Papers

One of the long-standing and only partially solved problems of theoretical condensed matter physics and mathematical physics is to demonstrate that ground states of some of the versions of the Hubbard model can exhibit a ferromagnetic ordering. It has long been speculated that the opportunity crucial for the occurrence of ferromagnetism is the structure of the lattice on which the Hubbard model is formulated \cite{TasakiMB}. As a consequence, while on simple cubic lattices no ferromagnetic ordering seems to be possible, it can naturally arise, even for low densities of magnetic moment carriers, on so-called frustrated lattices. We investigate the problem of ground state ferromagnetic ordering with the use of the formula for ground-state energy of interacting fermions as the first term of `density expansion', proven rigorously by Lieb, Seiringer and Solovej \cite{fermi exact} in continuum and by Giuliani \cite{hub exact} for the simple cubic lattice. Assuming that analogous expansion holds also for certain another lattices we apply this formula to five frustrated lattices – among them to the face-centered cubic one. The hypothesis is confirmed: most of examined models formulated on frustrated lattices do indeed have ferromagnetic ground states already for densities being moderate or even low. Although the approach adopted cannot be treated as a rigorous proof that the ground state is ferromagnetic, the results obtained here strongly indicate that it can be the case. Moreover, as in some cases FM occurs at low densities, one can hope that it would be possible to prove convergence of the density expansion and prove rigorously the occurrence of `wealthy ferromagnetism' in these cases.

We describe a fabrication process for preparing liquid suspensions of micron-scale Au and Au/graphene bilayer platelets using thin-film deposition, optical lithography, ion milling, hydrofluoric acid (HF) substrate etching, and release from the substrate into a liquid suspension. Residual HF is removed through repeated centrifugation, decanting, and dilution cycles. The resulting suspension is characterized by electrospray deposition onto a secondary substrate, followed by electron and atomic force microscopy. The deposited platelets exhibit minimal aggregation, and the overall platelet yield reaches up to 30% of the platelets originally patterned on the wafer. Lateral force microscopy further confirms that the Au/graphene bilayer remains intact throughout fabrication, release, and electrospray deposition. This process provides a practical route for preparing high-quality platelet suspensions for levitated nanoparticle experiments and other applications requiring suspensions of two-dimensional nanostructures.

Recent experiments on molecular droplets have opened a new frontier of self-organization in strongly dipolar quantum matter. Microwave-dressing of polar molecules permits to tune both the strength and the angular structure of long-range interactions, potentially promoting a rich spectrum of quantum phases, from superfluid droplets with varying geometry and insulating or supersolid droplet arrays to strongly correlated crystals of individual molecules. Using path-integral Monte Carlo simulations of large molecular ensembles, we demonstrate that experimentally observed droplet arrays emerge as a metastable non-equilibrium state from the quenching of a gas-droplet phase transition under entirely broken rotational symmetry of the microwave-induced interaction potential. We moreover find that a crystalline phase of molecules, predicted for antidipolar interactions, is absent under conditions of recent experiments. This is traced back to the lack of angular symmetry in currently employed microwave-dressing, which qualitatively reshapes the many-body energy landscape and cannot be captured by effective scalar interaction parameters. Our results provide the first direct comparison of ab initio simulations and experiments and establish interaction anisotropy as a key aspect of molecular quantum gases.

We introduce a real-space, linear-scaling Bethe-Salpeter framework that enables excitonic spectroscopy in large and possibly disordered boron-nitride-derived systems. Thanks to the use of a sublattice-resolved perturbative decoupling that maps localized electron-hole pairs onto a sparse tight-binding model, we implement the Kernel Polynomial Method to compute absorption spectra with O(N) cost. To illustrate the capabilities of our method, we apply it to Anderson-disordered monolayer hexagonal boron nitride with up to $10^{5}$ orbitals. The method reveals a disorder-induced asymmetric broadening of bright excitons, a crossover from quadratic to linear redshift of the main absorption peak, and Anderson localization of the exciton center of mass. This approach extends excitonic calculations beyond the reach of conventional ab initio Green's function methods (GW approximation and Bethe-Salpeter equation), opening optical spectroscopy to large-scale, disordered, moiré, quasicrystalline, and structurally complex quantum materials.

