Papers

(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.

Posture control in slender bodies such as snakes and eels arises from the interplay between passive deformation, active internal actuation, and task-level constraints. We formulate a general framework for the selection of stable postures in active elastic filaments subject to distributed forcing from gravity and fluid drag, by combining the constraints of mechanical equilibrium with optimal control theory. Our theory leads to a minimal description in terms of parameters governing the competition between hydrodynamic and gravitational loading, elasticity, and activity. We show that posture selection reflects a trade-off between control cost, function and dynamical stability, leading to the coexistence of distinct solution branches and abrupt transitions between them. Applying the theory to sessile eels in flow, we recover the experimentally observed transition from upright to reclining postures and predict scaling laws for body shape and exposed length. More generally, our results provide a unified perspective on how active filaments can regulate geometry to maintain function in external fields, with implications for biological and artificial systems.

We present a theoretical study of a semiconductor photon-pair source based on a radiative cascade enabled by a permanent exciton dipole. The source consists of a GaAs quantum dot placed between a metal nanoparticle and a mirror. The dot exciton and the localized electromagnetic mode mix to form upper and lower polaritons. Without a permanent dipole, a symmetry separating states with even and odd excitation numbers forbids photon emission between the polaritons. Separation of the mean electron and hole positions gives the exciton a permanent dipole and breaks this symmetry. The upper polariton can then emit an idler photon as it decays to the lower polariton. The lower polariton can emit a signal photon as the system returns to its ground state. Using an effective model, we calculate the probability that a prepared upper polariton emits both photons through the metal antenna. We also analyse fluctuations in the emitted photon counts and correlations between the two emission channels. The calculation establishes an operating principle for assumed emitter properties and optical loss rates. Whether the device can be built and its photon correlations measured remains open.

The surface chemistry of additively manufactured aluminum alloys plays a critical role in corrosion resistance and joining with external materials. In this work, the near-surface elemental composition of a laser powder bed fusion (PBF-LB/M) processed Al-Mg-Si-Zr alloy was characterized by glow discharge optical emission spectroscopy GDOES depth profiling. The measurements reveal pronounced Mg enrichment within the near-surface region extending to approximately 10 {\mu}m, consistent with the characteristic scale of surface roughness, together with an increase in oxygen concentration, whereas Al, Si, and Zr approach stable bulk-like levels at greater depths. To understand this observation on the atomic scale, first-principles calculations based on density functional theory (DFT) were performed on low-index Al surfaces. The calculated results show a strong thermodynamic driving force for Mg surface segregation, with diffusion energy differences ranging from approximately -0.30 eV to -0.41 eV, while Zr exhibits a pronounced preference for remaining in the bulk matrix. Vacancy migration calculations further demonstrate that full structural relaxation substantially reduces the migration barrier for Mg to below that of Si, which makes Mg diffusion kinetically highly favorable. Moreover, the presence of adsorbed surface oxygen dramatically promotes the tendency of Mg to diffuse toward the surface, which lowers the diffusion energy difference of Mg to as much as -3.0 eV. This promotes the formation of a locally reconstructed Mg-O-Al coordinated precursor structure accompanied by localized electron transfer shown by an electron localization function analysis.

We examine the different methods of extracting the anomalous Hall conductivity using SrRuO$_3$ and GdAlSi. For SrRuO$_3$, where the ordinary Hall background is well defined and the magnetoconductance is small, subtracting the ordinary Hall contribution either before or after conversion from resistivity to conductivity yields nearly identical anomalous Hall conductivities. In GdAlSi, in contrast, the transverse response does not exhibit clear saturation, and both low- and high-field regions can appear approximately linear. We show that different interpretations of these linear regions as the ordinary Hall background, together with the treatment of the measured longitudinal resistance in the resistivity-to-conductivity conversion, can produce completely different estimates of the anomalous Hall conductivity. We also examine whether the nonlinear Hall response can instead be described within an ordinary Hall framework without invoking an anomalous contribution. Our analysis provides practical cautions for extracting excess Hall contributions in quantum materials.

