Papers

The study of spins and particles on graphs has broad applications, from the dynamics of interacting systems on networks to combinatorial problems. Here, we study the large-$n$ limit of the $O(n)$ model on graphs, which is considerably more challenging than on regular lattices, as the loss of translational invariance gives rise to an infinite set of saddle point constraints in the thermodynamic limit. We show that the free energy at low and high temperature $T$ is determined by the spectrum of two fundamental graph-theoretic objects: the Laplacian matrix at low $T$ and the Adjacency matrix at high $T$. Their interplay is studied across several classes of graphs. For regular lattices the two coincide. We obtain an exact solution on trees, where the Lagrange multipliers interestingly depend solely on the number of nearest neighbors. We further contrast these classical results with those for a quantum spin model on an exemplary tree. For decorated lattices, the singular part of the free energy is governed by the Laplacian spectrum, whereas this is true for the full free energy only in the zero temperature limit. Finally, we discuss a bipartite fully connected graph to highlight the importance of a finite coordination number in these results.

Field-free deterministic switching of perpendicular ferromagnets is a central challenge for spintronics applications, typically requiring explicit symmetry breaking. Here we show that deterministic switching can instead be achieved through higher angular harmonics of spin-orbit torques, even in systems that preserve in-plane mirror symmetries. Using a vector spherical harmonics expansion, we demonstrate that these higher-harmonic torque components naturally give rise to additional out-of-equator fixed points, enabling reliable magnetization reversal when their magnitude is comparable to conventional lowest-order torques. We illustrate this mechanism with first-principles calculations on the noncentrosymmetric Weyl ferromagnet PrAlGe, where the combination of Weyl-node band topology and strong spin-orbit coupling produces sizable higher-harmonic torque components. Because the Fermi surface is small, the conventional lowest-order torques are relatively weak, allowing the higher-order harmonics to compete on equal footing and strongly reshape the magnetization dynamics. The resulting spin dynamics confirm deterministic switching without additional symmetry breaking. Our results establish higher-harmonic spin-orbit torque as a key ingredient for understanding and controlling magnetization dynamics in topological and spintronic materials.

The charge carrier localization length {\alpha} is a crucial, yet often ignored parameter of conjugated polymers that exponentially influences electronic conductivity. Here, we argue it is a unique proxy of the energy landscape as determined by sample morphology and experienced by mobile charges. To determine {\alpha}, we use that in disordered organic semiconductors, slow thermalization of charge carriers after excitation, e.g. by hopping in a finite electric field, can lead to an effective electronic temperature (T_eff) exceeding the lattice temperature, thereby enhancing conductivity. We experimentally probe this effect by combining temperature- and field-dependent conductivity measurements for a range of representative conjugated polymers, using different dopants, doping protocols and doping concentrations. We find that in the high-field regime (F>1E6V/m), T_eff exhibits distinct trends vs. structural order and doping level, which can be used to extract (effective) localization lengths ranging from ~1nm in fully amorphous systems to over ~10nm in highly ordered polymers. Tight-binding and kinetic Monte Carlo simulations are used to connect measured values to morphological properties and to rule out alternative explanations. Our results demonstrate that finite-field conductivity measurements provide a powerful probe of a characteristic length scale of charge transport that is complementary to conventional structural characterization.

One of the characteristics of disordered semiconductors is the slow thermalization of charge carriers after excitation due to photoabsorption or high electric fields. An elegant way to capture the effects of the latter on the conductivity is through a field-dependent effective electronic temperature T_eff that can significantly exceed that of the lattice. Despite its elegance, its actual use has been limited, which, at least in part, can be attributed to the concept originating from computer simulations; experimental confirmations have largely been indirect (through scaling of conductivity) and did not establish that T_eff equals the real temperature of the electron distribution. Moreover, it has hardly been tested for important classes of disordered materials, including quantum dot solids. Here, we investigate whether the effective temperature concept is applicable to quantum dot solids, using zinc oxide as relevant model system. To verify that field-driven conductivity increases indeed reflect an actual increase of the electronic temperature, we combine direct and indirect measurements of T_eff: we convert conductivity changes at high fields to an effective temperature that we show to be consistent with a direct measurement of the electronic temperature using the Seebeck effect. These results not only confirm the relevance of the effective temperature concept to quantum dot solids but also confirm its general physical reality and open the way to systematic investigations into charge carrier (de)localization in disordered media.