We perform density functional theory (DFT) calculations to investigate five-metal high-entropy borides (HEBs) in the hexagonal AlB$_2$ structure, considering all 126 possible elemental combinations among the nine group 4-6 transition metals (Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W). The entropy forming ability (EFA) descriptor is employed to evaluate their single-phase synthesizability, and the resulting EFA predictions show good agreement with the experimental data for selected HEBs. Mechanical properties are computed using special quasi-random structures. Several mechanically unstable compounds – primarily those containing Cr – are also predicted to be less synthesizable. Machine learning (ML) models are developed to analyze the results. This combined ab initio and ML study provides a systematic roadmap for identifying mechanically superior single-phase HEBs.

We study finite-size properties of Schulz-Shastry-Luttinger liquids to reveal anyonic signatures, realized as low-energy excitations on top of the helical ground state in saturated spin-1/2 zigzag chains. The model features asymmetric and marginal couplings of density and phase gradients and belongs to the Schulz-Shastry class. We investigate periodic and Dirichlet boundary conditions and discuss its diagonalization as well as its stability. Although Dirichlet boundary conditions require a fine-tuning of coupling constants and universal parameters, only their magnitude is restricted for cyclic systems. We derive boundary characteristic quantities like Friedel oscillations and persistent currents. Finally, we discuss the bulk and boundary behavior of the longitudinal spin correlations including subleading corrections.

Physical heterogeneities in the context of sliding friction, such as a human finger exploring an object, have been well studied, yet the behavior of chemical heterogeneities in mesoscale soft sliding remains underexplored, despite the similar prevalence of chemical and physical variations in real systems. Here, we experimentally characterized the friction of a planar soft elastic probe sliding across a single chemical heterogeneity that was formed at the interface of two silanes on silicon wafers. By constructing phase maps across multiple loads and velocities, we quantified the occurrence of several frictional phenomena at and around the chemical edge, including stiction spike formation, edge slope direction, baseline shifts, and baseline drift, and quantified their sliding direction-dependent formation. We found that chemical heterogeneities made by more disparate materials (butyl- and aminopropyl-terminated) exhibited several phenomena that were more often direction-independent compared to chemical heterogeneities formed from more similar materials (butyl- and hexyl-terminated). We attributed this directional asymmetry to elastic body effects. In subsequent human testing (n=36), we observed that humans also exhibited directional-dependent accuracy (66.7% versus 38.9%) on one pair (butyl- and hexyl-terminated) but not the other (77.8% versus 75%), which in the context of our phase maps, suggests that the slope of the friction force when sliding over a chemical edge is important for generating a clear edge of a tactile feature, rather than the differences in simple material properties or other friction phenomena.

We discuss a nonequilibrium Andreev reflection at an interface between quark-gluon plasma (QGP) and two-flavor color superconducting (2SC) quark matter. Based on the Schwinger-Keldysh framework and a relativistic tunneling model, we evaluate the momentum-resolved tunneling current generated by a chemical-potential bias between the QGP and 2SC phases. We find that the Andreev reflection appears as at the fourth order of the tunneling strength, in which an incident quark in QGP is converted into a reflected hole, while a Cooper pair is injected into the 2SC condensate. We show that the Andreev reflection is enhanced when the bias becomes comparable to the gap and is suppressed in the supergap region, which is similar to that in superconducting materials. The present formulation provides a field-theoretical pathway to strongly-correlated transport across dense-matter interfaces relevant to nonequilibrium dynamics in compact stars.

The controlled confinement of high-frequency acoustic phonons in semiconductor nanostructures has emerged as a key ingredient for functional nanophononic and hybrid quantum technologies. In this Review, we summarize recent advances that have established GaAs/AlAs acoustic nanocavities as a versatile and scalable platform for GHz-THz phonon engineering. Compared with alternative nanophononic platforms, GaAs/AlAs offers a particularly favorable combination of mature epitaxial growth, strong photoelastic coupling, and simultaneous optical-acoustic mode colocalization across the GHz-THz regime. We focus on distributed Bragg reflector (DBR)-based architectures, with particular emphasis on micropillar resonators enabling three-dimensional phonon confinement and strong colocalization of acoustic and optical fields. Recent developments in ultrafast optical techniques, including picosecond ultrasonics and Brillouin scattering, have provided unprecedented access to phonon dynamics, coherence, and dissipation at the nanoscale. These advances, combined with strong optophononic coupling, have enabled efficient coherent generation, detection, and manipulation of confined acoustic modes. We discuss key performance metrics, integration strategies, and remaining challenges, notably in acousto-optic transduction efficiency and scalable electrical control. Finally, we outline near-term perspectives for nonlinear phononics, hybrid quantum systems, and integrated phononic circuits, positioning GaAs/AlAs heterostructures as a robust and scalable platform for next-generation nanophononic functionalities.