Determining which microscopic states remain thermally active when tunneling and interactions compete is a central question in Hubbard physics. Here we develop an entropy measurement protocol for a double quantum dot, extending the charge-based approach established for a single dot, and measure the total entropy of a tunable two-site Hubbard molecule realized in a GaAs double dot. By shifting both dot levels together at fixed detuning, the entropy is correctly probed with only a single charge sensor. As interdot tunneling increases, the system evolves from two atomic-like dots through hybridized molecular states to a merged single dot. Across this evolution, the entropy decreases as tunnel-induced energy splitting exceeds the thermal energy and suppresses the occupation of higher-energy states. The measurements resolve the diminishing contribution of antibonding states and the changing thermal contributions of hybridized singlet and triplet states, in quantitative agreement with a two-site Hubbard model. By distinguishing states with the same charge configuration but different orbital and spin content, entropy reveals how tunneling and interactions determine the thermally active states of the minimal Hubbard system.

Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the “instantaneous” part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.

Dielectric interfaces are ubiquitous in manufactured and natural systems, such as iontronic devices, supercapacitors, and living cells. These, often rough, dielectric surfaces host ionic charge distributions that depend on the surface geometry and the electric fields present. In this work, we study the effect of electric fields on such ionic charge distributions. We demonstrate, by molecular dynamics (MD) and perturbative analytic calculations, that the pattern of alternating regions of ionic charge density created by a sinusoidal interface can be modified and reversed by applying an electric field. We determine the strength of the critical electric field required to cancel the effect of dielectric interface-driven modulation in ion density and develop an analytic expression for that field for small amplitude sinusoidal variations in surface height. We show that ion concentrations near a surface with height given by a sum of Fourier modes can be found by adding the contributions from the concentration modulation due to each mode, allowing the possibility to predict ion distributions near rough surfaces. We updated and validated a LAMMPS package for MD simulation of polarizable surfaces, the DIELECTRIC package, by implementing a new version that achieves a 2.4-24 times speed increase by GPU parallelization on our test system and adds the capability to simulate an applied electric field on simple and complex electrolytes near dielectric interfaces with arbitrary roughness.

Traditional theoretical treatments of ferroelectricity do not straightforwardly extend to sliding ferroelectrics, which are increasingly-studied layered materials where a switchable electrical polarization is controlled by two-dimensional relative motion of the stacked layers. Therefore, in-depth analyses of the underlying processes which dictate their polarization behavior remain challenging. In this paper, we present a comprehensive approach for identifying the symmetry-adapted microscopic parameters which are responsible for driving the emergence of this polarization. First, we outline our approach, which appeals to group theory arguments and the distortion of Wannier orbital densities to connect macroscopic symmetries to the microscopic electronic distortions which dictate the appearance of ferroelectricity. Then, we illustrate this process by using density functional theory to apply our strategy to honeycomb bilayer systems, including hexagonal boron nitride. In this way, we find that combinations of dipole-like and quadrupole-like distortions of lone pair electron orbitals control electronic reorganization, and by extension, ferroelectricity in such systems.

Most molecular transitions occur on timescales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration reaches a product state before a reactant state, is a central kinetic statistic, providing a mechanism-independent reaction coordinate and a foundation for transition path theory and the calculation of rates. This review surveys modern approaches for estimating the committor and related kinetic statistics from molecular simulations, with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data. We develop a common operator viewpoint connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks. Empirical and theoretical evidence points to the efficiency of these methods. We provide theoretical and practical guidance for realizing their full potential in applications, including strategies for treating non-Markovian effects and for sampling. We conclude by identifying opportunities for further research, including connections to reinforcement learning and generative modeling.

We investigate the dynamics of entanglement asymmetry in periodically driven two-dimensional conformal field theories with a global U$(1)$ symmetry, using a dynamical-system description based on iterated conformal maps, in particular Möbius maps. Starting from a symmetry-breaking excited state prepared by a local operator insertion, we show that a broad range of nonequilibrium phenomena, including local symmetry restoration, the quantum Mpemba effect, and its inverse, admit a simple geometric description in terms of the invariant data of the conformal map. We explicitly demonstrate this using Möbius maps, for which the invariant structure is described by the conjugacy classes. In particular, the dynamics of entanglement asymmetry is determined by the relative positions of the state-preparing operator insertion, the subsystem, and the fixed points, yielding distinct patterns of growth, decay, oscillation, and saturation. We further argue that this geometric picture extends to general holomorphic maps, establishing the conformal-map dynamics as a natural framework for organizing the phenomenology of entanglement asymmetry in periodically driven two-dimensional conformal field theories.