Strong optical drives have been shown to induce transient superconducting-like response in materials above their equilibrium $T_c$. Many of these materials already exhibit short-range superconducting correlations in equilibrium. This motivates the question: can external driving enhance coherence in systems with superconducting correlations but no long-range order? We explore this scenario in the two-dimensional XY model with a periodically modulated stiffness using overdamped Langevin dynamics. We find that, even though the modulation leaves the average coupling unchanged, the drive can markedly increase long-range, time-averaged correlations in systems well above the equilibrium Berezinskii-Kosterlitz-Thouless temperature. The outcome depends on the ratio of the drive frequency to the intrinsic relaxation rate: faster drives primarily heat the system, suppressing correlations and conductivity. For slower drives, the optical conductivity is modified so that the real part exhibits a prolonged effective Drude scattering time, while the imaginary part has a strengthened low-frequency $1/\omega$ behavior. We map out these regimes across temperature, frequency, and amplitude, and rationalize them via simple analytics and vortex-thermalization arguments. Overall, we identify a generic nonequilibrium route to enhance coherence in XY-like systems, with potential relevance to experiments reporting light-induced superconductivity.

We approach the search for optimal element ordering in bimetallic alloy nanoparticles (NPs) as a reinforcement learning (RL) problem and have built an RL agent that learns to perform such global optimization using the geometric graph representation of the NPs. To demonstrate the effectiveness, we train an RL agent to perform composition-conserving atomic swap actions on the icosahedral nanoparticle structure. Trained once on randomized $Ag_{X}Au_{309-X}$ compositions and orderings, the agent discovers previously established ground state structure. We show that this optimization is robust to differently ordered initialisations of the same NP compositions. We also demonstrate that a trained policy can extrapolate effectively to NPs of unseen size. However, the efficacy is limited when multiple alloying elements are involved. Our results demonstrate that RL with pre-trained equivariant graph encodings can navigate combinatorial ordering spaces at the nanoparticle scale, and offer a transferable optimization strategy with the potential to generalize across composition and reduce repeated individual search cost.

Quantum computation departs from the classical paradigm of deterministic, bit-based processing by exploiting inherently quantum phenomena such as superposition and entanglement. We propose a framework for qubit realization based on skyrmionic states stabilized by the Dzyaloshinskii-Moriya interaction (DMI) in two-dimensional spin lattices. The model incorporates competing exchange interactions, perpendicular magnetic anisotropy, and Zeeman coupling, solved via exact diagonalization under periodic (PBC) and open boundary conditions (OBC). A quantum skyrmionic phase emerges for PBC within a parameter space defined by DMI, exchange, field, and anisotropy, while OBC favor classical-like, topologically protected skyrmions. Quantum logic gates (Pauli X, Y, Z, Hadamard) are implemented on both skyrmion types. Energy density and entanglement entropy analyses reveal that quantum skyrmions suffer from DMI-driven decoherence and reduced gate fidelity, whereas classical-like skyrmions maintain stability. Exact simulations of qubit dynamics, including drive effects and Lindblad decoherence, demonstrate tunable anharmonic energy levels and coherent Bloch-sphere manipulation, making these skyrmionic states promising candidates for qubit implementation. Overall, the Dzyaloshinskii-Moriya interaction plays a dual role-stabilizing skyrmionic qubits while simultaneously inducing decoherence during gate operations.