We develop a field-theoretic framework for work statistics in $O(N)$ models driven through criticality. By analyzing the dynamic renormalization group flow of composite power operators, we find the Kibble-Zurek scaling laws as a natural consequence of the flow, and we derive the scaling of work cumulants relevant to Kibble-Zurek scaling of topological defects from first principles, bypassing heuristic freeze-out argument. This yields the universal scaling $c_n \sim \tau_Q^{-\alpha_n}$ for the $n$-th work cumulant density: isolated quantum systems exhibit a scaling of $\alpha_n = p(d+nz)\nu/(1+pz\nu)$, whereas open quantum and classical systems undergo a dimensional collapse to $\alpha_n = pd\nu/(1+pz\nu)$. Validated by exact Gaussian solutions and numerical simulations, our theory establishes a foundation for general work statistics far from equilibrium, thereby bridging stochastic thermodynamics and the renormalization group theory.

We report low-temperature ultrasound measurements on single crystals of the layered van der Waals superconductor 4Hb-TaS$_2$. Specific heat and ac magnetic susceptibility show a sharp bulk superconducting transition at $T_{\rm c}\approx 2.9$~K. Ultrasound measurements reveal an additional anomaly deep inside the superconducting state near $T^{*}\approx 1$~K. The most direct signature is observed in the relative ultrasonic attenuation change $\Delta\alpha$: instead of being rapidly suppressed at $T_{\rm c}$, $\Delta\alpha$ remains large throughout the intermediate superconducting regime and drops strongly only near $T^{*}$. This loss of acoustic dissipation is accompanied by a pronounced anomaly in the relative sound velocity change $\Delta v/v$, indicating strong coupling to the lattice. The low-temperature anomaly is rapidly suppressed by magnetic field and by Se substitution, suggesting a possible superconducting origin of the anomaly. We speculate that this feature may be related to induced superconductivity in the 1T layers.

Conventional materials derive their properties from microscopic composition and arrangement, whereas mechanical metamaterials are defined by mesoscopic structure rather than constituent material. Bridging these paradigms, using macroscopic geometric alterations to orchestrate microscopic degrees of freedom and program mechanics, remains a central challenge. Here, we demonstrate that cuts in anisotropic, responsive solids provide such a connection. Using liquid crystal elastomer (LCE) sheets with kirigami patterns, we reveal that engineering strain through cuts harnesses molecular anisotropy to control emergent mechanics. Similarly, the interplay between cut patterns and the molecular phase transition of LCEs enables soft robotics functionalities such as supersoft grippers with remote actuation and architectures that reversibly morph under temperature variations, behaviors inaccessible to conventional kirigami or LCE sheets alone. LCE kirigami thus establish a new class of multiscale metamaterials in which geometry governs access to microscopic degrees of freedom, to program macroscopic function.

Herein it is shown spontaneous symmetry breaking in supramolecular aggregates of D4h-symmetric zinc phthalocyanine (ZnPc). Ab initio density functional theory calculations at the M06/DGDZVP level reveal that intermolecular interactions induce a subtle relaxation of the macrocyclic framework, producing a characteristic red shift of the aza-bridge (C-N-C) stretching mode and symmetric stretching of the pyrrole ring. Confocal Raman Optical Activity measurements further reveal a negative Cotton effect at 1505 cm^-1 and 1338 cm^-1, providing evidence of emergent supramolecular chirality. Our findings identify pristine ZnPc as a model system for spontaneous self-assembled chiral symmetry breaking in molecular condensates and suggest new opportunities for chiroptical, spin-selective, and quantum functional materials.

