Papers

Recent advances at the intersection of control theory, neuroscience, and machine learning have revealed novel mechanisms by which dynamical systems perform computation. These advances encompass a wide range of conceptual, mathematical, and computational ideas, with applications for model learning and training, memory retrieval, data-driven control, and optimization. This tutorial focuses on neuro-inspired approaches to computation that aim to improve scalability, robustness, and energy efficiency across such tasks, bridging the gap between artificial and biological systems. Particular emphasis is placed on energy-based dynamical models that encode information through gradient flows and energy landscapes. We begin by reviewing classical formulations, such as continuous-time Hopfield networks and Boltzmann machines, and then extend the framework to modern developments. These include dense associative memory models for high-capacity storage, oscillator-based networks for large-scale optimization, and proximal-descent dynamics for composite and constrained reconstruction. The tutorial demonstrates how control-theoretic principles can guide the design of next-generation neurocomputing systems, steering the discussion beyond conventional feedforward and backpropagation-based approaches to artificial intelligence.

Spin-boson systems have attracted increasing attention as accessible experimental platforms and for their potential applications in designing quantum technologies. One characteristic of these systems is the transition from regular to completely chaotic behavior when certain control parameters are varied. However, the characterization of their mixed phase space has not been thoroughly explored. In this work, we investigate the properties of mixed eigenstates in spin-boson systems, comparing one-photon interactions with two-photon interactions. We propose a generalized definition of the phase-space overlap index to identify genuine mixed eigenstates. Our study highlights the fundamental differences that arise when two-photon processes are considered compared to one-photon processes and provides complementary evidence supporting the validity of the principle of uniform semiclassical condensation of quasiprobability functions in spin-boson systems.

Exponential complexity of many-body wave functions limits accurate numerical simulations of real-time dynamics, especially beyond 1D, where rapid entanglement growth poses severe challenges. Neural Quantum States (NQS) have emerged as a powerful approach for real-time dynamics in 2D, but their scalability and accuracy in 3D have remained an open challenge. Here, we establish NQS as a scalable framework for 3D quantum dynamics by introducing a residual-based convolutional architecture tailored to cubic spin lattices. Focusing on the 3D transverse-field Ising model, we demonstrate that NQS reliably capture distinct quench regimes, including collapse-and-revival dynamics and, most challengingly, the dynamics following a sudden quench to the quantum critical point. We perform finite-rate quenches to the critical point on lattices containing up to $1000$ qubits, an unprecedented system size for numerical simulations of real-time dynamics beyond 1D. This enables the first large-scale numerical demonstration of the 3D quantum Kibble–Zurek mechanism. The QKZM in 3D is particularly intriguing because it lies at the upper critical dimension of the Ising universality class, where the standard power laws are modified by logarithmic factors together with prominent sub-leading logarithmic corrections. By deriving these corrections from renormalization-group flow equations up to two-loop order, we obtain a robust data collapse across all simulated system sizes for the correlation function, the excess energy, and the quantum Fisher information, the latter revealing universal multipartite-entanglement dynamics. In all cases, we find compelling agreement with the expected scaling dimensions. Our findings establish NQS as a scalable and reliable tool for exploring nonequilibrium phenomena in 3D quantum matter and for providing numerical benchmarks for 3D quantum simulators.

Understanding the structure of operators that commute with $k$ identical replicas of unitary ensembles, also known as their $k$-commutants, is an important problem in quantum many-body physics with deep implications for the late-time behavior of physical quantities such as correlation functions and entanglement entropies under unitary evolution. In this work, we study the $k$-commutants of free-fermion unitary systems, which are heuristically known to contain $SO(k)$ and $SU(k)$ groups without and with particle number conservation respectively, with formal derivations of projectors onto these commutants appearing only very recently. We establish a complementary perspective by highlighting a larger $O(2k)$ replica symmetry (or $SU(2k)$ respectively) that the $k$-commutant transforms irreducibly under, which leads to a simple geometric understanding of the commutant in terms of coherent states parametrized by a Grassmannian manifold. We derive this structure by mapping the $k$-commutant to the ground state of effective ferromagnetic Heisenberg models, analogous to the ones that appear in the noisy circuit literature, which we solve exactly using standard representation theory methods. Further, we show that the Grassmannian manifold of the $k$-commutant is exactly the manifold of fermionic Gaussian states on $2k$ sites, which reveals a duality between real space and replica space in free-fermion systems. This geometric understanding also provides a compact projection formula onto the $k$-commutant, based on the resolution of identity for coherent states, which can prove advantageous in analytical calculations of averaged non-linear functionals of Gaussian states, as we demonstrate using some examples for the entanglement entropies. In all, this work provides a geometric perspective on the $k$-commutant of free-fermions that naturally connects to problems in quantum many-body physics.

