonconservative components that originate from dissipation, i.e., optical absorption. This effect is demonstrated in two nontrivial examples. In excitonic insulators, via interband excitations, the light field generates a nonconservative force on the phase of the excitonic order parameter. This force leads to an acceleration of the phase, which manifests as a shift of the photon emission peak from an exciton condensate. In materials with an incommensurate charge density wave, a propagating light field generates a nonconservative force on the phase of its order parameter. It drives the charge density wave into sliding motion, leading to a DC electric current via topological Thouless pumping.

Let $\mathbf{c}=(\lambda,\alpha,\mu,\nu)\in\mathbb{R}^{4}$ denote the four running couplings of four-dimensional nonplanar Euclidean scalar $\varphi^{4}$ theory, and let $B(\mathbf{c})=\sum_{p\ge2}\sum_{|\mathbf{m}|=p}\beta(\mathbf{m})\mathbf{c}^{\mathbf{m}}$ be its formal beta-function series. Assuming the factorial coefficient bounds $|\beta(\mathbf{m})|\le (p-1)!C^{p-1}$ for $|\mathbf{m}|=p$, we construct an explicit summation rule $\mathcal{S}$, given by a cut Borel–Laplace transform whose cut is placed by a scale-covariant real-analytic gauge. We prove that it assigns a well-defined real value to $B$ on an explicit nonempty open domain, in fact on all of $\mathbb{R}^{4}$. The summed function $\mathcal{S}B$ is linear and real, real-analytic on $\mathbb{R}^{4}\setminus\{0\}$, $C^\infty$ on $\mathbb{R}^{4}$ with Taylor series $B$ at the origin, and Gevrey-$1$ asymptotic to $B$ to all orders with an explicit remainder bound. At optimal truncation the remainder is $O(e^{-\eta/(C\|\mathbf{c}\|_\infty)})$ for any $\eta<1$. We show that $\mathcal{S}B$ reproduces the classical Borel sum and the ordinary sum of a convergent series up to errors of the same exponentially small order. Exact reproduction is impossible for any linear rule defined on the whole admissible class: regularity forces all weights to equal $1$, leading to divergence. Finally, we prove optimality under the stated hypothesis. Admissible series may diverge at every $\mathbf{c}\ne0$, and their Borel transforms may have the circle $|\tau|=1/(C\|\mathbf{c}\|_\infty)$ as a natural boundary, so classical Borel-type summation need not be available on the class. Moreover, there exist two functions indistinguishable at the level of the coefficient bounds yet differing by exactly $(2\pi/C)e^{-1/(C\|\mathbf{c}\|_\infty)}$. All constants are explicit and all arguments are self-contained.

Flows in random networks are known to exhibit heavy-tailed statistics, giving rise to anomalous transport in a range of biological, environmental and engineered systems. Yet, how structure determines flow remains an open question. Here we derive a dual network approach that relates flow statistics and network properties. Conditional statistics in a range of networks reveal the existence of two interlaced subnetworks with distinct hydraulic behaviors. Based on this hidden structure, we derive a universal analytical approach that predicts heavy-tailed flow statistics based on network topology and disorder distribution across a range of random networks.

Every crystal is a Bravais lattice decorated by a basis, so the dipolar ordering of the fourteen Bravais lattices is the natural starting point for any systematic theory of dipolar magnetism in three dimensions. We determine it here in a single common framework: the interaction tensor is Ewald-summed, the classical ground state is obtained by minimising the lowest Luttinger–Tisza band over the entire Brillouin zone, and the linear spin-wave spectrum with its zero-point corrections is computed for every lattice whose order is collinear. Three results emerge that are not properties of individual lattices but of the landscape. First, two structural principles — the exact tracelessness of the dipolar tensor in three dimensions, and its identical vanishing at $\mathbf k=0$ for every cubic-symmetric lattice — explain the ordering type, the absence of first-order cubic anisotropy, and the systematics of the zero-point moment reduction. Second, exactly one lattice defeats the Luttinger–Tisza construction: for face-centred orthorhombic the optimal eigenvector is not circular, the single-$\mathbf k$ state is a spin-density wave of non-constant length, and the tabulated energy is a strict lower bound; direct supercell minimisation gives the true ground state. Third, optimising each family over its free metric parameters collapses the whole of Bravais space onto only four attractors, with body-centred tetragonal the global optimum and a single interior optimum at rhombohedral $\alpha=62.42^\circ$ lying below face-centred cubic. Three independent published benchmarks are reproduced.