We compute the full probability distribution of the moment of inertia $I \propto \sum_{i=1}^N \vec{r}_i^2$ of a gas of $N$ noninteracting bosons trapped in a harmonic potential $V(r) = (1/2) m \omega^2 r^2$, in all dimensions and at all temperatures. The appropriate thermodynamic limit in a trapped Bose gas consists in taking $N\to\infty$ and $\omega\to 0$ with their product $\rho = N\omega^d$ fixed, where $\rho$ plays a role analogous to density in a translationally invariant system. In this thermodynamic limit and in dimensions $d>1$, the harmonically trapped Bose gas undergoes a Bose–Einstein condensation (BEC) transition as $\rho$ crosses a critical value $\rho_c(\beta)$, where $\beta$ denotes the inverse temperature. We show that the nature of the condensation is different for $1<d\leq 2$ and $d>2$. Near the condensation transition, for simplicity, we provide the analysis only for $d>2$. We show that the probability distribution $P_\beta(I,N)$ of $I$ admits a large deviation form $P_\beta(I,N) \sim e^{-V\Phi(I/V)}$, where $V = \omega^{-d} \gg 1$. We compute explicitly the rate function $\Phi(z)$ and show that it exhibits a singularity at a critical value $z=z_c$, where its second derivative undergoes a discontinuous jump. In addition, on the condensed side, $\Phi(z)$ becomes independent of $\rho$ for $z<z_c$. We show that the existence of $z_c$ and the associated freezing below $z_c$ is directly related to a BEC transition and disappears when the system does not have one, as in $d\leq 1$. An interesting consequence of our results is that even if the actual system is in the fluid phase, i.e., when $\rho < \rho_c(\beta)$, by measuring the distribution of $I$ and analysing the singularity in the associated rate function, one can get a signal of the BEC transition in $d>1$. This provides a real-space diagnostic for the BEC transition in the noninteracting Bose gas.

In this work, we investigate many-body phase transitions in a one-dimensional anisotropic XY model subject to a complex-valued transverse field. Within the biorthogonal framework, we calculate the ground-state correlation functions and entanglement entropy, confirming that their scaling behavior remains identical to that in the Hermitian XY model. The preservation of Hermitian phase transition features in the non-Hermitian setting is rooted in the persistence and emergence of symmetries and their breaking. Specifically, the ferromagnetic (FM) phase arises from the breaking of a $Z_2$ symmetry, while the Luttinger liquid (LL) phase is enabled by the emergence of a $U(1)$ symmetry together with the degeneracy of the real part of the energy spectrum. The nontrivial topology of the LL phase are characterized by the winding number around the exceptional point (EP). Given that non-Hermitian systems are inherently open, this research opens a new avenue for exploring conventional quantum phase transitions that are typically vulnerable to decoherence and environmental disruption in open quantum systems.

Structure optimization, which yields the relaxed structure (minimum-energy state), is essential for reliable materials property calculations, yet traditional ab initio approaches such as density-functional theory (DFT) are computationally intensive. Machine learning (ML) has emerged to alleviate this bottleneck but suffers from two major limitations: (i) existing models operate mainly on atoms, leaving lattice vectors implicit despite their critical role in structural optimization; and (ii) they often rely on multi-stage, non-end-to-end workflows that are prone to error accumulation. Here, we present E3Relax, an end-to-end equivariant graph neural network that maps an unrelaxed crystal directly to its relaxed structure. E3Relax promotes both atoms and lattice vectors to graph nodes endowed with dual scalar-vector features, enabling unified and symmetry-preserving modeling of atomic displacements and lattice deformations. A layer-wise supervision strategy forces every network depth to make a physically meaningful refinement, mimicking the incremental convergence of DFT while preserving a fully end-to-end pipeline. We evaluate E3Relax on four benchmark datasets and demonstrate that it achieves remarkable accuracy and efficiency. Through DFT validations, we show that the structures predicted by E3Relax are energetically favorable, making them suitable as high-quality initial configurations to accelerate DFT calculations.