Motivated by recent experiments on ultracold fermionic spin-1/2 $^6$Li atoms in a Lieb lattice at various Hubbard repulsion $U$ and filling fractions $n$ (Lebrat et al., arXiv:2404.17555), we conduct a density matrix renormalization group (DMRG) analysis of the Hubbard model on a two-leg Lieb ladder. At half-filling, we find a ferrimagnetic Mott insulating ground state, consistent with Lieb's theorem. Away from half-filling, a state with finite total spin $\vec{S}^2 \neq 0$ and vanishing charge gap persists down to filling $n_c \approx 2/3$. For lower, incommensurate fillings, the system is described by a Luttinger liquid with one charge and one spin mode. Intriguingly, in a narrow window near $n_c = 2/3$, close to the onset of ferromagnetic order, we identify a superconducting Luther-Emery phase with dominant $s_{xy}$-wave pairing.

Elephant random walks were studied recently in \cite{mukherjee2025elephant} on the groups $\mathbb{Z}^{*d_1} * \mathbb{Z}_2^{*d_2}$ whose Cayley graphs are infinite $d$-regular trees with $d = 2d_1 + d_2$. It was found that for $d \ge 3$, the elephant walk is ballistic with the same asymptotic speed $\frac{d - 2}{d}$ as the simple random walk and the memory parameter appears only in the rate of convergence to the limiting speed. In the $d = 2$ case, there are two such groups, both having the bi-infinite path as their Cayley graph. For $(d_1, d_2) = (1, 0)$, the walk is the usual elephant random walk on $\mathbb{Z}$, which exhibits anomalous diffusion. In this article, we study the other case, namely $(d_1, d_2) = (0, 2)$, which corresponds to the infinite dihedral group $D_\infty \cong \mathbb{Z}_2 * \mathbb{Z}_2$. Unlike the classical ERW on $\mathbb{Z}$, which is a time-inhomogeneous Markov chain, the ERW on $D_{\infty}$ is non-Markovian. We show that the first and second order behaviours of the signed location of the walker agree with those of the simple symmetric random walk on $\mathbb{Z}$, with the memory parameter essentially manifesting itself via a lower order correction term that can be written as an explicit functional of the elephant walk on $\mathbb{Z}$. Our result demonstrates that unlike the simple random walk, the elephant walk is sensitive to local algebraic relations. Indeed, although $D_{\infty}$ is virtually abelian, containing $\mathbb{Z}$ as a finite-index subgroup, the involutive nature of its generators effectively neutralises memory, thereby ruling out any potential superdiffusive behaviour, in contrast to the superdiffusion observed on its abelian cousin $\mathbb{Z}$.

The distant dipolar field (DDF) is a long-range, nonlocal contribution to liquid-state spin dynamics that arises from intermolecular dipolar couplings and can generate multiple-quantum coherences and novel MRI contrast. Its sign-changing kernel makes Bloch-DDF dynamics strongly geometry dependent, and FFT-based dipolar convolutions naturally assume periodic or padded Cartesian domains rather than bounded samples with reflective diffusion boundaries. We study the Bloch equations with the DDF on bounded domains under homogeneous Neumann diffusion conditions. We derive a finite-element weak formulation that supports spatially varying diffusion and relaxation parameters and uses a short-distance regularization of the secular DDF kernel with length a>0. For fixed a we prove boundedness of the DDF operator, establish an L2 energy balance in which precession is neutral while diffusion and transverse relaxation are dissipative, and obtain local well-posedness with continuous dependence on the data, with global existence under energy-neutral transport. For the Galerkin semi-discretization we show a discrete energy identity mirroring the continuum estimate. For computation, we evaluate the DDF in real space with a matrix-free near/far scheme and advance in time using a second-order IMEX splitting method that treats diffusion and relaxation implicitly and precession explicitly. The explicit stage applies a Rodrigues rotation at DDF quadrature points followed by an L2 projection, enabling stable multi-cycle lab-frame simulations. We validate against three closed-form benchmarks and quantify curved-boundary effects by comparing mapped finite elements with a voxel-mask finite-difference baseline on spherical Neumann eigenmode decay. These results provide an analyzable and reproducible route for Bloch-DDF dynamics on bounded domains with complex geometry.

