Papers

In this work, we investigate the finite-bias charge current, shot noise, and Fano factor in an Aharonov-Bohm interferometer composed of two parallel quantum dots, each side-coupled to a topological superconducting nanowire represented by an effective Kitaev chain hosting Majorana bound states at its ends. The transport properties are calculated using the nonequilibrium Green's function formalism within the equation-of-motion approach. Our results show that coupling to the Majorana bound states significantly modifies the interference pattern, producing distinctive signatures in the current, shot noise, and Fano factor. These signatures are particularly pronounced at the half-flux condition, where destructive interference suppresses the conventional transport background and enhances the visibility of Majorana-assisted transport. These findings demonstrate that finite-bias shot-noise spectroscopy provides a sensitive indirect probe of Majorana bound states in hybrid superconducting-nanowire interferometers.

Spintronic crossbars are promising hardware platforms for energy-efficient neuromorphic computing, but conventional magnetic tunnel junctions (MTJs) are binary, limiting the information density and synaptic precision of each crosspoint. Here, MuMax3 micromagnetic simulations are used to investigate how size and aspect ratio control the switching and remanent-state landscape of crossed-ellipse MTJ free layers, with permalloy as the main model system and CoFeB checks for transferability. At fixed 8:1 aspect ratio, shrinking the device from 16 micron x 2 micron to 80 nm x 10 nm lowers the absolute switching current but raises the switching field from about 11 Oe to about 301 Oe and increases the SOT current density. At fixed major axis 1.6 micron, aspect-ratio tuning produces a low-field four-state regime, while lower aspect ratios stabilize additional remanent states with lower switching fields and current densities. A 1.6 micron x 0.8 micron device exhibits twelve accessible remanent plateaus in its angle-resolved planar Hall response, with the resolved state count depending on both aspect ratio and absolute size. Projected MTJ readout gives multiple electrical levels, while minimum-energy-path calculations show that the twelve configurations are not all thermally independent. Independent MuMax+ calculations reproduce the multistate topology and reveal lower-barrier multistep escape pathways between nominally distant states. These results define a geometry-dependent design window for scalable multistate spintronic crossbar cells.

The characteristic feature of counterflow superfluids consisting of $N\geq 3$ components – the so-called Borromean supercounterfluids (BSCF) – is the presence of $N$ distinct elementary topological excitations (vortices) despite having only $N-1$ independent Goldstone modes. We show that this remarkable property clearly manifests itself at the Berezinskii-Kosterlitz-Thouless-type transition from the BSCF to the normal state, under the conditions of slight to moderate deviations from the case of exact intercomponent symmetry. More generally, our analysis also applies to any multicomponent superfluid with intercomponent drag fine-tuned to the value when certain composite vortices compete energetically with elementary ones.

Within the entire gamut of magnetostrictive, piezomagnetic, and ferromagnetic shape memory alloy systems, the striction effect is found to vary from a few tens of parts per million to a few percent. Here, we report the observation of an unprecedentedly large magnetic-field-induced lattice strain along the $c$ axis (more than 60-100% at 90 kOe field) in single crystals of orthorhombic $R$FeO$_3$ ($R$ = Dy, Ho) below their spin-reorientation transition temperature $T_{SR}$. However, the striction effect is two orders of magnitude smaller along the $a$ and $b$ axes. Like magnetostriction, the magnetodielectric effect is highly anisotropic and very large along the $c$ axis. Such gigantic striction and dielectric effects along the $c$ axis arise as a result of a magnetic-field-induced first-order structural phase transition which possibly stems from large spin-orbit coupling (and, thereby, enormous magnetocrystalline anisotropy). The observed colossal striction in rare-earth orthoferrites could open new opportunities for applications requiring large, reversible magnetic-field-induced strain.

Quantum confinement restructures the electronic phase space of ultrathin metals, but the resulting density-of-states (DOS) change is not generically large. We show that, within a three-dimensional confinement theory based on the suppression of long-wavelength electronic states, the Fermi-level DOS enhancement on the weak-confinement branch is bounded by $(4/3)^{1/3}-1\simeq10.1\%$. Instead, confinement-induced redistribution of electronic phase space can be strongly amplified by resonant denominators in the second-order susceptibility. A minimal double-resonance closure predicts giant amplification when the film thickness approaches $L_c=(2\pi/n)^{1/3}$, where $n$ is the carrier density, and a dominant optical pathway lies within a dephasing linewidth of resonance. Applied to recent Ag(111) measurements, the theory gives an effective phase-space carrier density parameter $n_{\rm eff}\simeq3.6\times10^{20}\,\mathrm{cm}^{-3}$, a tenfold enhancement of $|\chi^{(2)}|$, and hence the observed $\sim100$-fold increase of thickness-normalized second-harmonic-generation efficiency, together with the observed non-oscillatory thickness dependence.