We consider a junction consisting of an extended one-dimensional Kitaev chain which incorporates both time-reversal symmetry (TRS) breaking and long-range interaction, sandwiched between two metallic leads from two sides. In this hybrid device, we study electrical transport under voltage bias for varying strength of the TRS breaking phase. We compare the transport characteristics of long-range type Kitaev chain with that of the short-range Kitaev chain as the strength of the TRS breaking phase varies. We find that the TRS breaking modifies the density of states and localisation/delocalisation property of the eigenstates which in turn affect the transport characteristics. Moreover, we find that the impact of the TRS breaking is not identical for the long-range Kitaev chain and its short-range counterpart. Therefore, noticeable differences in the transport properties can be observed due to the interplay between the TRS breaking and the range of interaction.

Graphene auto-kirigami describes the thermodynamically self-driven tearing, sliding and folding of graphene sheets to form micrometre-scale, folded ribbons. However, this process typically requires specialised multi-axial nanoindentation systems or highly laborious AFM-based scratching methods. We here introduce a novel, scalable, wholly AFM-based method to nucleate high yields of ribbons in comparable timeframes to previous multi-axial indentation methods, by AFM-based indentation and "hard tapping", whereby high setpoint AFM imaging can nucleate, manipulate and dynamically image the auto-kirigami ribbons. This can be performed with any conventional AFM, enabling extensional growth, rotation and reversal of ribbons towards potential applications as NEMS devices.

We study heat rectification through a quantum two-level system asymmetrically coupled to two thermal baths, as described by the Ohmic spin-boson model. We evaluate the steady-state heat current using a tensor-network approach, which enables us to access the strongly correlated regime, and benchmark the results against analytical formulas in several limiting regimes, including the weak-coupling and incoherent-tunneling regimes. We identify a scaling regime where the studied system flows from an ultraviolet regime, at temperatures larger than the Kondo temperature, to an infrared regime, at temperatures lower than the Kondo temperature. By applying perturbation theory near the infrared fixed point, we find that the rectification ratio follows a universal power law. Our numerical results agree well with this analytical prediction. Our results provide a fundamental understanding of how dissipation-induced many-body physics affects heat transport.

Neural-network quantum states (NQS) provide expressive variational representations for strongly correlated quantum many-body systems, but their practical accuracy depends sensitively on architecture-level hyperparameters and optimization schedules. Here we develop NQS-Agent, an implemented open-source software framework for health-aware hyperparameter optimization (HPO) in NQS calculations. Its workflow monitors energy trajectories, detects destructive optimization events, stops unstable calculations, modifies the learning-rate schedule, resumes optimization from safe checkpoints, and ranks candidates with an anomaly-aware score. We demonstrate the approach on a residual convolutional NQS for the square-lattice Heisenberg $J_1$-$J_2$ model, using architectures with parameter counts comparable to aCNN, a convolutional NQS architecture used here as a reference. The results show that NQS-Agent improves over the reported human-tuned aCNN baseline for the aCNN reference architecture and identifies a structurally distinct wide-and-shallow competitive candidate within the parameter-count-matched residual-CNN search space. These results show that the stability and recovery history of an optimization trajectory should be considered when assessing an NQS result. Health-aware HPO therefore provides a reproducible tuning protocol that goes beyond selecting a single lowest-energy calculation.

For a process in which a system is driven irreversibly from equilibrium state $A$ toward equilibrium state $B$, the free energy difference $\Delta F = F_B-F_A$ can be estimated using the work fluctuation theorem $\langle e^{-W/T}\rangle = e^{-\Delta F/T}$, where $W$ and $T$ denote work and temperature. The estimate often suffers from poor convergence with the number of trajectories used to calculate the average. Borrowing ideas from escorted free energy estimation, and from diffusion models of machine learning, we show how to construct infinitely many work-like quantities, $W_\theta$, that satisfy $\langle e^{-W_\theta/T}\rangle = e^{-\Delta F/T}$, for the same underlying dynamics. Our method involves a virtual control field ${\boldsymbol u}_\theta$ that does not modify these dynamics. We show how to choose parameter values $\theta$ to optimize convergence of the free energy estimate, for a fixed set of trajectories. We identify conditions under which our method provides a zero-variance estimator of $\Delta F$. We use numerical simulations of model systems to illustrate the gains in convergence that our method can achieve.

