Papers

Grain-boundary chemistry is central to the coercivity and thermal stability of Nd2Fe14B permanent magnets, particularly in recycled magnets where recovery of the hard-magnetic phase does not by itself restore the intergranular microstructure. Our recent experimental study showed that nanoscale ZrB2 precipitates can emerge at grain boundaries and triple junctions during recycling despite an overall Zr concentration of only about 0.1 at.%, where they are associated with boundary stabilization and suppression of grain coarsening. Here we use spin-polarized density-functional theory with a Hubbard correction (DFT+U) to determine the atomistic thermodynamics underlying this preferential localization. A systematic set of composition-matched bulk/grain-boundary DFT+U supercells provides a common correlated-electron description across boundary chemistries. We compare B, Zr, Dy, and ZrB2-like local configurations in bulk and grain-boundary environments of Nd2Fe14B. Excess B is strongly stabilized at the boundary, while Zr also shows an independent thermodynamic preference for the interfacial region. When Zr and B are combined in a ZrB2-like configuration, the boundary preference is retained, indicating that the interface remains favorable as Zr-B coordination develops. These results establish a thermodynamic pathway for the co-localization of Zr and B prior to ZrB2 formation. Magnetic-state analysis further shows that all compared structures remain within the same high-moment Fe-sublattice regime, and boundary-localized defects generally perturb the normalized magnetization less than their matrix counterparts. The calculations therefore provide a first-principles explanation for why Zr-B chemistry concentrates at intergranular regions and how such boundary-localized states can support the microstructural stability required for high-coercivity recycled Nd-Fe-B magnets.

Eutectics offer a route to overcome plastic incompatibility in disparate-phase heterostructures by coupling microstructural refinement with phase-specific chemical and crystallographic hierarchy. Here, we investigate laser-rapid-solidified Al-(Si,Ge) eutectic composites designed along the univariant ternary eutectic path, solidifying with an Al-rich face-centered cubic (fcc) matrix and (Si,Ge)-rich diamond-cubic (dc) fibers as constituent eutectic phases with faceted interfaces. The microstructure was hierarchical in nature with finer structures within eutectic phases: nanoscale (Si,Ge) clusters in the Al phase and growth twins within the (Si,Ge) fibers with some Al retention. Although increasing Ge content coarsens the eutectic spacing, the yield strength is slightly enhanced compared to the relatively finer Al-Si, and tensile ductility of Al-(Si,Ge) is higher than that of Al-Si. In situ SEM micromechanical testing combined with post-mortem STEM and TEM showed that in the Al-rich phase, Ge segregated to the deformation-induced sub-grain boundaries that confined glide dislocations. Simultaneously, the (Si,Ge)-rich fibers remain crack-resistant at large plastic strain and exhibit deformation-induced planar faults, consistent with localized partial-dislocation activity at highly stressed interfaces and twin boundaries. These coupled mechanisms due to interface confinement and hard phase chemistry enable co-deformation of the metallic and covalent phases, providing a pathway for designing high-tensile-strength and ductile hierarchical eutectics beyond conventional length-scale-controlled strengthening.

We propose a symmetry-preserving Boson-informed neural network (BINN) for the variational Monte Carlo computation of interacting-boson ground states in continuous space. The framework explicitly separates the two dominant physical scales of the system. At the microscopic interaction scale, a cell Jastrow factor absorbs the leading near-contact stiffness, while at the macroscopic scale, a potential-aware envelope encodes the external confinement, leaving the neural network to capture a smoother many-body residual. Across both two- and three-dimensional tests, the BINN approaches the Hartree and Gross-Pitaevskii limits with an empirical $\mathcal{O}(N^{-1})$ finite-size trend in both energy and density. The energies agree with diffusion Monte Carlo to within $0.06\%$ for the particle number tested up to $350$ in the three-dimensional shrinking-range case. Applications are made under various trapping scenarios, justifying robust performance of BINN.