Fractional Chern insulators (FCIs) in ideal flat bands with Chern number $C$ are commonly understood as color-entangled states constructed from $C$ copies of the lowest Landau level. In realistic moiré systems, however, the band geometry is generally non-ideal, and the mechanism that stabilizes such FCIs remains unclear. Using twisted monolayer-bilayer graphene as a platform, we find two FCIs separated by a topological transition that occurs in a regime signaled by a local geometric instability of the Bloch states. Below the transition, the target $C=2$ conduction band is geometrically stable, and the resulting fractional phase is naturally described by the Halperin-$(112)$ state. Above the transition, the system becomes geometrically unstable and enters a Laughlin-$1/3$ phase within the same target $C=2$ manifold, which persists even as standard quantum-geometry indicators degrade further. We attribute this Laughlin-$1/3$ phase to a hidden near-ideal $C=1$ component of the non-ideal $C=2$ Bloch states that becomes relevant under interactions, while its strongly non-ideal partner becomes irrelevant. We support this picture by applying a weak perpendicular magnetic field that acts as a “color separator,” directly visualizing the ideal subcomponent at the single-particle level. Together, these results clarify how non-ideal flat bands can stabilize FCIs, greatly expanding their parameter range and sharpening the role of quantum geometry in strongly correlated topological phases.

The extensive use of pesticides and synthetic dyes poses critical threats to food safety, human health, and environmental sustainability, necessitating rapid and reliable detection methods. Raman spectroscopy offers molecularly specific fingerprints but suffers from spectral noise, fluorescence background, and band overlap, limiting its real-world applicability. Here, we propose a deep learning framework based on ResNet-18 feature extraction, combined with advanced classifiers, including XGBoost, SVM, and their hybrid integration, to detect pesticides and dyes from Raman spectroscopy, called MLRaman. The MLRaman with the CNN-XGBoost model achieved a predictive accuracy of 97.4% and a perfect AUC of 1.0, while it with the CNN-SVM model provided competitive results with robust class-wise discrimination. Dimensionality reduction analyses (PCA, t-SNE, UMAP) confirmed the separability of Raman embeddings across 10 analytes, including 7 pesticides and 3 dyes. Finally, we developed a user-friendly Streamlit application for real-time prediction, which successfully identified unseen Raman spectra from our independent experiments and also literature sources, underscoring strong generalization capacity. This study establishes a scalable, practical MLRaman model for multi-residue contaminant monitoring, with significant potential for deployment in food safety and environmental surveillance.

A mechanism for electrically tunable PT-symmetric magnonic lasing and anti-lasing is proposed along with a device consisting of a current-biased region in a magnetically ordered planar waveguide. Within the bias area, several heavy-metal wires carrying dc charge current are periodically attached to the waveguide and exert so spatially periodic spin-orbit torques, producing current-controllable modulated magnon gain and loss. It is demonstrated that this decorated waveguide can emit a strong, single frequency magnon mode at the Bragg point (lasing) and also absorb at the same frequency phase-matched incoming coherent magnons (anti-lasing). The underlying physics is captured by an analytical model and validated with full material and device-specific numerical simulations. The magnonic laser absorber response is tunable via the current density in the wires, the extent of the biased region, and the intrinsic damping, enabling the control of lasing frequency and emission power. The structure is shown to amplify thermal magnons, offering a route to low-noise on-chip microwave sources. The concept is compatible with planar waveguides, ring geometries, and antiferromagnets. The results establish an experimentally realistic platform where a single element functions simultaneously as both magnon laser and absorber, opening opportunities for reconfigurable non-Hermitian magnonics and integrated magnon signal processing.