We show that microscopically inversion-asymmetric, permeable active fluid membranes are statistically flat and effectively inversion-symmetric at large scales. Their fluctuations are governed by an asymptotically exact linear hydrodynamic equation giving orientational long-range order and positional quasi-long-range order. At intermediate scales, their dynamics is described by a Kardar-Parisi-Zhang equation with spatially long-range noise, producing rough membranes with short-range translational and long-range orientational order described by exactly known scaling exponents. Active stresses can destabilize the membrane at long wavelengths, while sufficiently strong active permeation flow can drive finite-wavevector instabilities and pattern formation. These results reveal a novel activity-driven route to the destruction of flat fluid membranes.

Phononic frequency combs have been demonstrated experimentally and theoretically in the kHz-MHz regime under nonlinear driving; however, their spontaneous formation in the GHz-THz regime remains rare. We investigate the spontaneous formation of frequency combs in van der Waals solid CrGeTe$_3$, where combs of spacing $\sim$2 cm$^{-1}$ were experimentally proposed to occur in a flat phonon mode but are now reported to originate from isotopic distribution. Our spectral energy density calculations using machine-learning-augmented molecular dynamics simulations show comb-like features with reduced spacings of $\sim$0.1 and 0.6 cm$^{-1}$ in the same mode at 50 and 200 K. However, the spacings of the comb-like features are comparable to the phonon linewidth, making precise identification of the frequency comb challenging. From a comprehensive analysis of different modes of CrGeTe$_3$, we identified two conditions to distinctively observe the combs beyond the experimental resolution: (i) an intramolecular or isolated mode with reasonably large third- or higher-order anharmonicity from phonon self-interaction and (ii) limited phonon scattering channels. Our analysis of other van der Waals solids highlighted that these conditions are met for the nearly flat intramolecular $E_{2g}$ and $A_{2u}$ phonon modes of WSe$_2$. The detailed calculations showed the formation of a spontaneous frequency comb with spacings of 1.7 and 0.67 cm$^{-1}$ from coherent superposition of four and five-phonon eigenstates in the $E_{2g}$ and $A_{2u}$ phonon modes, respectively. Available Raman scattering data of the $E_{2g}$ mode in the literature provide preliminary, if not conclusive, evidence of comb formation. Our findings offer a deeper understanding and open avenues for engineering long-lived phononic frequency combs for various practical applications.

Micron-sized particles moving through a fluid are subject to viscous resistance and thermal fluctuations. Beyond steady Stokes friction, colloids also exhibit hydrodynamic memory effects arising from conservation laws of the surrounding fluid. Although fluid-flow problems in complex geometries and confinements are often highly involved, numerical or approximate solutions can be obtained; translating these solutions into closed-form equations of motion for individual colloids, however, is rarely possible. Here, we develop a theoretical framework that provides both underdamped and overdamped colloidal dynamics from the solution of an arbitrary flow problem: (i) Using the Lorentz reciprocal theorem, we express the colloidal equation of motion in terms of the geometry's Green's function and the fluid-flow profile. This formulation yields both the corresponding Stokes drag as well as a Basset-like hydrodynamic memory contribution. (ii) As colloid inertia is often negligible, we furthermore derive the corresponding overdamped (colloid-inertia-less) limit, which inherits the Stokes and Basset-like resistances and additionally gives rise to a spurious drift. We propose applications of this framework to passive and active particles subject to involved confinements and problem geometries.