Recent experiments on metallic nanohybrids have revealed unusually strong electron-phonon effects emerging from nanoscale interfaces, despite the weak coupling character of the constituent bulk materials. Motivated by these observations, we investigate the electronic and lattice spectral properties of an inhomogeneous electron phonon system in which strong coupling is confined to interfacial regions embedded in a weakly coupled metallic background. Using a real-space formulation of the Holstein model combined with Langevin dynamics for lattice equilibration, we compute both electronic and phonon spectral functions in the presence of spatially varying coupling. We find that increasing the fraction of interfacial sites leads to a pronounced broadening of electronic spectral features, reflecting enhanced quasiparticle scattering from lattice distortions, but leaves the underlying band dispersion largely intact. Simultaneously, the phonon spectrum exhibits significant softening and damping, originating from strongly distorted interfacial regions. These modifications result in a redistribution of the Eliashberg spectral function toward low frequencies, producing a substantial enhancement of the effective electron-phonon coupling constant. Our results demonstrate that spatial inhomogeneity alone can strongly renormalize both electronic and lattice spectra, and provide a microscopic framework for understanding interface-driven transport and interaction effects in metallic nanohybrids.

Intrinsic topological superconductors with protected boundary modes obeying non-Abelian statistics constitute a vanishingly small class of quantum materials. A defining spectroscopic signature of such phases is the presence of in-gap topological surface states (TSS). However, despite extensive theoretical proposals, their unambiguous experimental identification has remained elusive. Here we use vector magnetic-field scanning tunnelling microscopy to obtain direct spectroscopic evidence of TSS in the spin-triplet superconductor UTe2. Atomic-scale spectroscopy reveals striking site-dependent superconductivity: Te sites host a large in-gap density of states that nearly fills the superconducting gap, whereas neighboring atomic sites remain gapped. Upon application of a magnetic field, the in-gap states on the Te sites are selectively suppressed, yielding a spatially homogeneous superconducting state with a markedly deeper gap relative to zero field. This site-selective gap evolution is in quantitative agreement with theoretical predictions for TSS in UTe2 that possess dominant Te-orbital character. Spectral-function calculations incorporating the Zeeman coupling reproduce the observed magnetic-field response. Our results provide a spectroscopic fingerprint of the long-sought TSS in superconductors and establish UTe2 as a compelling system for exploring intrinsic topological superconductivity.

Ferrimagnetic spinel materials of formula AB2X4, where A and B are transition metals and X is oxygen or sulphur, hold promise for the realization of multiferroic characteristics. In this work, we report synthesis of spinel CoMn2O4 and explore its magnetic, dielectric, and ferroelectric aspects and their correlations. Polycrystalline CoMn2O4 was synthesized by using the conventional solid-state method. The X-ray diffraction (XRD) and Raman spectroscopy confirmed the phase purity of the synthesized compound. The crystal structure was identified with tetragonal symmetry (I41/amd space group). DC magnetization measurements indicate two magnetic transitions: one at temperature T1 ~ 186 K, followed by another Yafet-Kittel (YK) ferrimagnetic transition at T2 ~ 86 K. A frequency independent anomaly in the temperature dependent dielectric permittivity is observed near the low magnetic ordering temperature (T2). This reflects the possibility of the correlation between lattice dynamics and spin ordering in spinel CoMn2O4. A substantial exchange bias was also observed below T2 ~ 86 K. The change in dielectric permittivity in the presence of applied magnetic field follows the square of the magnetization dependence, which is consistent with Ginzburg-Landau theory. However, the detailed pyroelectric current measurements reveal the absence of intrinsic ferroelectric order.