The conventional interpretation of elastomeric fracture treats the tearing energy G as an output determined by tear speed, taken to equal crack velocity vc, concluding that higher vc produced greater viscoelastic dissipation to increase G. Based on spatially and temporally resolved polarized optical microscopic (str-POM) measurements of tip stress tip stress, we use prenotched pure shear experiments to clarify the causality: Local crack-tip stress determines the network lifetime, making vc the passive kinetic output. In the elastic limit that can be readily achieved for a well crosslinked elastomer in a wide range of temperatures, Rivlin-Thomas scaling holds, and vc depends only on the applied strain, independent of stretch rate, indicating one-to-one correspondence between vc and tip stress. In a highly stretchable elastomer made with reduced crosslink density, vc no longer correlates well with the far-field load as rate-dependent viscoelastic processes emerge to affect network lifetime. Because of the rheological effects on how chain tension builds in the elastomeric network, vc is higher at a common nominal strain when it is imposed with higher stretch rate. confirm that different stretch rates produce different levels of tip stress. The same tip stress still produces the same vc. With str-POM measurements we are also able to elucidate the nature of temperature dependence: at a given tip stress,, crack growth is slower at lower temperatures; conversely it requires higher tip stress to produce the same vc at lower temperatures.

Appeals to typicality are common in physics, but it is often unclear what it means for a physical state to be typical relative to a probability measure, and correspondingly unclear what a law that appeals to typicality asserts. Here we consider how one might characterize physical typicality using ideas from the theory of algorithmic randomness. As a concrete example, we show how taking a physical state to be typical relative to a computable measure when it is Martin-Löf random allows one to formulate the distribution postulate in Bohmian mechanics as a statistical constraining law of the theory. Using a toy model, we show how this constraint guarantees the standard Born statistics for computable experimental protocols. Algorithmic Bohmian mechanics (aBM) thus illustrates how algorithmic randomness may be used to provide precise content to a statistical law.

We numerically implement full quantum circuits of optimal tapered Quantum Phase Estimation (in the form of an implementable approximate bandwidth-limited DPSS taper) for the purpose of minimum eigenvalue computation, where the Hamiltonian time-evolution unitary is implemented using standard Trotterization, and the taper state is constructed using an optimized bandwidth-limited taper. We illustrate, on representative quantum Hamiltonians, with tractable exact classical numerical quantum circuit simulations, how tapered QPE performs with respect to optimal phase sampling rate, absolute error, Shannon entropy of the optimal phase distribution, when the tQPE algorithm parameters are changed. Those algorithm parameters are Trotter error, finite sampling, imperfect initial states, total evolution time, and digitization error (number of phase qubits). The reported numerical experiments include up to $\ell=10$ phase qubits of precision with $m=3$ additional phase-register error suppression qubits, on a $4$-qubit Heisenberg quantum magnet model Hamiltonian, using up to 12th-order Trotterization. We numerically show i) the steady-state optimal phase sampling rate is determined by the initial state overlap with the ground-state, ii) with respect to phase sampling probability, or overall eigenvalue sampling error rate, there is no strong evolution time dependence for tQPE unless there is high Trotter error, iii) the approximated time-evolution unitaries in tQPE, like in standard QPE, can result in substantial ringing, which leads to non-physical eigenvalue estimates.

We present magnetic-field-dependent evolution of magnetization and spin dynamics in the quasi-two-dimensional spin-$1/2$ magnet $\mathrm{Cu_2(OH)_3Br}$, consisting of alternately coupled ferromagnetic Cu1 and antiferromagnetic Cu2 spin chains. Terahertz spectroscopy reveals a pronounced field-direction dependence of the low-energy magnetic excitation spectrum. For magnetic fields applied perpendicular to the spin chains, $B\parallel a$ and $B\parallel c^*$, the spectra undergo abrupt reconstructions at the spin-flop transitions identified independently by high-field magnetization measurements. For $B\parallel b$, by contrast, no spin-flop occurs; instead, the excitation spectrum evolves continuously with field and exhibits a strong terahertz radiation polarization dependence as the ferromagnetic Cu1 subsystem becomes progressively polarized. At higher fields, the complex low-field spectrum is replaced by a reduced set of broad excitations, consistent with a weakening of the coupling between the ferromagnetic and antiferromagnetic chain subsystems. Complementary Raman spectroscopy resolves magnon and spinon excitations alongside several phonon modes and traces the characteristic temperature- and magnetic-field-dependent evolution of the magnetic excitations. The combined spectroscopic and magnetization results map out how a magnetic field reorganizes the coupled ferromagnetic and antiferromagnetic subsystems in $\mathrm{Cu_2(OH)_3Br}$ across field-induced phase transitions.