We study classical Heisenberg spins interacting through the dipole–dipole interaction on the eleven Archimedean and eight Laves planar lattices at canonical geometry, which reduce to fifteen distinct vertex sets. For each lattice we compute the Fourier-space interaction matrix $\Am(\bk)$, extract the Luttinger–Tisza ordering wave vector $\bk_{0}$, determine the classical ground state by unconstrained minimization on the commensurate magnetic cell, and evaluate the linearized spin-wave dispersion $\varepsilon_{i}(\bk)$ along the high-symmetry path of the (magnetic) Brillouin zone together with the Holstein–Primakoff moment reduction. The ground states fall into three classes: five are collinear, two are non-collinear at angles commensurate with the lattice symmetry, and eight cant at transcendental angles, which we determine to thirty digits. Across the family, failure of the Luttinger–Tisza strong condition coincides exactly with the appearance of incommensurate canting, with no exceptions in either direction. Truncating the interaction range shows that whether a lattice cants is fixed by the local coordination geometry, whereas the value of the canting angle is set by the long-range tail. The quantum corrections are governed by the magnon spectrum through the size of the magnetic basis and are uncorrelated with frustration, so that the frustration and fluctuation classifications are independent; the corner-sharing lattices host the narrowest low-energy branches. The results constitute a spectral atlas of dipolar Heisenberg systems on the full family of $1$-uniform planar tilings and their duals, and provide predictions for inelastic neutron scattering in materials whose magnetic ions occupy Archimedean or Laves lattices, and for artificial arrays of dipolar-coupled nanomagnets.

Planar $k$-uniform states have maximally mixed reductions on every $k$-site interval of a ring. We introduce planar $k$-purity—the mean purity of those intervals—as a faithful cost function for this simultaneous constraint. For a Haar-random pure state of $n$ parties with local dimension $p$, the joint purity of two intervals depends only on their overlap. An exhaustive four-replica calculation therefore yields the complete cyclic covariance kernel and a closed variance for every $1\le k\le\lfloor n/2\rfloor$. In the balanced qubit case, $k=\lfloor n/2\rfloor$ and $N=2^n$, the variance is asymptotic to $20/(3nN^2)$ for even $n$ and $6/(nN^2)$ for odd $n$. A site-factorized permutation representation gives all raw moments and permits exact finite-sum evaluation of the skewness. Fixed-seed simulations validate nonbalanced qubit and qutrit cases, while balanced-qubit simulations through $n=10$ validate the parity formulas and finite-size skewness. Balanced planar and absolute balanced purity have the same Haar mean but different fluctuations; the planar variance is approximately $2.83$ times larger at $n=10$. Thus subsystem incidence, although invisible to every one-cut marginal distribution, controls the collective fluctuations of geometrically related cuts. Together with universal attainability and a linear number of interval constraints at balance, this provides a geometry-aware benchmark for multipartite entanglement beyond AME existence regimes.