The Boltzmann-Loschmidt dispute of 1876 questioned the possibility of a statistical irreversible description by time reversible classical equations of motion of atoms. Here we show analytically and numerically that the quantum chaos diffusion of cold atoms, or ions, in a harmonic trap and pulsed optical lattice can be inverted back in time with up to 100% efficiency. This is in sharp contrast to classical evolution where exponentially small errors break time reversibility. We argue that the existing experimental skills allow highlighting the Boltzmann-Loschmidt dispute from a quantum perspective.

We present a thorough magnetization and magneto-transport study of the diluted Fe-intercalated CrTe2 family member, Fe1/5CrTe2, a van der Waals ferromagnet. Fe1/5CrTe2 shows an elevated Curie transition temperature of 182 K in comparison to the Fe1/3CrTe2 composition, indicating the sensitive role of Fe concentration in modulating magnetic exchange interactions within the CrTe2 framework. The saturated magnetization exhibits a quadratic dependence with temperature, indicating the presence of long-wavelength spin fluctuations. Analysis of the temperature dependent resistivity reveals a dominant T3/2 contribution over the typical T2 behavior, signaling substantial coupling between conduction electrons and localized spins. The magnetoresistance shows a linear and non-saturating negative field dependency throughout a wide temperature range below TC, which is compatible with the increasing suppression of spin-disorder dispersion related to ferromagnetic spin fluctuations. A thorough analysis of the anomalous Hall effect (AHE) shows that extrinsic skew-scattering contribution, which is associated to Fe-related disorder, dominates the anomalous Hall response. The systematic separation of intrinsic and extrinsic components reveals that, over a wide temperature range, the intrinsic anomalous Hall conductivity scales linearly with the saturation magnetization, despite the substantial extrinsic dominant background. The linear behavior of intrinsic anomalous Hall conductivity with magnetization is in line with a long wavelength spin-fluctuation framework, where thermal spin disorder lowers net magnetization without significantly altering the underlying electronic structure. These findings reveal Fe1/5CrTe2 as a newly investigated van der Waals ferromagnet where spin fluctuations and disorder coexist with a well-defined intrinsic Berry-curvature contribution to the Hall response.

We investigate the impact of the quantum effects of protons on the electronic structure of high-pressure H$_3$S, a benchmark hydrogen-rich superconductor with a critical temperature ($T_c$) exceeding 200 K. Using Nuclear-Electronic Orbital Density Functional Theory (NEO-DFT), we treat hydrogen nuclei quantum mechanically on the same footing as electrons within a first-principles framework. Our calculations reveal that nuclear quantum effects (NQEs) induce subtle modifications to the electronic band structure and density of states (DOS) near the Fermi energy, including features associated with van Hove singularities. However, the resulting changes in the DOS would increase $T_c$ by only a few percent. On the other hand, calculations of the phonon dispersion with the NEO-DFT method show large changes in the hydrogen-dominated phonons that arise from a stiffening of the S-H bonds due to NQEs. These findings imply that the experimentally observed reduction in $T_c$ upon deuteration arises predominantly from changes in the phonon properties, while NQEs-induced modifications to the electronic structure itself are minimal.

We propose a representative, globally-admissible phenomenological spectral density of the bath for the non-Markovian Brownian motion of an optomechanical resonator, motivated by the near-resonance experimental observation of a non-Ohmic spectrum in [Nat. Commun. 6, 7606 (2015)]. To avoid divergences arising from a naive global extrapolation, we propose a globally-admissible, phenomenological bath spectrum that extends the experimentally-observed, near-resonance non-Ohmic behavior beyond the measurement window while ensuring finite bath-induced renormalizations and quadrature fluctuations of the resonator. The corresponding model of the structured environment produces a nonlocal mechanical response whose analytic pole structure encodes the observed linewidth. The resulting dissipation kernel exhibits a power-law-modulated exponential decay with transient negativity, signaling memory effects. In the weak-coupling regime, the optical readout based on homodyne detection enables near-resonance spectroscopy and, with a calibrated drive on the resonator, permits, in principle, the reconstruction of the full mechanical susceptibility, thereby providing access to both the dissipative and dispersive bath contributions. Our results provide a consistent route from locally-inferred spectral properties to globally-admissible open-system descriptions and establish a framework for probing structured environments in cavity optomechanics.