Non-homogeneous, non-magnetic impurities in superconductivity have recently gained traction as a promising approach to reduce surface resistance and increase the superheating field. We aim to deepen the understanding of impurities' role from a theoretical perspective by utilizing Eilenberger's equation, and to investigate the validity of a more phenomenological approach based on London's equation for determining the magnetic field profile within the superconductor. We show that the microscopic and macroscopic theories produce identical electromagnetic field distributions for any spatial distributions of impurities inside the superconductors. However, the two approaches provide different magnetic field-related quantities. The macroscopic model only gives the Bean-Livingston barrier, while the microscopic theory provides the experimentally-relevant superheating field. Based on the microscopic formalism, we determine a family of impurity profiles that make the superheating field $H_{\rm{sh}}$ equal to the critical field $H_c$, which is the maximum achievable.

Precisely timed, multi-device control in atomic, molecular and optical physics is provided by specialized real-time systems, which impose their own terms on the description of the experiment: a program over a global clock, in which every stage boundary is an absolute time computed from everything preceding it. Such descriptions are tightly coupled – changing one stage affects all later ones – and are correspondingly hard to reuse, inspect, or move elsewhere. We introduce Wigner Time, a Python package in which the experimental procedure is instead represented as data: a table of timed updates, assembled by composing functions and referred to named points in the experiment rather than to absolute instants. Hardware enters only at a final conversion step, leaving the description readable and back-end agnostic. Wigner Time has run two cold-atom setups for more than two years, where replacing a hand-written real-time program improved the achievable temporal resolution five-fold; the design applies to any domain requiring precise multi-device timing.

Electrical control of topological magnetism is central to realizing energy-efficient topological spintronics. Yet most electric-field approaches modify the competing magnetic interactions through a nonselective rearrangement of low-energy electronic states, yielding coarse magnetic phase control that often requires external magnetic fields to stabilize topological quasiparticles, while few schemes solely based on electric fields are restricted to specific conducting materials. Here, we establish a general approach for purely electric-field control of topological magnetism, in which an applied electric field electrostatically dopes a selected orbital-angular-momentum-polarized band edge of a two-dimensional (2D) van der Waals (vdW) magnetic semiconductor via proximity to an adjacent nonmagnetic vdW metal. We show that the resulting electrostatic doping predominantly tunes magnetic anisotropy of the 2D magnet, while leaving exchange interaction and Dzyaloshinskii-Moriya interaction nearly unchanged, thereby reversibly driving the system through ferromagnetic, skyrmion, spiral, and bimeron phases. We demonstrate this mechanism for CrBr3/graphene and Cr2Ge2Te6/TaS2 vdW heterostructures hosting electron and hole pockets of different orbital characters. These results establish a broadly applicable strategy for purely electric-field control in topological spintronics.

Synchro-shear is the primary plastic deformation mechanism in Laves phases at elevated temperatures, mediated by synchro-Shockley partial dislocations-zonal dislocations that proceed via localized events such as kink-pair nucleation and propagation. Using atomistic simulations, we identified a novel slip mechanism in Laves phases, namely coupled synchro-shear slip, involving the synchronized glide of two synchro-Shockley partial dislocations on adjacent slip planes, leading to the formation of extrinsic stacking faults. High-resolution scanning transmission electron microscopy revealed the extended core structures consistent with coupled synchro-Shockley partial dislocations bounded by extrinsic stacking faults in C15 NbCr2 and their involvement in twinning. These results highlight the critical role of coupled synchro-shear slip in enabling phase transformations between Laves polytypes and in governing twinning behavior, providing new atomistic insight into the kinetic nature of plasticity in topologically close-packed intermetallic phases.