We introduce determinant quantum-quantum Monte Carlo (DQ$^2$MC), a quantum algorithm that lifts the auxiliary-field sampling and averaging at the operational core of determinant quantum Monte Carlo onto a quantum computer. A determinant oracle synthesizes the DQMC amplitudes directly from a block encoding of the single-particle action matrix via quantum singular value transformations, so that the exponentially many Hubbard-Stratonovich weights are never enumerated, precomputed, or stored. Since the fermions are free for fixed auxiliary fields, the construction operates entirely at the single-particle level, requiring $O(\log N_{\mathrm{st}})$ system qubits and no Jordan-Wigner or Bravyi-Kitaev encoding, where $N_{\mathrm{st}}$ is the space-time volume. A full-quantum protocol makes observables interference amplitudes, eliminating the Markov chain and its autocorrelation time altogether; a hybrid quantum-classical protocol retains a constant-size active block of qubits and replaces the Metropolis-Hastings acceptance step with an exact heat-bath draw, so that cluster updates of any size are rejection-free, and passes only classical information between updates, admitting parallel tempering and distributed execution across quantum processors. The circuit-depth scales more favorably with spatial volume than classical DQMC, at the price of a post-selection overhead determined exactly by the largest target probability — polynomial for smooth distributions, exponential for sharply peaked ones. Finally, the reweighting estimator underlying the fermion sign problem maps exactly onto a quantum weak value, placing the exponential cost of sign-problematic DQMC in precise correspondence with the post-selection overhead of weak-value extraction.

We investigate the fluctuating nonlinear dynamics of multiple modes of a nanomechanical doubly clamped beam resonator. Each mode is driven by Gaussian force noise centered around the resonance; the mode response is monitored while the force magnitude is increased, inducing a transition from harmonic to the nonlinear Duffing regime. To characterize the dynamics, we introduce an effective temperature based on the mode fluctuation amplitude. As the nonlinearity becomes prominent at large amplitudes, we observe a reduction in the effective thermal energy and a crossover in response statistics from Gaussian to platykurtic, consistent with the dynamics expected in a Duffing potential.

Leading eigenvalues of the truncated propagator, known as Ruelle-Pollicott (RP) resonances, are an elegant way of addressing the dynamics of unitary many-body systems. We study unitary propagators in their canonical form, known in the mathematical literature as the CMV matrices, and obtain a number of exact results for RP resonances and the associated norm-diverging eigenvectors. For the simplest CMV class describing a unilateral shift with an impurity, motivated by operator dynamics in dual-unitary circuits, we obtain closed-form results and in particular show that the three independent ways of obtaining RP resonances – the truncated propagator, analytic continuation of the resolvent, and the rigged Hilbert space approach – all give the same results. In more realistic CMV matrices, in which shift-like operator dynamics characteristic of chaotic systems is only asymptotic, we rely on the rich theory of orthogonal polynomials on the unit circle and identify two phases. In the first phase, relaxation occurs due to local operators effectively evolving into increasingly nonlocal ones with negligible backflow. Especially interesting is the second phase, which, surprisingly, exhibits faster relaxation because of contributions from the backflow of large operators. Additionally, in the second phase, RP resonances are not equal to the eigenvalues of the truncated propagator, instead, they are “hidden” within a ring of ill-conditioned eigenvalues.

Magic, or nonstabilizerness, is the resource that lifts Clifford circuits to universal quantum computation and has become a standard diagnostic of many-body states. For a state shared between two parties, however, a basic question has remained open: how much of the magic resides in the correlations between the parties rather than in their local bases? Isolating this nonlocal magic requires minimizing over all local bases, an optimization that has so far resisted exact solution. Here we solve it for the stabilizer fidelity: the nonlocal magic of every pure multiqubit state is the distance of its entanglement spectrum from the closest spectrum of Bell pairs. The same quantity governs an apparently unrelated task: a family of states universally embezzles entanglement under local operations and classical communication if and only if its nonlocal magic diverges. The deciding property is not the amount of entanglement but the way the entanglement spectrum spreads its weight across factor-of-two windows of rank, so that critical chains and random-singlet states, with identical logarithmic entanglement scaling, carry unbounded and vanishing nonlocal magic, respectively. Nonlocal magic thereby becomes an operationally meaningful property of quantum correlations, directly accessible to tensor-network simulations and, through entanglement spectroscopy, to experiments.