The Iridium-based oxides are the subject of great recent interest due to the non-conventional physics that may emerge from the strong spin-orbit coupling present in 5d ions. Here, we explore the coupling between Ir and Co in the La2-xBaxCoIrO6 perovskites (x = 0, 0.5, 0.75 and 1.0), where the structural, electronic, and magnetic properties of the series are investigated by means of x-ray powder diffraction and magnetometry. The system's crystal structure evolves from the monoclinic P2_1/n to the triclinic I-1 space group as the Ba concentration increases. Measurements of magnetization revealed ferrimagnetic behavior in x = 0, 0.5 and 0.75 compounds, possibly resulting from antiferromagnetic coupling between Co2+/3+ and Ir4+. In contrast, for x = 1.0 a clear collinear antiferromagnetic character is observed for the Co2+ ions, resulting from the quenching of the Ir5+ magnetic moment. The evolution of the magnetic properties of the series is discussed in terms of the structural and electronic changes, as well as the spin-orbit coupling in Ir.

This work treats the dynamics of pairs of microelectromechanical ultrasound transducers (MUTs) that are immersed in water and acoustically coupled through the fluid medium. A series of these transducer pairs with varying diameters (and thus resonance frequency) and pitch separation (and thus coupling strength) are fabricated and measured. The work presented here models and quantifies the open-loop coupling between the MEMS transducer pairs and its dependence on pitch. Furthermore, a gain feedback loop is systematically applied to one of the device pair and the dynamics of the acoustically-coupled gain-loss system is investigated, and the formation of an exceptional-point or of an Hopf bifurcation is equally used to quantify the coupling coefficient. This work provides an experimental study of acoustic coupling in MUT transducers, as well as an exploration of the formation of exceptional points in acoustically-coupled MEMS transducers.

Understanding charge transport in networks of two-dimensional crystals is essential for developing reliable applications such as chemiresistors or electromagnetic shields. For this purpose, intra- and inter-flake contributions to the network resistance must be disentangled. MXenes, such as Ti3C2Tx, are prime examples of 2D crystals often employed as thin networks of interconnected flakes deposited on substrates to realize functional devices. While a significant number of studies focused on transport in individual MXene flakes, inter-flake transport remains scarcely explored. Here, we demonstrate that charge transport in multi-flake conductive paths of Ti3C2Tx is dominated by interflake junctions and provide quantitative estimates of junction resistances. Scanning probe measurements reveal that in a MXene multi-flake conductive path, individual flakes behave as isopotential domains, since the voltage drop is localized precisely at the inter-flake junctions. We further investigate the chemiresistive response to humidity at the single flake, multi-flake and flake network scale, evidencing the leading impact of junctions on sensing kinetics. These findings underline the crucial role of junctions in charge transport and sensing capabilities of MXenes.

CeRu$_2$Si$_2$ is a well-known heavy fermion paramagnet, and substituting Ge for Si induces antiferromagnetism. This antiferromagnetism is Ising-like and has a tricritical point in the magnetic field ($H$) -temperature ($T$) phase diagram. Since the temperature of the tricritical point is expected to decrease with increasing pressure ($P$), we investigated the pressure dependence of the magnetic phase transitions. We determined the $H$-$P$ phase diagram and revealed that a first-order phase-transition line changes to a quantum critical line, which implies the existence of the quantum tricritical point. A ferromagnetic quantum fluctuation arises in the vicinity of the possible quantum tricritical point.

Understanding O2 bubble nucleation and growth during the oxygen evolution reaction (OER) is crucial to comprehend their influences on catalytically active sites in the process. To achieve this goal, mapping the spatial variation of nanoscale dynamic individual steps at the electrocatalytic interfaces is vital, as it further enables a detailed understanding of the mechanism of the process. Here, we combined tapping mode AFM imaging with a Pt ultramicroelectrode to investigate oxygen bubble nucleation, growth, and detachment. Our AFM feedback error signal and topography data reveal that bubbles of O2 gas nucleate at the step edge sites and interact with the catalytically active sites. This interaction between primary catalytic sites and bubble nucleation sites is the primary reason for a decrease in the current density at a given high overpotential of the OER. Our findings advance the understanding of the complexity of phenomena involved in gas evolution on catalytic surfaces.