PulsePol is an elegantly designed pulse-sequence-based quantum control scheme that enables polarization transfer between electron and nuclear spins, for example, in nitrogen-vacancy (NV) centers. However, previous analyses of PulsePol assumed very strong, near-ideal, instantaneous microwave pulses, which is rarely achievable at higher magnetic fields. We revisit the PulsePol scheme under finite-pulse constraints and show that its performance significantly degrades due to finite-pulse effects. Using bimodal Floquet theory, we identify the symmetry-breaking mechanism responsible for this deterioration in fidelity. By phase adjustment, we reestablish the proper symmetry of the interaction-frame spin Hamiltonian, leading to a sequence called Q-PulsePol, where "Q" reflects the restored quadrature symmetry. Our results demonstrate robustness to finite-pulse effects and improved polarization transfer efficiency, establishing Q-PulsePol as a practical and reliable scheme for bulk hyperpolarization of nuclear spins in solids using a single-mode (zero-quantum or double-quantum) transfer. This work bridges idealized quantum control with realistic pulse engineering, establishing design rules for spin-based quantum control protocols.

We present QCommute, a software tool implemented in C++ for symbolic computation of nested commutators between a Hamiltonian and local observables in quantum many-body spin-1/2 systems on one-, two-, and three-dimensional hypercubic lattices. The computation is performed algebraically directly in the thermodynamic limit, and the Hamiltonian parameters are kept symbolic. Importantly, this way the entire parameter space is covered in a single run. The implementation supports extensive parallelization to achieve high computational performance. QCommute can serve as a computational backend for Heisenberg-picture approaches to quantum dynamics in strongly correlated regimes, ranging from direct Taylor expansion in time to advanced techniques such as the recursion method.

Stochastic resetting has emerged as a powerful mechanism for driving systems into nonequilibrium stationary states with tunable properties. While most existing studies focus on global resetting, where all degrees of freedom are simultaneously reset, recent work has shown that resetting only a subset of degrees of freedom (subsystem resetting) can qualitatively alter collective behavior in interacting many-body systems. In this work, we develop a general theoretical framework for analysing subsystem resetting in Kuramoto-type coupled-oscillator systems. Building on a continued-fraction approach, we derive self-consistent equations for the stationary-state order parameter of the non-reset subsystem, applicable to both noisy and noiseless dynamics and to models with arbitrary interaction harmonics. Using this framework, we systematically investigate how the stationary state and phase transitions depend on the resetting rate, the size of the reset subsystem, and the reset configuration. We show that subsystem resetting can shift or even suppress synchronization transitions, and can give rise to nontrivial features such as re-entrant behavior and restructuring of phase boundaries. In specific cases, including the noiseless Kuramoto model with a Lorentzian frequency distribution, our results recover known analytical predictions and extend them to more general settings. These results establish subsystem resetting as a versatile control protocol for engineering collective dynamics in nonequilibrium interacting systems.

Two-dimensional (2D) ferromagnetic materials with high Curie temperature ($T_{\rm c}$) and large magnetic anisotropy energy (MAE) are critical for nanoscale spintronics but remain rare. We propose, via first-principles calculations, that adsorbing alkali atoms ($A$ = Li, Na, K, Rb, Cs) onto a tetragonal CoSe monolayer transforms it into a series of stable 2D ferromagnetic metals, $A$CoSe, with an in-plane easy axis. Notably, LiCoSe is a half-metal. These functionalized monolayers exhibit dramatically enhanced ferromagnetism compared to the pristine layer, with $T_{\rm c}$ > 300 K and MAE > 800 $\mu$eV/Co. The coupled alkali atoms amplify the local magnetic moment of Co ions, reinforce ferromagnetic Ruderman-Kittel-Kasuya-Yosida (RKKY) and superexchange couplings, and concurrently weaken the direct antiferromagnetic exchange between Co ions. Furthermore, tensile strain can further elevate the MAE (via band shifting) and increase $T_{c}$ (by strengthening the nearest-neighbor exchange $J_1$). Among them, NaCoSe exhibits the highest MAE and excellent strain-modulated $T_{c}$, rendering it the most promising candidate material. Our results establish alkali-metal decoration as an effective strategy for realizing 2D ferromagnets with high $T_{\rm c}$ and large MAE in tetragonal lattices.