We generalize a one-dimensional random sequential adsorption model (RSA) of charged unit segments in which the deposition position follows a beta kernel determined by the charges bounding the available gap and those of the incoming particle. The interaction parameter \(0\leq\lambda<1\) interpolates between uniform car parking and strongly localized deposition. We derive a four component generating function equation that provides exact recursions for the complete occupation statistics, although only the mean and variance are analyzed in detail here. Exact finite-shell solutions serve as benchmarks for the Gauss–Jacobi quadrature and Monte Carlo simulations. We prove that, although boundary charges affect finite size behavior, the four boundary states have the same asymptotic mean and variance densities, consequently, we prove that the jammed density is self-averaging. Numerical results show that charge selectivity increases the coverage, especially for mixtures dominated by opposite endpoint charges, which also exhibit strongly reduced fluctuations near \(\lambda=1\). The model provides a tractable connection between uniform RSA, dynamically generated disorder, and interaction-driven deposition.

The lattice Green's functions of the cubic lattices are classical: each is a symmetric square of a second-order operator, with a closed form in complete elliptic integrals. The hyperkagome lattice, realized by the iridium sublattice of the spin-liquid candidate Na4Ir3O8, has resisted such a treatment: Varma and Monien reduced its density of states to a threefold integral they found no way to solve exactly. From exact lattice moments we obtain an irreducible third-order linear differential (Picard-Fuchs) operator annihilating the Green's function. It is not a literal symmetric square, yet its symmetric square carries a rational solution: the differential Galois group is orthogonal, and an order-two differential intertwiner makes the operator projectively a symmetric square. Our main result is that the underlying second-order operator is the uniformizing equation of the genus-zero modular curve of Gamma_0(30)+, the level-thirty group generated by Gamma_0(30) and all its Atkin-Lehner involutions, an explicit eta quotient parametrizing the natural variable. That uniformizing equation is itself not new - it is a row of the Lian-Yau table of genus-zero groups - so what is new here is the identification of a lattice Green's function with it, together with a proof: the Schwarzian identity is established by an a priori pole-degree bound rather than checked numerically, which also proves the tabulated entry. The hyperkagome Green's function is therefore modular at level thirty, supplying the closed form Varma and Monien sought. Its weight-two period is obtained explicitly: a depth-one quasimodular form which we prove is not a modular form times an algebraic function at any weight.

Collective behaviour in living systems is usually modelled as the outcome of a direct social drive: agents are rewarded, or hard-wired, to align with or approach their neighbours. Here we show that aggregation can instead emerge from an indirect objective. We let reinforcement learning foragers, initially performing a random walk, optimize their dynamics from a purely individual reward for finding replenishable targets, while perceiving only their conspecifics and never the targets themselves. As the visual range grows, the agents undergo a sharp crossover from an environment-tuned individual search to a scale-agnostic collective one, and this crossover coincides with the onset of spatial aggregation. Thus a collective phase arises as a by-product of optimal foraging, without any direct reward for grouping. A minimal analytical first-passage model reproduces the transition as a crossover between the two search strategies. Our results identify indirect, resource-driven reward as a generic route to emergent collective phenomena.

Can quenched disorder generate ordering in driven systems? Using a recently proposed hydrodynamic model, we show that sufficiently long-ranged quenched disorder can induce long-range order in two-dimensional (2D) nonreciprocal XY systems, even when the clean system exhibits only short-range order at finite noise. Active surfaces tangentially advected by quenched velocities, governed by the same hydrodynamic equation, become statistically flat with super- or subdiffusive relaxation. In three dimensions (3D), quenched disorder combined with nonreciprocity produces a novel transition between strong-coupling and asymptotically noninteracting regimes, supporting either long- or short-range order. In both 2D and 3D, the exponents are nonuniversal, which vary continuously with the degree of transversality of the quenched disorder. The degree of transversality of the quenched disorder can be tuned to induce transitions in the model for fixed disorder and noise variances.