We apply preference learning to the task of language model-guided design of novel structural alloys. In contrast to prior work that focuses on generating stable inorganic crystals, our approach targets the synthesizeability of a specific structural class: BCC/B2 superalloys, an underexplored family of materials with potential applications in extreme environments. Using three open-weight models (LLaMA-3.1, Gemma-2, and OLMo-2), we demonstrate that language models can be optimized for multiple design objectives using a single, unified reward signal through Direct Preference Optimization (DPO). Unlike prior approaches that rely on heuristic or human-in-the-loop feedback (costly), our reward signal is derived from thermodynamic phase calculations, offering a scientifically grounded criterion for model tuning. To our knowledge, this is the first demonstration of preference-tuning a language model using physics-grounded feedback for structural alloy design. The resulting framework is general and extensible, providing a path forward for intelligent design-space exploration across a range of physical science domains.

We demonstrate that the ground state of a spin-1 $XXZ$ chain with uniaxial anisotropies, single-ion anisotropy $D$ and Ising-like anisotropy $J$, within the Haldane phase can serve as a resource state for measurement-based quantum computation implementing single-qubit gates. The gate fidelity of both elementary rotation gates and general single-qubit unitary gates composed of rotations about the $x$, $y$, and $z$ axes is evaluated, and is found to exceed 0.99 when $D$ or $J$ is appropriately tuned. Furthermore, we derive an analytic expression for the rotation-gate fidelity under the assumption that the state lies within the $\mathbb Z_2\times \mathbb Z_2$-protected Haldane phase, showing that it is determined by the postmeasurement spin-spin correlation function and the failure probability. The observed enhancement of gate fidelity in the spin-1 $XXZ$ chain originates from the strengthening of antiferromagnetic (AFM) correlations near the AFM phase, which effectively suppresses failure states.

Building on the recent success of a quantum-classical method for computing transport properties in the Holstein model with a single phonon mode [P. Mitrić et al., Phys. Rev. B ${\bf 111}$, L161105 (2025)], we now assess its reliability in more realistic scenarios involving multiple phonon modes in the Holstein model, as well as single- and multi-mode Peierls models. For parameters relevant to the prototypical organic semiconductor rubrene, we compute the frequency-dependent charge mobility and find excellent agreement with results from the state-of-the-art hierarchical equations of motion method. These results show that the method, previously validated only for the single-mode Holstein model, preserves quantitative accuracy in substantially more complex and material-relevant regimes. Our microscopic approach complements the phenomenological transient-localization theory and is readily applicable to realistic electron-phonon Hamiltonians.

Future lithium-based batteries are expected to use solid electrolytes to achieve higher energy density and fast charge capabilities. The majority of solid electrolytes are thermodynamically unstable against layered oxide cathodes. Here, the stability of LiCoO2 (LCO) cathode with Li10GeP2S12 (LGPS) solid electrolyte is investigated using ab initio molecular dynamics (AIMD) and machine learning molecular dynamics (MLMD). The propensity of ionic interdiffusion, formation of a passivation layer, and corresponding decay in cell performance is addressed using a continuum model. The large-scale MLMD simulations confirm that the LCO|LGPS interface permits interdiffusion of Co and other ionic species, leading to the formation and growth of a resistive interphase and dramatic capacity fade even in the first cycle. We then examine the literature evidence that incorporating a thin layer of LiNb0.5Ta0.5O3 (LNTO) between LCO and LGPS prevents the interdiffusion of ions. Atomistic simulations suggest that the substitution of Li in LNTO with Co is not thermodynamically favorable, which helps to minimize the ionic interdiffusion process. The stable Nb/Ta5+ states form a rigid metal-oxide framework, which consequently also prevents the substitution of Nb/Ta. However, continuum level analysis suggests that due to the higher mechanical stiffness of LNTO, interfacial delamination between the LCO and LNTO is possible, which can minimize the effectiveness of the protective layer. This paper suggests the need for the development of novel interlayers that balance low interdiffusion with low stiffness.