Quantum entanglement is one of the most intriguing features of quantum mechanics. To investigate the entanglement between two excitons in a biexciton, an experimental technique called density matrix spectroscopy (DMS) has recently been developed. DMS combines stimulated emission tomography and pump-probe techniques to obtain a time-resolved density matrix of the polarization state of a photon pair emitted from the biexciton. The reconstructed density matrix is expected to encode information about the biexciton state and its entanglement dynamics, but the precise nature of this connection has remained unclear. In this paper, we derive an analytical relationship between the density matrix obtained by DMS and the biexciton state. In addition, we perform numerical simulations to compare the entanglement dynamics obtained by DMS with the biexciton's entanglement dynamics in a two-dimensional electron-hole system using an extended ionic Hubbard model. We find that DMS can partially capture the entanglement in the biexciton, in particular, the dynamics of the difference $S_{\mathrm{bi}} - S_k$, where $S_{\mathrm{bi}}$ is the entanglement entropy of the biexciton and $S_k$ is the entanglement in terms of the wavevectors of the excitons that constitute the biexciton. These results demonstrate the validity of DMS for obtaining information about the entanglement dynamics of the biexciton.

Mechanical stresses are fundamental regulators in biological tissues, where the vertex model (VM) is pivotal for theoretical and force-inference studies. Yet, no uniform expression for the stress tensor exists for the VM. Here we provide a microscopic derivation of it, linking mesoscopic stresses to the VM forces. The stress field presents a freedom on how tensions are distributed across cells, which allows previous expressions to emerge as particular realizations of the field and suggests a link between mesoscopic stresses and cytoskeletal force-transmission architectures in real cells.

Training in artificial neural networks can be viewed as a trajectory evolving through a high-dimensional loss landscape. However, the large number of trainable parameters makes the direct analysis of these dynamics challenging. In this work, we treat such training trajectories as temporal networks and apply recently proposed strategies for the scalar embedding of temporal networks. We investigate whether such a scalar embedding provides a meaningful low-dimensional representation of neural network training dynamics. Using a multilayer perceptron trained on the MNIST classification task, we show that the embedding preserves the main dynamical features observed in the original parameter space, including the emergence of sensitivity to initial conditions for specific learning rate regimes and an accurate reconstruction of the network's maximum Lyapunov exponent. We then use the embedded scalar trajectory to define a characteristic time, analogous to a Lyapunov time, after which the exponential separation between initially close embedded trajectories saturates. This characteristic time captures the typical decorrelation time between initially close network trajectories in the original high-dimensional system. Finally, we investigate the statistical organization of asymptotic training states through a spacing observable defined in the embedded space. We find that the distributions of rescaled asymptotic spacings collapse onto a common form across initial conditions and are compatible with a skew lognormal distribution. Altogether, our results suggest that scalar low-dimensional embeddings provide a useful framework for studying and visualizing the dynamical properties of neural network optimization trajectories.

Defect engineering in monolayer MoS$_2$ is a promising route to tune field-effect transistors (FETs), but the electronic response of defects in processed devices can be masked by contacts, substrate effects, adsorbates, and chemical passivation. Here, we irradiate MoS$_2$ FETs with low-energy 40~eV Ar$^+$ ions to preferentially create sulfur vacancies (V$_S$) in the channel while minimizing substrate damage. We compare dark and illuminated electrical characterization with surface analysis and first-principles calculations. Dark transfer characteristics show an apparent robustness against irradiation up to moderate fluences, with pronounced degradation only at the highest fluence. Under 532~nm illumination, however, the photocurrent and light-induced photodoping decrease systematically with increasing ion fluence, revealing irradiation-induced changes that are hidden in standard dark measurements. Atomic force microscopy and X-ray photoelectron spectroscopy show substantial carbon-containing residues on processed devices even after extended cleaning. We propose that such residues may provide a reservoir for hydrocarbon-mediated passivation of sulfur vacancies. Density-functional-theory calculations provide a microscopic model consistent with this scenario: unsaturated V$_S$ introduce in-gap states, H-C$_S$ configurations suppress these states, and carbon substitution without hydrogen leaves defect states in the band gap. Our results highlight carbon-containing surface contamination as a key factor in interpreting defect engineering experiments on MoS$_2$ and related TMDC devices.