Heat engines that convert thermal energy into work are a cornerstone of classical thermodynamics and remain an active area of contemporary research. Notable examples include microscopic heat engines, trade-off relations between power and efficiency, and the attainability of Carnot efficiency at finite power. We propose a cyclic heat engine based on the Ising model, in which the thermodynamic cycle involves variations of both temperature and magnetic field. We analyze the one-dimensional and mean-field Ising models, which allow for simple analytical results and provide new insight into the role of interactions in cyclic heat engines. In particular, we show that interactions can enhance both power and efficiency. Moreover, a system that does not operate as an engine in the absence of interactions can become an engine upon tuning the interaction strength. The mean-field model enables us to investigate the relevance of the phase transition for the performance of this Ising heat engine. Owing to the emergence of spontaneous magnetization, the mean-field model can still operate as an engine even when one of the magnetic fields is set to zero. Remarkably, when the work is maximized, we find that the optimal parameters are numerically consistent with this regime, in which one magnetic field vanishes and the cycle explores the phase transition. We also consider an alternative cycle for the mean-field model, obtained by varying the interaction strength while keeping both temperatures below the critical temperature and setting the magnetic field to zero throughout the cycle. The power and efficiency of this cycle are analyzed as well. Finally, while our analytical results are valid for the limit of large period we use numerical simulations for finite periods and show that the power decreases monotonically with the period.

We present a two-channel extension of the Allen-Dynes framework that unifies phonon-mediated and spin-fluctuation-mediated pairing channels for predicting superconducting critical temperatures. Channel 1 employs the standard Allen-Dynes formula with material-specific electron-phonon coupling; Channel 2 incorporates a spin-fluctuation coupling parameter extracted from inelastic neutron scattering data. Blind predictions for 19 materials spanning conventional superconductors, MgB2, iron pnictides, iron chalcogenides, heavy fermions, cuprates, and hydrides achieve R-squared = 0.96 across five orders of magnitude in Tc (0.4-250 K) without free parameters. We further demonstrate a quantum-metric no-go result: the Peotta-Torma geometric superfluid weight, while essential for flat-band systems, cannot serve as a universal predictor of Tc because it correlates with band-structure topology rather than pairing strength. The framework identifies the spin-fluctuation channel as the dominant contributor to Tc enhancement in unconventional superconductors, providing quantitative design rules for materials with Tc above 100 K.

With the increase in the complexity of the materials used in various sophisticated electronic devices, recycling of E-waste is becoming challenging. In the present study, we have converted thermoelectric (TE) waste into functional HER electrocatalyst by considering circular-economy and low-carbon approach. The as received TE waste was processed through ball milling (TE waste-BM) and melting casting (TE waste-M) routes. Morphological and structural evaluations revealed that the formation of BiSbTe3/ZnTe heterostructure in TE-waste-M promote HE efficiency when compared to the presence of Bi2Te3/BiSbTe3 heterostructure (TE-waste-BM). TE waste-M exhibited lower overpotential (641 mV at 10 mA/sq.cm), smaller Tafel slope (233 mV/dec) and stable operation for 5.5 h with negligible current decay than that of TE waste-BM, attributed to the accelerated charge transfer, fast water dissociation steps and rapid hydrogen adsorption in TE waste-M, originated from the presence of BiSbTe3/ZnTe heterostructure, defect enriched interfaces. Density functional theory calculations supported the experimental findings, revealing that heterostructures strengthens the bonding states near the Fermi level, thereby enhancing the HER activity of BiSbTe3/ZnTe heterostructure. This work simultaneously integrates waste management with green hydrogen production by offering an economically viable, scalable and low-carbon approach for HER catalysts.