Micron-sized colloid particles diffusing through a fluid experience hydrodynamic inertial and memory effects, the latter causing velocity autocorrelation to decay as a power law. At the same time, many theoretical descriptions treat colloidal diffusion in a fluid using overdamped Langevin dynamics for its convenience, eliminating velocity, omitting inertia, but also ignoring the power-law memory. In this Letter, we show that hydrodynamic memory survives in the overdamped (colloid-inertialess) limit. By identifying the dimensionless parameter controlling the crossover between early- and late-time dynamics, we derive in closed form the overdamped Langevin equation in the presence of hydrodynamic memory. This provides a theoretical framework for realistically describing colloidal dynamics in a fluid, and establishes a rigorous basis for the positional memory observed in high-resolution experiments. Our theory predicts that hydrodynamic memory becomes increasingly pronounced for smaller particles and under stronger external forcing, and offers experimental probes for the crossover from conventional exponential relaxation to memory-dominated power-law dynamics.

The impact of projective measurements on a many-body quantum state is tightly linked to its underlying entanglement structure. Critical states are particularly sensitive, as long-range entanglement allows local measurements to have global consequences. This has been extensively studied in the context of critical states described by a conformal field theory (CFT), where measurements can alter critical properties in post-measurement quantities ('measurement-altered criticality') and induce long-range entanglement with universal features ('measurement-induced entanglement'). By contrast, little is known about the role of measurements on critical states with quenched disorder, which admit no CFT description. Here, we develop a theory of measurements on one-dimensional critical states governed by infinite-randomness fixed points (IRFPs), focusing on two closely related examples: the random XXZ chain and the random transverse-field Ising model. We show that the measurement-induced entanglement decays as a power-law with universal exponent $(3-\sqrt{5})/2$ in both models, and that the minimum number of measurements required to establish this entanglement obeys a universal scaling form. When only a finite density of measurements is made, we show that the critical properties of the state are remarkably robust: `measurement-altered criticality' is absent, with measurements either preserving the critical exponents, or destroying the criticality entirely. These results establish IRFPs as an analytically tractable arena for measurements on critical states, complementary to the CFT case. The outcome randomness that necessitates replica methods in clean systems becomes trivial at infinite randomness, with the universal response governed by the statistics induced by the quenched disorder.

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals a broader asymmetric multifrequency structure. In thermal two-dimensional conformal field theory, exact two- and three-point functions saturate the corresponding bounds. At fourth order, where genuine dynamical information first appears, we show that the holographic CFTs studied here saturate the strongest full-ETH bounds. These results establish a direct connection between full ETH, free cumulants, and gravitational scrambling, and are consistent with the emergence of asymptotic freeness realized by the gravitational scrambling algebra.

Using thermal analyticity, we derive directional large-frequency bounds on the smooth functions entering full eigenstate thermalization in continuum quantum field theory. The strongest directions reproduce the scales previously identified for lattice systems, while the complete analyticity domain reveals an asymmetric multifrequency structure. Thermal conformal correlators saturate the second- and third-order bounds, and the leading gravitational Regge contribution saturates the strongest fourth-order direction.

Starting from a general Hamiltonian describing the quantum dynamics of probe particles interacting with a set of environment degrees of freedom, we derive the quantum master equation with which the reduced density matrix of a probe particle evolves, the general equilibration condition that they satisfy when the environment is prepared in a thermal state – encoded in a KMS property for line operators extended in real time – and the Langevin description that emerges. The novelty of our results resides in their generality: We do not assume a specific form of the environment self-coupling, of the environment operator that couples the particle to it, of the statistics of its correlation functions, whether the statistics of the momentum transfer is Gaussian or not, or whether the probe particles move relativistically. Our results only require that spacetime translations, parity and time reversal be symmetries of the Hamiltonian, and that there exists a separation of scales between those characterizing the dispersion relation of the probe particle and those of the environment. We also discuss the limiting case in which Gaussian Brownian motion emerges. Overall, our results constitute a first-principles derivation of what properties of the underlying quantum field theory govern the energy loss and momentum fluctuations of probe particles.