Community-detection algorithms usually return a single partition, even when independent initializations or small data perturbations yield several plausible outputs. We probe this output distribution through three paired observables: hard-partition variation of information (VI), a residual-gated fixed-point VI, and a cutoff-free Jensen-Shannon distance between belief-propagation (BP) marginal fields. For the symmetric sparse stochastic block model, linearizing BP around the uninformative fixed point gives the Kesten-Stigum onset at $\mathrm{snr}=(c_{\rm in}-c_{\rm out})/(q\sqrt{c})=1$. The hard VI maximum is instead a finite-size, readout-dependent detector curve on the detectable side, typically $\mathrm{snr}^\star \simeq 1.05\text{-}1.10$; moving the polarization cutoff from 0.001 to 0.1 shifts it across 1.047-1.128. The nontrivial-readout activation obeys $\mathrm{snr}_{50}(\tau)-1 = 0.0086 + 0.522\,\tau$ ($R^2=0.996$). Long-budget residual gating separates readout and critical slowing from fixed-point dispersion: at $\mathrm{snr}=1.05$ and 1.10 the hard VI is 1.49 and 1.58 bits but the gated subsets have zero VI, whereas from 1.15 to 1.30 nearly all runs pass the gate and retain VI 1.31 down to 1.24 bits. A high-replication audit through $N=100000$ disfavors a zero-asymptote power law and finds a small plateau $\mathrm{snr}^\star-1 \simeq 0.024$ (graph-bootstrap 90% interval [0.0227, 0.0316]). On real networks, a label-free Bethe-Hessian modularity margin with a Chung-Lu null gate is run on political blogs and six SNAP graphs: the measurement stays label-free, while heterogeneous networks can retain null-significant structure even after strong edge subsampling. The result is a detector-output decomposition near the Kesten-Stigum boundary, reporting hard readout, relaxation dynamics, and fixed-point-field dispersion separately.

Ultrafast demagnetization dynamics are often phenomenologically classified into type-I and type-II responses according to their temporal evolution following femtosecond laser excitation. However, finite experimental temporal resolution and noise can substantially obscure the intrinsic dynamics and complicate this classification. In this work, we investigate the distinguishability of type-I and type-II demagnetization dynamics using Gaussian-convolved phenomenological models and Bayesian information criterion-based statistical model comparison. Synthetic datasets with varying temporal resolution and noise levels are first analyzed to evaluate the conditions under which the two classes can be reliably discriminated. We show that convolution with the instrumental response function significantly reduces the observable differences between the intrinsic responses, thereby producing broad regimes in which model discrimination becomes statistically inconclusive. The applicability of the framework is further demonstrated through analysis of representative experimental ultrafast demagnetization data from NiCo2O4 thin films. These results suggest that the apparent classification of ultrafast demagnetization dynamics can be highly sensitive to experimental resolution, noise level, and analysis methodology.

A subwavelength quantum-photonic circuit element should simultaneously generate nonclassical light, suppress plasmonic loss, and remain dynamically tunable. We show that an orthogonal plasmonic nanorod dimer can satisfy all three requirements. A phase-locked control polarization induces plasmonic refractive-index enhancement, driving the probe response toward a near-zero-extinction regime while simultaneously tuning the local second-harmonic parametric interaction. The resulting nonlinear plasmonic source operates in an absorption-suppressed regime and enables all-optical control of quantum correlations. We demonstrate switchable logarithmic negativity and single-mode nonclassicality, establishing a route toward actively tunable quantum-plasmonic circuit elements operating well below the diffraction limit.