As CMOS technology continues to scale, metallic interconnects increasingly limit circuit performance through rising resistivity, self-heating, and reliability degradation. Although several alternative metals have been proposed, a quantitative framework for evaluating their transport performance under nanoscale confinement remains unavailable. Here, we establish a transport framework by combining independently measured thermal and electrical conductivities with normalized and unnormalized transport figures of merit. We apply this framework to Cu, Ru, W, Co, Ir, and Mo thin films using new steady-state thermoreflectance measurements of Mo, Co, and Ir together with previously reported Cu, Ru, and W data. While Cu exhibits the highest intrinsic transport performance, its effective performance is substantially reduced by thickness scaling and Ta liner resistance. In contrast, Ru and Mo maintain favorable transport properties while enabling barrierless integration, identifying them as promising candidates for next-generation CMOS interconnects

Magnetism has been a central theme of research in chemistry, physics, and materials science, with chemical composition and bonding playing key roles in determining magnetic behavior. Altermagnets are a newly identified class of magnetic materials that combine features of conventional ferromagnets and antiferromagnets, arising from specific symmetry and electronic structure motifs. In this review, we present a chemistry-driven viewpoint on altermagnetism, highlighting how crystal chemistry, bonding, and electronic structure enable this unconventional magnetic order. We begin by introducing the fundamental concepts required to understand altermagnets, with an emphasis on symmetry considerations, orbital character, and electronic structure signatures. We then survey the diverse material families in which altermagnetism has been identified, drawing attention to coordination environments and structure-property relationships that favor altermagnetic order. We subsequently present experimental approaches which are useful for the characterization of altermagnetic materials. We examine ab initio materials discovery as a promising strategy for identifying new altermagnets, emphasizing how chemical constraints, such as symmetry and bonding, can guide computational searches. Other than their intrinsic importance, altermagnets provide interesting possibilities for technology. For this reason, we highlight possible applications that may be enabled through altermagnetic materials, along with their coupling with existing orders such as ferroelectricity and superconductivity. In conclusion, we point out some challenges and prospects, where chemically-based design guidelines can play an important role towards advancing altermagnetism research. In summary, this review offers an account of recent developments in altermagnetism, from basic concepts to the current state-of-the-art.

Nanothermodynamics describes the process where large systems subdivide into equilibrium distributions of small subsystems. A key ingredient is Hill's subdivision potential (E) that ensures adherence to the 1st and 2nd laws of thermodynamics in systems of any size. In this review and reassessment, it is emphasized that nanothermodynamics gives new insight into many measurements, theories, and simulations. Measurements establishing the need for nanothermodynamics show thermodynamic heterogeneity from multiple effective temperatures (T_i) inside most types of materials. One theoretical result that requires E=0 is the stable solution of Ising's original model for finite chains of interacting spins, a solution Ising could not have found 40 years before Hill's work. Another result is a novel solution to Gibbs' paradox that makes the entropy of the semiclassical ideal gas exactly extensive. Molecular dynamics simulations reveal how a standard fluctuation relation is modified when local degrees of freedom fluctuate faster than their coupling to the heat bath, consistent with the measured thermodynamic heterogeneity. Simulations of a Creutz-like model, comprised of Ising spins coupled to an explicit heat bath of Einstein oscillators, are used to study the 2nd law. It is found that maximizing the total entropy (S_t) requires an intrinsically irreversible step, providing a counterexample to the usual claim that statistical mechanics emerges from reversible dynamics. Furthermore, fluctuations of this model are best described by Einstein's reversal of Boltzmann's relation and the 2nd-law, not by recent fluctuation theorems.

Evaporating sessile water droplets universally deposit surface charges while simultaneously becoming self-charged—a phenomenon that remains under-appreciated despite its potentially important consequences. Here, we investigate one such consequence: droplet self-propulsion driven by self-charging. This self-propulsion arises spontaneously in the absence of external stimuli and produces self-avoiding trajectories that can displace droplets by many times their own diameter. Our results have important practical implications for processes requiring spatial precision, such as inkjet printing. The coupling between self-charging and self-propulsion produces mosaic surface charge patterns characterized by alternating polarities, which we explain with a physical model based on properties of the electric double layer.