This thesis develops robust and efficient AI frameworks for accelerating crystalline materials discovery by addressing both major stages of the materials-design pipeline: crystal property prediction and crystal structure generation. Motivated by the high computational cost of Density Functional Theory (DFT) and the limited availability of labeled materials data, the thesis explores graph representation learning, pretraining, multimodal learning, and generative modeling for scalable materials design. For property prediction, the thesis first introduces CrysXPP, which learns transferable crystal representations through unsupervised graph autoencoding, reducing dependence on large property-labeled datasets. It then proposes CrysGNN, a large-scale self-supervised graph pretraining framework that captures atomic connectivity, chemical attributes, and global structural information and transfers this knowledge to downstream property predictors through knowledge distillation. CrysMMNet further enriches crystal representations by jointly modeling graph structure and textual descriptions, thereby incorporating both local chemical and global structural knowledge. For crystal generation, the thesis introduces TGDMat, a text-guided joint diffusion framework that jointly models lattice parameters, atomic types, and atomic coordinates while incorporating textual structural knowledge during denoising. This enables the generation of more valid and stable periodic materials while also supporting conditional generation from natural-language descriptions. Overall, the thesis establishes a unified AI-based framework for data-efficient property prediction and controllable crystal generation, demonstrating how graph learning, multimodal representations, and generative models can reduce computational cost and improve the scalability of materials

Spherical p-spin models provide a mean-field framework for glassy dynamics. Coupling such systems opens a controlled way to probe how they evolve jointly, develop cross correlations, and possibly share common aging scales. We study spherical p-spin systems with site-independent inter-system couplings and generally correlated quenched disorders. We derive closed multi-subsystem two-time equations for correlations, responses, and spherical constraints. A marginal one-step replica-symmetry-breaking construction provides static benchmarks for overlap plateaux, aging crossover scales, and effective temperatures. We then specialize to two ferromagnetically coupled p=3 systems and compare dynamical data with marginal 1RSB predictions. Independent quenched disorders reduce the equal-time correlation between the systems below its disorder-free value, while correlated disorders enhance it. For sufficiently strong coupling, finite-time fluctuation-dissipation estimates within and between the systems are compatible with a common effective temperature even when one or both subsystems would equilibrate as a paramagnet in isolation. This common value lies above the effective temperatures that the constituent systems would have separately and increases with disorder correlation and coupling strength. The marginal 1RSB value T/m captures these trends but is slightly below the finite-time dynamical estimate. For weak coupling, the dynamical results instead suggest that two aging regimes develop for each system, with partial equilibration within each. We perform a marginal replica analysis with two-step breaking, whose predictions compare favorably with the numerical measurements. Our numerical accuracy is insufficient to determine whether the observed finite-time crossover will eventually become a sharp transition.

Consider a branching random walk (BRW) of depth $n$ with standard Gaussian increments, conditioned on all endpoints lying in an interval of radius $r$ (which may depend on $n$), i.e. a small ball event. We prove that this conditioning results in exponential decay of correlations between the endpoints, with correlation length $O(r)$. Our proof is based on the renormalization group, which in this context captures the effect of the endpoint conditioning on earlier steps in the walk. This effect can be separated into so-called relevant and irrelevant parts, and in our setting the relevant part makes the conditioned BRW behave like a branching Ornstein-Uhlenbeck walk for the first $n-O(r)$ steps, leading to the correlation decay. The irrelevant part shrinks in a nontrivial manner, and the simplest argument to bound it uniformly only yields correlation length $O(r^2)$. To achieve the optimal $O(r)$ bound, we establish that the irrelevant part shrinks horizontally in space before decaying uniformly. The BRW is a prototypical example of a log-correlated Gaussian field, and it forms the basis of many hierarchical field theories in the mathematical formulation of quantum field theory. As such, we present our results in a general form which is applicable to other hierarchical field theories with confining potentials, of which the small ball conditioned BRW is an example. We apply our general result to two other models: first, the sinh-Gordon model which has a strictly convex potential, so at the level of covariances the model behaves like one with a quadratic potential, i.e. the model has a positive mass. Second, we consider generalizations of the $\phi^4$ model with any power $\alpha \geq 2$; as $\alpha$ increases from $2$ to $\infty$, these power potentials naturally interpolate between the massive (quadratic) potential and the infinite square well potential of the small ball event.