We investigate the periodic Anderson model composed of an itinerant $c$-band and a strongly localized $f$-band, featuring on-site electron-electron interactions in the $f$-orbitals. The two bands interact via a hybridization term with spin-orbit coupling, which enables spin-flip processes. In the non-interacting limit, these profoundly alter the electronic structure, leading to the emergence of flat bands, van Hove singularities, and, most notably, Dirac cones within a single Kondo-Dirac semimetal order. The strongly interacting regime is explored via the determinant quantum Monte Carlo method, in the absence of the sign problem, where we unveil a complete ground-state phase diagram revealing two distinct phases, the Kondo-Dirac semimetal phase and a novel antiferromagnetic semimetal phase. Their characterization by the spectral functions establishes an orbital-selective Mott transition in the antiferromagnetic semimetal phase, marked by the opening of a gap exclusively in the $f$-orbital while Dirac cones persist in the $c$-orbital. Conversely, in the Kondo-Dirac semimetal phase, both $c$- and $f$-orbitals sustain robust Dirac cones. We establish that spin-orbit coupling in the hybridization term gives rise to Dirac cones, which, combined with additional symmetry-breaking conditions, can generate novel topological states.

Thin elastic sheets bend easily, leading to mechanical instabilities such as wrinkling. Here, we investigate wrinkles at edges of bi-strips, which consist of two thin sheets, one that swells and one that does not, joined side-by-side. It is well known that when bending rigidity is uniform across an isolated bi-strip, swelling results in axisymmetric shapes like a wine bottle: two cylinders of different radii are joined by a smooth transition zone. However, when the bending rigidity of the swollen sheet differs from that of the non-swollen sheet, purely axisymmetric shapes are no longer energetically favorable, and wrinkles arise. When the bending rigidity of the non-swollen sheet is essentially infinite, the wrinkles coarsen with distance from the transition zone such that dimensionless wavelengths and widths are related by $\tilde{\lambda} \propto \tilde{w}^{2/3}$. If the bending rigidity of the non-swollen sheet is non-infinite (but~still significantly larger than that of the swollen sheet), then the non-swollen sheet assumes a non-infinite radius of curvature, $R_0$. We find that the wrinkles in this system extend a critical distance, $w_C$, beyond the junction of the two strips and that $w_C \propto R_0$. Local undulations of wrinkles are favorable in this system because they decrease the overall bending energy by allowing the non-swollen sheet to have a larger radius of curvature than would otherwise be dictated by its reference geometry. Our results are relevant to a wide range of sheets that experience non-uniform growth, whether in natural systems such as plants or in synthetic systems such as designed, responsive materials.

Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations. It is known that applying PCA to a rank-one signal corrupted by a dense, homogeneous noise, in the large matrix size limit, the celebrated BBP transition occurs, where the emergence of an outlying eigenvalue and the alignment of the corresponding eigenvector occur at the same critical signal strength. Here we study the case of sparse noise corruption. The noise matrix is modelled as the adjacency matrix of a weighted undirected graph with finite average connectivity. Using the replica method, we analytically compute the typical top eigenvalue, the top eigenvector component density, and the squared overlap with the signal, through recursive distributional equations solved by population dynamics. We identify two signal-strength transitions as functions of graph connectivity: $\theta_{\rm crit}$, marking signal recovery by the top eigenvector and generalising the BBP transition, and $\theta_{\rm b}$, where the signal-related eigenvalue detaches from the bulk. For noise with nonzero mean, these transitions need not coincide because of a structural sparse-graph outlier, leading to a discontinuous transition in the squared overlap with the top eigenvector. The same top-eigenpair formalism also predicts the overlap of the signal with the eigenvector associated with the second largest eigenvalue when the signal eigenvalue is an outlier but remains below the structural outlier, where the transition is continuous. We specialise the equations to Poissonian and Random Regular degree distributions, recover dense-noise results in the large-connectivity limit, and validate the theory by numerical diagonalisation of large matrices.