Topological materials provide a transformative arena for light-driven control of electronic motion; yet, direct manipulation of electron dynamics on sub-cycle timescale remains a significant challenge. We demonstrate that the strong-field-driven high-harmonic generation of a Weyl semimetal can be controlled and manipulated through bicircular pump-probe driving fields. While a lone probe pulse generates exclusively odd-order harmonics, the addition of a pump pulse triggers a series of sidebands arising from nonlinear frequency mixing of pump and probe photons. Our results reveal that the sideband intensities are highly sensitive to the relative helicity of the pulses and the orientation of the polarization plane. This sensitivity stems from the chiral nature of the Weyl nodes, which couples efficiently to the light's helicity only when the node-separation axis is perpendicular to the polarization plane. Furthermore, the significant suppression of sideband intensity with increasing pump-probe delay identifies these features as a potential clock for electron-hole decoherence. These findings establish frequency-mixed high-harmonic generation as a sensitive probe of chiral quantum dynamics and suggest a robust framework for manipulating topological currents via structured light, with implications for lightwave electronics and ultrafast quantum information processing.

In this work, we investigate surface polaritons (SPs) arising at the interface between a simple dielectric and a bi-isotropic medium, in the lossless regime and in the presence of small losses. For the former, non-Dyakonov surface polaritons can arise for positive permittivities and magnetoelectric parameters. General restrictions on the permittivities and bi-isotropic parameter (existence conditions) are derived. For the latter, the effect of small losses is considered, and the characteristic surface plasmon-polariton lengths are discussed. The propagation length can exhibit a local maximum for specific values of the magnetoelectric parameter, an unusual new behavior that can be regarded as a signature of these chiral surface polaritons. Surface waves in an interface involving a bi- isotropic medium with an anomalous Hall effect (AHE) are also examined. Multiple configurations for their occurrence are obtained, revealing a richer scenario with distinct regimes of propagation and coexistence in the parameter space. The presence of a non-null AHE contribution creates a magnetoelectric range for which the surface wave propagation is forbidden, providing an additional signature of surface-polariton propagation in bi-isotropic media with an AHE contribution.

Metastability in open quantum systems is usually inferred from spectral separation in the Liouvillian, which governs unconditional, ensemble-averaged dynamics. We show that this diagnosis is incomplete at the level of individual quantum trajectories: conditioned realizations of the same unconditional dynamics can bypass, transiently access, or operationally preserve a metastable memory, depending on the monitored channel and the observed record. We demonstrate these mechanisms in a driven-dissipative nonlinear oscillator realizing a quantum associative memory, by comparing spectra, target fidelities, and phase-space distributions. The non-Hermitian dynamics obtained by post-selecting on the absence of detected events supports metastable retrieval, but with a distinct long-time fate: normalization selects the least-decaying mode of the non-Hermitian spectrum rather than the addressed memory branch. In contrast, stochastic jump trajectories can preserve retrieval over extended times when the post-measurement update remains compatible with the coherent memory structure. Thus trajectory-level metastability is not determined by the averaged generator alone; it requires compatibility between the monitored channel, the measurement record, and the metastable manifold.

Quasicrystals lack the translational symmetry that underlies Bloch decomposition and Brillouin-zone integration, making full-band momentum-resolved electronic structure difficult to formulate and compute. We develop a systematically convergent reciprocal-space tight-binding framework for a broad class of quasicrystals. The method combines two systematically refinable components: a Fourier-module scattering-channel Hamiltonian that yields local spectral and current-current correlation quantities at each physical momentum, and an expanding hierarchy of pseudo-Brillouin zones that converts the resulting local quantities into bulk thermodynamic observables through an exact local-to-global relation. Applied to the Penrose and Ammann-Beenker models, the framework uncovers full-band momentum-resolved quasibands and a multichannel mechanism for pseudogap formation, both beyond the scope of low-energy effective models. It further resolves Zeeman-driven gap closings and reopenings, quantized Chern plateaus, and the phason invariance of bulk spectral and topological observables. This framework provides a unified reciprocal-space route to full-band spectral and topological properties of quasicrystals.