The area compressibility modulus is a key descriptor of lipid membrane mechanics, but the molecular interactions that determine this elasticity are not evident from the total modulus alone. Here, molecular dynamics simulations of a POPC bilayer described by the coarse-grained Martini 3 force field were combined with virial stress analysis to decompose the area compressibility modulus into contributions from molecular groups and their interactions. Partial lateral tensions were evaluated as functions of membrane area strain, and their derivatives at the equilibrium state were used to obtain the corresponding contributions to the area compressibility modulus. Hydrocarbon chains provided the dominant positive contribution, accounting for approximately 70% of the total modulus, whereas water-lipid interactions contributed approximately 30%, predominantly through water-headgroup interactions. Within the bilayer, the headgroup and headgroup-chain contributions were of similar magnitude but opposite in sign and nearly canceled. Direct intermonolayer interactions contributed only about 3% of the bilayer-only modulus, indicating an almost additive elastic response of the two monolayers. The hierarchy of elastic contributions differed markedly from that of equilibrium partial tensions, showing that interactions responsible for static stress balance are not necessarily those governing membrane stiffness. This decomposition provides a microscopic interpretation of lipid bilayer area elasticity.

Normally strong and tough, steel$\unicode{x2014}$with iron as its base$\unicode{x2014}$falls prey to severe embrittlement when infiltrated by hydrogen; the insights into why are not well understood. This work explores how hydrogen affects bond strength in iron during fracture and why it reduces cohesion between fracture surfaces, laying bare the central role of electrostatic repulsion.

$\text{SiGeSn}$ alloys are promising silicon-compatible semiconductors for monolithic infrared photonics. However, their metastable nature limits the thermal budgets available for post-growth device processing, and the mechanisms governing their thermal degradation remain unresolved. Here, we investigate the thermal stability of $\text{Si}_{0.08}\text{Ge}_{0.83}\text{Sn}_{0.04}$ alloys using in situ spectroscopic ellipsometry (SE) during isothermal annealing at 550 {\deg}C. We show that adding an ultrathin oxide cap kinetically suppresses Sn exchange with the free surface while leaving bulk diffusion pathways largely unaffected. Uncapped films undergo phase separation after 50 min, accompanied by void formation, a 60% thickness reduction, and a 400 meV blueshift of the $E_{2}$ critical point (CP) transition, consistent with substitutional Sn depletion from the probed volume through surface segregation. In contrast, oxide-capped films exhibit a small compositional change (<1 at.% Sn) and optical shift (<20 meV) over the same period, with suppressed void formation, strain relaxation, and alloy decomposition. This surface-kinetic control additionally yields a 25-fold reduction in contact resistivity relative to annealed uncapped alloys. These results identify surface Sn transport as the dominant degradation pathway in SiGeSn and demonstrate that an ultrathin oxide cap extends the thermal stability of metastable group-IV alloys, providing a practical route toward their integration into advanced silicon photonic and electronic platforms.

Circularly polarized light can open a topological gap in a gapless Dirac system, creating a Floquet-Chern insulator. However, its Berry curvature has not been directly resolved. Here we use circular-dichroism time- and angle-resolved photoemission spectroscopy (Tr-ARPES) to map the light-induced Berry curvature of Floquet-Bloch states on the surface of Bi$_2$Se$_3$. By comparing spectra for opposite helicities of the mid-infrared pump, we isolate the induced geometric response. We observe alternating-sign Berry-curvature features at Floquet gaps that repeat at intervals set by the pump photon energy and redistribute with pump field strength in agreement with calculations for a periodically driven Dirac Hamiltonian. Both the induced Berry-curvature and the Floquet Dirac gap decay faster than the replica intensity, showing that spectral replicas can persist even after coherent Floquet hybridization weakens. These results establish momentum-resolved Berry-curvature mapping as a direct probe of light-induced topology and coherent Floquet band formation.