Machine learning (ML) models have achieved strikingly high accuracies in spectroscopic classification tasks, often without a clear proof that those models used chemically meaningful features. Existing studies have linked these results to data preprocessing choices, noise sensitivity, and model complexity, but no unifying explanation is available so far. In this work, we show that these phenomena arise naturally from the intrinsic high dimensionality of spectral data. Using a theoretical analysis grounded in the Feldman-Hajek theorem and the concentration of measure, we show that even infinitesimal distributional differences, caused by noise, normalisation, or instrumental artefacts, may become perfectly separable in high-dimensional spaces. Through a series of specific experiments on synthetic and real fluorescence spectra, we illustrate how models can achieve near-perfect accuracy even when chemical distinctions are absent, and why feature-importance maps may highlight spectrally irrelevant regions. We provide a rigorous theoretical framework, confirm the effect experimentally, and conclude with practical recommendations for building and interpreting ML models in spectroscopy.

Twin boundaries play a central role in the functional behavior of martensitic materials, yet the mechanisms governing the initiation of their motion remain poorly understood for twins lying along irrational crystallographic directions. Here we present an atomistic investigation of the onset of motion of both rational and irrational twin interfaces in a two-dimensional model lattice with rectangular unit cells. Using quasistatic shear loading and full linear stability analysis, we show that the initiation of twin boundary motion is signaled by a nonlocal linear instability, marked by the vanishing of the lowest eigenvalue of the Hessian; the corresponding eigenmode predicts the atomic displacements that initiate motion. We find that irrational twin boundaries have significantly lower critical shear stress to initiate motion compared to rational twin boundaries. Further, we find that they display unusual mechanisms to initiate motion such as the formation of microtwins in directions orthogonal to the overall twin boundary. Finally, we compare various local measures against the nonlocal stability analysis, and find that the former do not capture that irrational twin boundaries initiate their motion at lower stresses compared to rational boundaries.

Power-law (PL) distribution functions (DF) are prevalent in highly diverse systems. The systems range in size from nanometer to mega light years, in complexity from dust grains to living organisms, and characterize the distribution of various events in nature and in various human activities. To gain some insight on why PL DF are so prevalent, we explore the conditions leading to the formation of a PL DF in a simple system of colliding hard sphere. We follow the time evolution of the energy DF through direct Monte Carlo simulations. In statistical equilibrium, the DF evolves into the Maxwell-Boltzmann (MB) DF. A transition to a PL DF occurs when: 1. The system is initially far from equilibrium. For example, a mix of light and heavy particles with the same velocity. 2. The system dynamics is scale-free, which holds in the intermediate asymptotic regime, far from the initial and the final equilibrium states. The scale-free dynamics leads to a DF which evolves in a self-similar form. 3. The system is open with a scale-free boundary condition. For example, a constant injection of particles far from equilibrium. The DF PL index is set by the time dependence of the self-similar DF and by the boundary condition. The PL index is independent of the self-similar DF form. Conditions 1-3 are common in a great variety of systems, which may explain why PL DF are so prevalent in nature.

Neural network grokking – the abrupt memorization-to-generalization transition – challenges our understanding of learning dynamics. Through finite-size scaling of gradient avalanche dynamics across eight model scales, we find that grokking is a dimensional phase transition: effective dimensionality~$D$ crosses from sub-diffusive (subcritical, $D < 1$) to super-diffusive (supercritical, $D > 1$) at generalization onset, exhibiting self-organized criticality (SOC). Crucially, $D$ reflects gradient field geometry, not network architecture: synthetic i.i.d.\ Gaussian gradients maintain $D \approx 1$ regardless of graph topology, while real training exhibits dimensional excess from backpropagation correlations. The grokking-localized $D(t)$ crossing – robust across topologies – offers new insight into the trainability of overparameterized networks.

Quasi one dimensional materials provide a compelling platform where reduced dimensionality stabilizes intertwined topological and superconducting phases. Here we report superconductivity in a new Bi based quasi 1D compound, PtPb3Bi, which hosts a nontrivial electronic structure. It exhibits type II superconductivity below 3.01(1) K. Heat capacity and transverse field muon spin rotation relaxation (muSR) measurements demonstrate a fully gapped isotropic s wave state with moderate electron phonon coupling, while zero field muSR confirms the preservation of time reversal symmetry (TRS). Transport measurements reveal low carrier mobility with diffusive normal state transport. Electronic structure calculations show strong dispersion along the quasi 1D direction and relatively flatter bands in the transverse plane, giving rise to pronounced Fermi surface nesting in the kx-ky plane. Consistent with this, the compound undergoes a charge density wave transition at 280(1) K. The flow of Wannier charge centers, together with surface state dispersion, establishes nontrivial band topology. These results identify PtPb3Bi as a new quasi 1D superconductor with nontrivial electronic structure and a promising candidate for topological superconductivity.