Two dimensional Potts model is a classical example where the symmetry of the order parameter controls the order of a phase transition: on a square lattice with nearest-neighbours interaction, when the number of states $q$ is less than or equal to 4, the second-order phase transition is observed, while for $q>4$ the first-order phase transition occurs. Recent research shows that even when the number of states is fixed, increasing the interaction range allows one to reach the point where the order of the phase transition changes. We focus on a $q=3$ 2D Potts model and, from the analysis of the partition function zeros, locate the number of interacting neighbours that change the order of the phase transition.

We derive an analog of the Lellouch-Lüscher (LL) relation for few-body bosonic systems, linking few-body scattering loss rates to the energies and widths of the corresponding harmonically trapped few-body states. Three-body numerical simulations show that the LL relation applies across a broad range of interaction strengths and energies and allows the determination of scattering rates within a single partial wave. Our work establishes a robust theoretical framework for understanding the role of the finite volume effect in few-body observables in optical lattice and tweezer experiments, enabling precise determination of multi-body scattering rates.

We consider the $S=1/2$ Heisenberg antiferromagnet on the Tasaki square lattice (flat-band spin system) and study its low-temperature thermodynamics around the saturation magnetic field. To this end, we construct a mapping of the ground states in the subspaces with total $S^z=N/2,\ldots,N/3$ ($N$ is the number of lattice sites) on the hard squares on an auxiliary square lattice and use classical Monte Carlo simulations to examine the latter classical system. The most prominent feature of the $S=1/2$ Heisenberg antiferromagnet on the Tasaki square lattice is an order-disorder phase transition which occurs at a low temperature just below the saturation magnetic field and belongs to the 2D Ising universality class.

We present a non-perturbative Hamiltonian mapping method for quantum systems strongly coupled to a quantized field mode (cavity), yielding compact closed-form representations of hybrid light-matter systems. The mapping method builds on an entangling transformation of photonic and atomic degrees of freedom. By truncating the resulting cavity-dressed Hamiltonian (CDH) to successively larger excitation sectors, we construct a series of compact models that converge to the exact limit, outpacing conventional approaches even in the challenging resonant and ultrastrong light-matter regime. The mapping principle also applies to multimode cavities coupled to matter through noncommuting operators and to leaky cavities. We benchmark the CDH framework on the quantum Rabi model, demonstrating accurate spectral predictions in both weak and strong coupling regimes, together with converging ground-state and thermal observables. We study the Dicke-Heisenberg lattice model and determine its phase diagram under resonant and strong light-matter coupling, achieving significant computational savings over brute-force simulations and identifying cavity-mediated spin correlations both analytically and numerically. The closed-form and compactness of the CDH provide both physical insight and enhanced computational efficiency, facilitating studies of strongly coupled hybrid light-matter systems.

Proton ceramic fuel cells (PCFCs) achieve high efficiency at reduced operating temperatures, but their performance is often limited by slow oxygen reduction reaction (ORR) kinetics at the cathode. The BaCoFeZrY (BCFZY) perovskite family is a promising triple-conducting air-electrode material, yet the role of Y dopants in governing oxygen transport remains unclear. In this study, we examine the effect of Y content on oxygen conductivity in three compositions: BCFZ, BCFZY0.1, and BCFY. Oxygen conductivity was evaluated from the product of oxygen tracer diffusivity and oxygen defect concentration. Ab initio molecular dynamics simulations were used to determine tracer diffusivity and migration energies, while defect concentrations were estimated from reference data. Y doping slightly decreases oxygen conductivity from BCFZ to BCFZY0.1, from 337 to 203 mS/cm at 500 C, with activation energies of 0.155 and 0.172 eV. BCFY shows much lower conductivity (99 mS/cm) and a higher activation energy of 0.261 eV. Computed conductivities are higher and more Arrhenius-like than experimental values, suggesting that microstructural features such as grain boundaries strongly limit oxygen transport in real materials. A series-circuit model combining bulk conductivity and fitted grain-boundary parameters provides semi-quantitative agreement with experiment. These results clarify the role of Y doping in oxygen transport and provide insight for optimizing cathode performance in PCFCs.