Quasicrystals occupy a distinctive position between the translational order of crystals and the disordered amorphous matter. Simulating this physics has remained challenging, since quasiperiodic structures lack the translational symmetry exploited for crystals and generally require costly diagonalization of large finite approximants. Quasicrystalline order admits two equivalent descriptions, a cut-and-project scheme from a higher-dimensional periodic crystal, and a discrete set of substitution rules acting on a finite alphabet. We show that the latter, written in a numeration system adapted to the substitution, defines a deterministic finite automaton with output, the digits of a site index are fed, and the automaton returns the letter occupying that site. We further exploit another equivalence to a different construction, the transition matrices are exactly the tensors of a matrix product state, whose bond dimension is the number of automaton states and is independent of system size. This allows efficient representation of extremely large tight-binding Hamiltonians in the tensor-train language, thereby yielding an exact matrix product operator for the quasicrystal Hamiltonian at any system size. We show how this framework works for two families of one-dimensional quasicrystals, the metallic-mean and $k$-bonacci families and we explicitly construct the Fibonacci, silver-mean, and Tribonacci quasicrystals. By leveraging efficient tensor-network compression and the kernel polynomial method, we compute spectral densities for chains with more than $10^9$ sites and directly resolve the hierarchical structure of the spectrum.

3D metal-organic frameworks (MOFs) are well known effective hosts for luminescent guests that improve tuneability, photostability and material fabricability. 2D guest@MOF systems, while less explored, offer competitive advantages over 3D guest@MOF systems due to their optical transparency, inter-layer spacing, and vertical thinness. This work examines luminescent organic dyes@ZIF-L to establish the underlying mechanisms of guest incorporation in ZIF-L and demonstrate the advantages of the 2D ZIF-L architecture for the material's functional luminescence. Analysing a case study system, fluorescein@ZIF-L (F@ZIF-L), using nanoscale FTIR, diffraction, and topology mapping, confirmed that fluorescein (F) resided in the ZIF-L framework cavities. Supported by surface energy simulations, the extent of guest incorporation was found to be indicated by a morphological continuum, from the characteristic leaf-shaped ZIF-L to rectangular F@ZIF-L. By modifying synthesis temperature and solvent ratios, the luminescent properties of F@ZIF-L could be rationally tuned in terms of guest loading (% mol) and arrangement (i.e. guest monomer to aggregate ratio). When optimised, F@ZIF-L exhibited tuneable emission chromaticity, 99.7% photoluminescent quantum yield, minimal guest leaching in solution over 12 months, and high photostability. Perylene@ZIF-L exhibited unique white light emitting properties, with CIE coordinates (0.33, 0.34) arising from a combination of yellow alpha-phase excimer and blue monomeric perylene emission. Finally, oriented luminescent thin films of guest@ZIF-L materials were grown on malleable Zn foils, demonstrating an in situ fabrication technique. Together, the work highlights the potential for luminescent dye@ZIF-L systems in developing tuneable and resilient luminescent components of next-generation optoelectronics, sensors, and lighting systems.

Oxidation and ablation of 200 nm tantalum films were carried out by three routes: (i) femtosecond (fs-)laser direct write, (ii) high-temperature annealing (HTA) in a tube furnace, and (iii) annealing in a 2.45 GHz microwave cavity. Complete conversion of the 200 nm Ta layer into 409 nm of Ta2O5 required one hour at 600 C in the furnace, but only minutes at ~ 50 W of microwave power. Fs-laser (515 nm/200 fs) oxidation of the Ta nano-film set in at an average single-pulse fluence of ~ 0.1 J/cm2 under strong pulse-to-pulse overlap (900 pulses per focal spot), i.e. within a narrow window bounded from above by the onset of ablation. Under microwave annealing, both the cavity resonance frequency and the quality factor Q changed markedly at the metal-to-oxide transition, reflecting the collapse of the real and imaginary parts of the permittivity at 2.45 GHz. This dielectric contrast turns the cavity into a sensor: the oxidation can be followed in real time from the shift of the cavity resonance, providing a non-invasive, in-situ diagnostic tool.