Ruddlesden-Popper (RP) nickelates have recently emerged as a new family of high-temperature superconductors. In bilayer RP nickelates, magnetic excitations with large exchange couplings have been observed, supporting a spin-mediated pairing mechanism. Whether comparable spin correlations persist in trilayer nickelates, however, remains unknown. Here, we present a Ni $L$-edge resonant inelastic X-ray scattering (RIXS) study of La$_4$Ni$_3$O$_{10}$ single crystals. While the orbital excitations remain similar to those of La$_3$Ni$_2$O$_{7}$, the collective spin excitations in La$_4$Ni$_3$O$_{10}$ exhibit a comparable bandwidth of about $60$ meV but substantially suppressed spectral weight, implying a weaker electronic correlation in the trilayer compounds. Our results underscore the three-dimensional and multi-orbital electronic character in La$_4$Ni$_3$O$_{10}$, highlighting important differences from the bilayer nickelates. These findings provide crucial insights into the evolution of magnetism across the RP nickelate family and its connection to superconductivity.

This work presents a comprehensive benchmark and validation of a recently proposed method called Effective Bethe Ansatz (EBA). It is a variational method that deforms the exact Bethe wavefunctions of one-dimensional spin chains at integrable points to approximate non-integrable systems. We apply this method to the non-integrable regime of the spin-1 bilinear-biquadratic chain. By performing EBA method starting from the two integrable endpoints, the Takhtajan-Babujian point and the Lai-Sutherland point, we systematically evaluate the accuracy of the EBA for the ground state and first excited state. Our validation is based on a direct comparison with exact diagonalization, assessing energy, fidelity, and entanglement entropy. The results confirm that the EBA provides a quantitatively accurate description in a finite window around the integrable points, while its fidelity and entanglement properties degrade in a controlled way as the perturbation increases. The method successfully captures key finite-size effects, such as level crossings, manifested as sharp drops in fidelity, and provides a probe to potential phase transitions. This study establishes the EBA as a reliable and efficient semi-analytical tool, clarifying its scope and limitations for studying low-energy physics in non-integrable quantum spin chains.

Characterizing crystalline energy landscapes is essential to predicting thermodynamic stability, electronic structure, and functional behavior. While machine learning (ML) enables rapid property predictions, the "black-box" nature of most models limits their utility for generating new scientific insights. Here, we introduce Kolmogorov-Arnold Networks (KANs) as an interpretable framework to bridge this gap. Unlike conventional neural networks with fixed activation functions, KANs employ learnable functions that reveal underlying physical relationships. We developed the Element-Weighted KAN, a composition-only model that achieves state-of-the-art accuracy in predicting formation energy, band gap, and work function across large-scale datasets. Crucially, without any explicit physical constraints, KANs uncover interpretable chemical trends aligned with the periodic table and quantum mechanical principles through embedding analysis, correlation studies, and principal component analysis. These results demonstrate that KANs provide a powerful framework with high predictive performance and scientific interpretability, establishing a new paradigm for transparent, chemistry-based materials informatics.

The stochastic series expansion (SSE) algorithm is one of the most powerful quantum Monte Carlo methods and has been extensively applied to the study of quantum many body systems. Its efficiency is particularly enhanced with a deterministic loop update scheme in the study of the S=1/2 quantum spin systems that preserve SU(2) spin rotational symmetry. Once the symmetry is broken, such as by an external field, a directed loop method is typically required, resulting in a significant reduction in efficiency. Inspired by the SSE approach developed for the quantum Ising model, we introduce a deterministic loop SSE method that is particularly suited for antiferromagnetic systems under a staggered magnetic field. This method enables separate investigations of longitudinal and transverse modes in magnetically ordered phases arising from spontaneous symmetry breaking. We benchmark the performance of our algorithm against the standard directed loop approach applied to the antiferromagnetic Heisenberg chain and demonstrate that our method substantially reduces CPU time per Monte Carlo step, thereby can outperform the directed loop algorithm in efficiency.