In three-dimensional compact U(1) lattice gauge theory color confinement can be understood analytically through the dynamics of magnetic monopoles. However, its continuum limit is pathological, since the ratio of the glueball masses to the square root of the string tension vanishes as the continuum limit is approached. We investigate a simple extension of the Wilson action in which the total number of lattice monopoles is coupled to an additional parameter $\mu$. By tuning $\beta$ and $\mu$ simultaneously, we identify a line of constant physics along which the ratio of the lightest glueball mass to the square root of the string tension remains constant. We further show that the same scaling is satisfied, within numerical uncertainties, by the other low-lying glueball masses considered in this work. Along this trajectory, the string tension in lattice units decreases with increasing $\beta$, thus suggesting that the modified lattice action may provide a regularization of three-dimensional compact U(1) gauge theory with a physically well-behaved continuum limit.

We numerically investigate the dynamics of a deformable closed ring filled with active particles. The ring is modeled as a flexible boundary made up of passive beads interacting with a harmonic spring force. The interior of the ring is filled with active Brownian particles (ABPs), and their activity is controlled through the rotational diffusion coefficient. We explore how, by systematically varying the activity of ABPs, packing fraction, and size of the ring, we can control the shape deformation and dynamics of the ring. At low packing fractions, low rotational diffusion coefficients, and smaller ring sizes, the ring exhibits highly irregular and strongly deformed shapes due to the uneven spatial arrangement of active particles along the boundary. Increasing the packing fraction, rotational diffusion coefficient, or ring size promotes a more even distribution of active particles within the ring, thereby suppressing shape deformations and fluctuations, driving the ring toward a more circular shape. We further analyze the mean-squared displacement (MSD) of the ring's center of mass and observe a crossover from ballistic to diffusive dynamics, which can be tuned by varying the system parameters. Our results demonstrate that, despite its internal complexity and deformability, the ring exhibits emergent behavior analogous to that of a single effective active particle. This study provides insight into the collective effects of confined active matter and the resulting macroscopic dynamics of deformable systems.

Thermodynamic computers are stochastic physical devices designed to perform calculations at the thermal energy scale. Their operation is constrained by the equations of stochastic thermodynamics, among which are a set of bounds, known as speed limits, that relate a thermodynamic computer's run time to its computational progress and the heat it dissipates. Using the Wasserstein speed limit we assess the thermodynamic efficiency of a simulation model of a thermodynamic computer trained to perform a standard machine-learning classification task. On this task the thermodynamic computer is as capable as a simple multilayer perceptron. We show that different inference protocols allow the computer to operate within 40% of the thermodynamic limit of efficiency without loss of accuracy, or to perform inference increasingly rapidly at fixed accuracy and thermodynamic efficiency. These results indicate that a thermodynamic computer designed for a particular task retains considerable freedom in its thermodynamic operation.

How do organisms navigate when the signals guiding them are noisy? Variance adaptation, the rescaling of sensitivity to noise, is common in sensory systems, but its role in navigation is unexplored. We introduce a minimal active Brownian particle whose run-and-tumble policy follows from an optimality principle. Variance adaptation emerges as part of this policy. Adaptation keeps chemotactic drift finite as noise grows, while a non-adaptive particle's collapses exponentially. Adaptation also carries a cost, degrading performance in quiet environments and requiring a tuned adaptation sensitivity.