We present an extended Ginzburg-Landau (GL) method for calculating the superconducting coherence length and magnetic penetration depth at temperatures well below the transition temperature $T_{\mathrm c}$. In contrast to conventional GL theory, which expands the free energy in both the order parameters and their gradients, our method applies a perturbative expansion only to the covariant-gradient terms, while retaining the full dependence on the superconducting order parameters. The coefficients of these terms are determined from finite differences of microscopic free energies evaluated at small imposed pair momenta. The method applies to both single-band and multiband superconductors and therefore provides a framework for incorporating more realistic electronic structures. For the models examined here, the extended GL method agrees well with real-space Bogoliubov-de Gennes (BdG) calculations over a wide temperature range, while requiring substantially less computational effort.

Rotating magnetic microparticles are building blocks for field-driven assembly and microrobotic control. As the elementary interaction rule for larger assemblies, pair motion in these systems is governed not only by magnetic forcing, but also by hydrodynamic coupling and other long-range interactions. Here we develop a reduced framework for two synchronized rotating magnetic particles by resolving the interactions into radial components that change the interparticle distance and transverse components that rotate the line of centers. The competition between magnetic dipolar interaction, additional radial repulsion, and rotation-induced transverse coupling selects three pair-motion modes: rigid-body rotation, contact-separation rotation, and irreversible separation. We derive transition criteria for the rigid-body state, reversed orbital motion, and the separation boundary, and obtain an asymptotic solution for the separation dynamics. Lattice Boltzmann simulations of particles rotating near a wall provide a hydrodynamic realization of the model, in which inertial secondary flow generates radial repulsion and rotational flow produces transverse coupling. The resulting phase diagram in the physical $(\mathrm{Re},C_m)$ plane is consistent with the reduced-model predictions. These results provide design rules for programming elementary pair interactions in rotating magnetic-particle systems and may help guide the control of microrobotic assemblies.

A static deformation of graphene can act on its Dirac electrons as a valley-odd magnetic field. In sublattice-gapped graphene this field makes the two valleys add in the parity-odd response rather than cancel. We derive the equilibrium thermodynamics of this effect and separate it from the finite-frequency transport response. At fixed electrochemical potential, reversing the pseudomagnetic field removes every nonzero pseudo-Landau level in the continuum theory. The remaining grand-potential difference is fixed by the spectrally asymmetric zeroth level. The static charge response is a thermally broadened plateau confined to the gap and has no metallic $m/|\mu|$ tail. Near a band edge, pseudofield reversal transfers $\mathrm{B}\ln2$ of entropy per unsplit zero-mode state in the low-temperature window. The fixed-$\mu$ heat capacity has two side lobes per edge and a universal peak $0.439229\,D_B k_{\mathrm B}$. We then formulate a definite constant-gate-voltage circuit and show that the measured sheet heat capacity depends on the electrical boundary condition. The full massive-Dirac density of states and an exact finite-field pseudo-Landau-level calculation give the same gate crossover in their common limit. At fixed carrier number, the low-temperature edge value is $-2(\ln2)^2 D_B k_{\mathrm B}$, rather than a node. A finite geometric capacitance gives a continuous and experimentally tunable interpolation. Finally, we give a trace-free triaxial strain geometry, a disorder–interaction window, and realistic calorimetric and quantum-capacitance scales. The field-reversal protocol isolates an equilibrium electromechanical anomaly without a real magnetic field.

Functional materials realize functionalities through pre-designed structures, whereas physical neural networks are trained by prescribing input-output behavior. Unifying these views would allow materials to acquire functions directly from dynamical tasks. Here we introduce an in situ local learning framework for dynamic network materials. A forward drive and a time-reversed adjoint error drive are applied to the same mechanical network, enabling the material to compute gradients of a time-domain loss through its own dynamics. The resulting update rules are local, compatible with the principle of physical learning. Each bond or node requires only co-located forward and adjoint fields. The method trains spring constants, nodal masses, bond damping coefficients and nodal damping coefficients, and programs dynamical functions including broadband wave cloaking, evanescent-wave imaging, passive transient output enhancement and vowel classification. These examples involve distinct physical mechanisms, such as wave scattering, near-field information transfer, dissipative non-normal dynamics and machine learning, but are obtained by simply changing the loss function, rather than leveraging expert knowledge. Therefore, dynamic network materials can act both as programmable matter and as physical neural networks, providing a route to material systems that learn temporal responses in situ.