The Bose-Hubbard system has been studied extensively both theoretically and experimentally, in particular in the context of ultracold atomic gases in optical lattices. Even in the two-mode case the many-particle dynamics display complex interference effects resulting in revival and breakdown phenomena as well as tunnelling. The most basic theoretical description is the mean-field approximation, which can be derived from a time-dependent variational principle assuming the many-particle wave function is an SU(2) coherent state. Here we build on this to construct a simple initial-value coherent state propagator, summing over mean-field trajectories and keeping track of their phases, given by the corresponding mean-field actions. This yields an approximation to the full time-dependent many-particle state, and is able to reproduce breakdown and revival dynamics. Applying a time-slicing procedure on top of this, we are able to accurately capture many-particle tunnelling effects. While in this paper we focus our analysis on the Bose-Hubbard dimer, the methods developed can be applied to more general SU(2) Hamiltonians, and can be extended to SU(M) systems.

Clathrin assemblies in cells can persist as flat plaques, abort after partial invagination, or close into clathrin-coated vesicles, but the determinants of these different fates remain unresolved. To investigate the stochastic and complex dynamics of clathrin assemblies, we have developed a kinetic Monte Carlo simulation framework that couples individual clathrin agents to an adaptive continuum membrane. In this hybrid discrete-continuum description, the effective coat bending rigidity and the preferred coat curvature emerge during growth, rather than being prescribed as material parameters. Once connected, curved lattices stiffen from molecular bending modes to coat-level rigidities, because curvature changes require increased stretching or compression, while newly incorporated triskelia hardcode a history-dependent preferred curvature. An analytical theory for non-Euclidean elasticity identifies the relevant internal variables and predicts growth laws that are validated by the simulations. The same microscopic assembly rules yield flat, stalled, and closed coats through two sequential gates in the effective membrane-coat energy landscape. Comparisons with experimentally observed coat geometries and nanodissection-induced curvature changes agree with our theoretical predictions without any fitting parameters. The clathrin coat thus emerges as an adaptive assembly with prestress and memory, whose fate and material parameters reflect the environment in which it has been growing.

The problem of storing secure information on a network is studied. A formal framework for distributed secret storage is introduced, and possible applications in technological and social systems are discussed. The problem is formulated as the optimization of a robustness functional in which two competing requirements are balanced: survivability under network-degrading processes and resistance to adversarial compromise. An exact representation of survivability is derived in terms of minimal information-carrying subgraphs (MICS), which provide a reduced description of the reconstruction events relevant to the stored information. This representation is then used to construct semi-local optimization methods whose dynamics do not require global knowledge of the network structure. Finally, it is shown that, in a limiting case, the robustness functional can be mapped naturally to an effective spin Hamiltonian.

We investigate the nonlinear optical response of a two-dimensional mesoscopic quantum ring subjected to a spiral dislocation, with emphasis on third-harmonic generation (THG). The topological defect is modeled through a torsion-induced deformation of space, which modifies the effective metric without introducing curvature. By combining the minimal-coupling prescription in curved space with a radial ring confinement and a perpendicular magnetic field, we derive the effective radial Schrödinger problem, obtain the bound states, and evaluate the nonlinear susceptibilities within the electric-dipole approximation. We show that the axial symmetry of the topologically deformed ring preserves the dipole selection rule $\Delta m=\pm 1$ and therefore suppresses second-harmonic generation, while THG remains allowed through multistep transition chains. The study is further expanded through three complementary analyses that can be implemented without changing the Hamiltonian: a dephasing-controlled study of spectral resolution, three-dimensional waterfall spectra showing the dependence on $\beta$ and $B$, and a channel-resolved decomposition of the THG amplitude. Together, these results establish the spiral dislocation as a robust geometric knob for tuning nonlinear optical activity in mesoscopic ring-shaped nanostructures.

We consider a population dynamics model in which each diffusing particle that hits a catalytic surface can split into two independent copies (clones). The particles of such a growing-in-size population search in parallel for a hidden partially reactive target to trigger a reaction event (e.g., a viral attack). We investigate the statistics of the fastest first-reaction time (FRT) among all the particles. We establish a nonlinear integral equation for the survival probability and then analyze the associated probability density of the FRT and its moments. Lower and upper bounds on the mean FRT are then deduced in terms of the system parameters (target reactivity, catalytic rate, diffusivity, etc.). Because autocatalytic replication can rapidly increase the number of searchers, it can substantially accelerate the diffusive search. We solve the nonlinear equations numerically in a basic geometric setting and reveal advantages and limitations on the autocatalytic search.