The absolute capacity of dense associative memory has mainly been analyzed for unbiased patterns. Here we examine the effect of bias in centered binary patterns under the Krotov-Hopfield single-site criterion $P_{\mathrm{error}}=1/N$, where $P_{\mathrm{error}}$ is the probability that a single-site flip lowers the energy of a stored pattern and $N$ is the number of neurons. Each pattern component takes $1-q$ with probability $q$ and $-q$ otherwise, where $0<q\le1/2$. For polynomial interactions of order $n$, a signal-to-noise analysis gives an absolute capacity of order $N^{n-1}/\ln N$ at $q=1/2$. For fixed $q<1/2$, however, the capacity is $O(N^{n/2})$ for even $n\ge4$ and $O(N^{(n+1)/2})$ for odd $n\ge5$. For $n=3$, both the unbiased and fixed-bias capacities remain $O(N^2/\ln N)$. For $n\ge4$, these different asymptotic forms imply a nonuniform large-$N$ limit near $q=1/2$. Asymptotic matching predicts a bias-induced crossover in the region $1-2q=O(\ln N/N^{\lfloor n/2\rfloor-1})$. The crossover originates from a bias-dependent crosstalk mean that reduces the stability of sites carrying the more frequent value $-q$. Computer simulations are compared with the finite-size conditioned-Gaussian predictions. An activity-dependent control potential that cancels the conditional crosstalk mean restores the $N^{n-1}/\ln N$ capacity for fixed $0<q<1/2$ within the conditioned-Gaussian approximation.

Metastable $\beta$ titanium alloys are attractive for biomedical and structural applications owing to their low elastic modulus, high specific strength, and excellent corrosion resistance. Laser powder bed fusion (PBF-LB) enables complex-shape production and controlled compositional variation through powder blending. However, processing elemental Ti-Nb blends often results in chemical heterogeneity from incomplete dissolution of Nb-rich particles and non-equilibrium phase formation. To address this, low-modulus Ti-Nb-Fe-Sn alloys were produced by PBF-LB using Ti-42Nb, Ti-20Nb-15Fe, and Ti-20Nb-20Sn master-alloy powders blended with commercially pure Ti. Ti-23Nb-3Fe-4Sn, Ti-26Nb-2Fe-4Sn, Ti-29Nb-1Fe-4Sn, and Ti-32Nb-4Sn were fabricated using an uncommonly large 70 $\mu$m layer thickness with layer remelting, followed by heat treatment at 1000 $\deg$C for 2 h and water quenching. After heat treatment, all alloys exhibited low porosity, homogeneous chemical distribution, and single $\beta$-phase microstructures with predominantly equiaxed grains and weak crystallographic texture. Thermodynamic calculations indicated that solidification descriptors alone could not explain the non-monotonic grain-size evolution, which was attributed to inherited solidification structure, transient TiFe-like phase formation, Nb/Sn partitioning, and/or solute-drag-controlled $\beta$-grain growth. Hardness and yield strength decreased with decreasing Fe and increasing Nb contents, from 268 to 224 HV and 691 to 468 MPa, respectively. Young's modulus, determined by resonant ultrasound spectroscopy, ranged 63-81 GPa. These results demonstrate that pre-alloyed master-alloy blends combined with remelting and heat treatment provide an effective route for producing chemically homogeneous Ti-Nb-Fe-Sn $\beta$ alloys while revealing how small compositional changes govern grain-growth behavior and mechanical response.

We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.

Electron-phonon interactions underpin a variety of phenomena, ranging from transport and superconductivity to polarons and ultrafast carrier dynamics. Despite being one of the most intensely studied subjects in condensed matter physics, research on electron-phonon physics mostly focused on linear, first-order couplings. Second- and higher-order nonlinear couplings are commonly ignored because their calculations are too demanding and we lack computational frameworks that can provide both diagonal and off-diagonal coupling matrix elements. In this work, we report a theory and computational method for computing nonlinear electron-phonon interactions of any order in real materials. Our approach combines the advantages of unit-cell calculations of electron wavefunctions and supercell calculations of phonon perturbations, is systematically improvable, can be used with either semilocal or nonlocal exchange-correlation functionals, and is amenable to Wannier-Fourier interpolation. As a first proof of concept, we illustrate this method by computing second-order electron-phonon coupling matrix elements in diamond, lithium fluoride, and graphite as representative nonpolar semiconductors, polar semiconductors, and metals, respectively. Furthermore, we generalize the ab initio polaron equations to second-order electron-phonon couplings, and we show that second-order couplings are essential to achieve quantitative accuracy in polaron formation energies and hopping barriers. The present methodology will find application in the study of all properties and phenomena that are currently being investigated within the linear electron-phonon coupling approximation, from phonon-mediated superconductivity to excited-states dynamics, both in harmonic and anharmonic systems.