Molecular and material properties, from the polarizability to the elastic constants, are described by tensors. Their behavior under rotations is made explicit when a tensor is decomposed into irreducible parts that transform independently. In Cartesian form these parts are the symmetric and traceless irreducible Cartesian tensors (ICTs), whose decomposition and coupling underlie selection rules, orientational averages, and the use of symmetry. The decomposition is a textbook result at rank two, but higher rank and the intrinsic symmetry of physical tensors make it nontrivial. What has been lacking, unlike in the well-established spherical formalism, is a general construction for a given intrinsic symmetry, together with reusable operators that extract the ICTs and rebuild the original tensor exactly. Here, we develop such a construction and obtain these operators explicitly. These operators depend on rank and symmetry alone, and therefore each need only be built once and then applied to any tensor of that class. Building on them, we further obtain the Cartesian harmonics of a vector and the operators that couple two ICTs into a third, both central to equivariant machine learning. The construction is demonstrated on the elastic tensor, in both its second-order form of rank four and its third-order form of rank six. The ICTs of the rank-4 tensor also define a rotation- and scale-invariant measure of anisotropy, which we evaluate across the first-principles elastic tensors of crystalline materials from the Materials Project. The construction is implemented in the open-source package natto, which produces the operators in both exact symbolic and numerical form.

The electromagnetic vacuum stress tensor in a system consisting of classical point-like atoms on a cubic lattice is derived directly from the electric field and, alternatively, using the known more phenomenological formula involving the (usually unknown) derivative of the dielectric tensor. The results agree. The stress tensor contains a nontrivial constant and therefore cannot be obtained from macroscopic electrodynamics alone. A system consisting of a mosaic of randomly oriented grains of a cubic crystal is used as a model of an amorphous solid. The electromagnetic stress tensor in this system is deduced by averaging the corresponding quantity in a cubic crystal over all orientations. Two components remain: the component in the direction of the electric field and the component perpendicular to it. The transverse component agrees with the analogous quantity for liquids derived by Peierls in an entirely different way.

The Normalized Energy Density (NED) was introduced in Goto et al.(2011) as a quantity that, unlike the conventional energy, is conserved across material interfaces in a layered elastic medium. Its conservation was proved analytically only for a two-layer structure; for three or more layers it was supported by Monte Carlo simulation. I supply the missing proof for a general multi-layer (n-layer) structure in the 2D SH problem. The key step is to stop treating the angular frequency as a single variable and instead lift the layer phases to independent coordinates on the n-torus. The obstruction identified in the original paper—that the ratio of travel-time combinations is generically irrational, so that the periodicity argument used for two layers fails and disappears, and the proof reduces to Weyl's equidistribution theorem combined with n repetitions of the same elementary integral used in the two-layer case. I prove conservation in two independent settings that together cover all cases of practical interest: travel times that are linearly independent over Q, and commensurable travel times, including the equal-travel-time (Goupillaud) discretization. I also show that an arbitrary layered structure can be subdivided by reflectionless interfaces into one whose travel times take only d distinct, Q-independent values, where d is the dimension of the Q-span of the original travel times; this places the two proved cases at the endpoints d=1 and d=n and isolates the remaining open case 1<d<n in a canonical form.

Diffusion sampling can be viewed as imaginary-time annealing of probability densities. From a forward/backward Euclidean Schrödinger pair, we show that fixing the noising drift forces the reverse score term, and that the same logarithmic force is the one-sided imaginary-time counterdiabatic connection of a supersymmetric Score Hamiltonian. The correspondence turns score-learning error into a Hamiltonian perturbation and yields a schedule principle: if the first $r$ terminal derivatives vanish, Morita–Nishimori boundary cancellation suppresses the residual Hellinger error from $T^{-2}$ to $T^{-2r-2}$ until score or sampling floors are reached. Reverse-SDE benchmarks, including two-dimensional learned-score tests, confirm the predicted improvement.