Topological quantum memories need decoders that are both reliable and scalable, but these goals compete: globally informed decoders are accurate near threshold yet expensive, while strictly local rules are fast but can miss long-range structure. Motivated by recent recoverability and mixed-state viewpoints, we make this tradeoff operational for the dephased toric code through a decoder-level local recoverability diagnostic. We compare global MWPM corrections to quasi-local corrections inside a target region and define a matching ratio $R_{\mathrm{match}}$, with mismatch $\epsilon_{\mathrm{match}}=1-R_{\mathrm{match}}$. Across geometry families, $\epsilon_{\mathrm{match}}$ shows strong buffer-controlled suppression and is well organized by a two-geometry scaling form. For scaled families, especially $a=b=d/8$, $R_{\mathrm{match}}$ exhibits a clear crossing and finite-size collapse near $p\!\sim\!0.09$, consistent with a growing recoverability scale near the decoding transition. We use this scaling to formulate an adaptive buffer-selection rule and to identify a distance-scaled initialization for a composite quasi-local RG decoder on the full torus. In the tuned family $a_0=b_0=d/8$, the resulting logical-failure curves show an apparent finite-size crossing at $p\simeq0.09$–$0.10$, below the conventional MWPM threshold scale. We focus on dephasing noise with perfect syndrome measurements to cleanly isolate the underlying behavior.

Quantum Monte Carlo simulations confirm the existence of a bound state of a single He-3 atom at a free superfluid He-4 surface in three dimensions, localized within a ~10-A thick low-density He-4 surface layer, with a binding energy of approximately 4 K with respect to vacuum. As the temperature is raised above ~ 1 K the He-3 atom leaves the surface to dissolve into the superfluid. The situation is entirely different in two dimensions, as the He-3 atom is excluded from the superfluid and no surface bound state exists. Results are also presented for the a He-3 atom binding to nanoscale size He-4 clusters adsorbed on weak substrates, a physical system that may allow for the observation of some of the physics predicted for extended surfaces. It is shown that a He-3 bound state localized at the perimeter of sufficiently small (a few tens of atoms) clusters exists not just on Cs, as previously reported, but on all alkali substrates.

Specialization and task allocation enhance efficiency and innovation across diverse systems, from biological organisms to socioeconomic institutions. The evolution of task distribution and its influence on organizational productivity encapsulate the dynamics between task dependencies and adaptive strategies. We explore the organizational division of labor, inspired by the NK model of rugged landscapes, which is widely applied in evolutionary biology, and incorporate interdependencies among the attributes of technical experts within an organization. Our model considers two types of employees characterized by their task allocation strategies: specialists, who are permanently assigned to a single task, and generalists, who stochastically select a task at each time step. We investigate how the ruggedness of the productivity landscape, shaped by task interdependency, affects the organization's capacity to optimize labor division and meet market demands. Using group selection algorithms, we reveal the emergence of nonlinear adaptive dynamics, providing insights into how companies can adapt their strategies to meet market demands and foster innovation.

Identifying the smallest set of elements whose removal dismantle a complex network, known as the network dismantling problem, is a fundamental task with many practical applications. Whereas network dismantling has been extensively studied over the past decade, most work has focused on developing efficient algorithms for large but finite networks. By contrast, the physics of the network dismantling process, namely how the network structural connectivity is affected by the removal of nodes or edges, remains largely unexplored in the thermodynamic limit. Here, we shed light on this understudied aspect of network dismantling by introducing an adaptive biased percolation process able to optimally dismantle a network. Through a systematic analysis of synthetic network models, we find that the proposed percolation process displays a universal phase transition, characterized by the abrupt and simultaneous disappearance of both the giant connected component and the largest 2-core, across networks with markedly different degree distributions. Simulations on real networks further support this universality, indicating that the physics of network dismantling is insensitive to a broad range of topological properties. Together, these results suggest that a topology-agnostic theory could be developed to explain the critical behavior of network dismantling.

Scale-free correlations are believed to be generic in out of equilibrium systems but their explicit derivations are rare and often involve approximations. Here we analyze a system of infinitely persistent active Brownian particles in the low density and small-swim-velocity limit. We show that both the density and swim velocity correlations decay algebraically as r^{-(d+1)} (with logarithmic corrections in d=2). In reciprocal space these correlations manifest themselves as cusps at k=0. The analytical predictions are confirmed by numerical simulations. The results were obtained through interaction with Claude (Opus 4.8 and 5, and Fable 5) and verified by the author.