This paper investigates the holographic Casimir effect in AdS/BCFT with a brane-localized scalar field. The scalar field takes different values at the strip's two boundaries, leading to mixed boundary conditions. The massive brane-localized scalar field typically breaks the boundary conformal symmetries, allowing us to study the holographic Casimir effect in non-CFTs. In two-dimensional spacetime, we apply the holographic g-theorem to prove the holographic bound on the Casimir effect for general brane-localized matter fields. In higher dimensions, we find that the brane-localized scalar field reduces the Casimir amplitude when the mass squared \(m^2=0\), but can increase it when \(m^2 < 0\). Additionally, there is a no-hair theorem for the cases where \(m^2>0\). These findings indicate that relevant boundary deformations can enhance the Casimir effect. As a byproduct, we obtain a gravitational dual of the repulsive Casimir force under mixed boundary conditions and argue that it aligns with the cosmic censorship conjecture.

Studying the multistability of origami structures presents challenges due to the nonlinearity of their kinematics and the high-dimensional configuration spaces that are difficult to visualize and explore exhaustively. To address this, we utilize the Lagrangian framework for origami to exploit symmetries and obtain reduced-dimensional slices of the configuration space. Our analysis of degree-6 vertices with reflection symmetry reveals topological transitions in their kinematic space as sector angles are varied, with implications for the number of symmetry-constrained minima and the emergence of metastable regions. These lower-dimensional slices are amenable to exhaustive search and visualization. A subsequent full-space stability analysis shows that 18 of 41 degree-6 and 14 of 45 degree-8 symmetry-constrained minima remain minima when all locally compatible perturbations, including those that break symmetry, are admitted. The metastable regions, which would likely be overlooked by numerical optimization alone, are influenced by the interplay between the boundaries of admissible kinematic space and crease mechanical properties. We extend our analysis to cone-like vertices with higher symmetry and one-degree-of-freedom kinematics, exploring symmetry-breaking phenomena, combinatorial structure, and their consequences for branchwise stability. The stability landscapes uncovered have potential applications in mechanical metamaterials, mechanical computing, origami-based robotics, and structures designed to self-deploy and retain their shape.

We study the far-from-equilibrium dynamics of domain-wall initial states in the integrable lattice Landau–Lifshitz spin chain. Building on the linear spin-wave description of domain-wall spreading, we derive the long-wavelength magnon dispersion directly from the microscopic integrable Hamiltonian and use it to characterize the propagation and broadening of the resulting wavefronts. The dispersion interpolates between a quadratic form at the isotropic point and a linear form in the easy-plane regime. In the isotropic limit, the quadratic dispersion leads to diffusive broadening, whereas in the easy-plane regime the domain-wall front propagates ballistically. Keeping the leading nonlinear correction to the linear dispersion gives a cubic dispersive term, which produces a characteristic $t^{1/3}$ broadening of the ballistic front. We further show that the sign of this cubic correction changes at a critical anisotropy, leading to a reversal of the dispersive wake from trailing to advancing. The resulting critical point occurs at $\Delta_c=1/7$, corresponding to $\gamma_c\simeq 1.047$. Numerical simulations of the full nonlinear spin dynamics confirm the analytical scaling and demonstrate the coexistence of the amplitude-independent spin-wave front with amplitude-dependent nonlinear soliton propagation.

Artificial spin ices built on quasiperiodic geometries remain under-explored. Here we investigate an ASI based on the octagonal Ammann-Beenker tiling, whose six vertex types present local environments inaccessible in periodic lattices. Combining Monte Carlo simulations of dipolar-coupled macrospins with micromagnetic calculations of individual vertex energies, we find that vertex types freeze in an order set not by coordination number, but by quasi-degenerate levels at five-island vertices and their local environment. Excitations in the low energy state are correspondingly localised to specific, geometrically determined sites. Using twice-inflated substitution rules as an energetic backbone, we propose an analytical ground state combining a long-range ordered fixed spin network with a sparse set of degenerate regions.

The discrete quasi-static response of rate-independent dissipative granular media is addressed. Granular systems are conventionally simulated with methods that are intrinsically dynamic, such as the discrete element (DEM) and discontinuous deformation (DDA) methods, with the particles' accelerations and damping being essential aspects. In contrast, quasi-static methods derive from the static stiffness relationships among the particles. With frictional contacts, an assembly's stiffness is incrementally non-linear and dependent on the direction of loading. The paper resolves this difficulty by casting the response as a linear complementarity problem (LCP). The approach benefits from a foundation of past research on existence, uniqueness, and stability of LCP solutions, which are expounded in a concise set of rules. The LCP of a granular system is derived, accounting for geometric effects that arise from curvatures of particles at their contacts, frictional contact stiffnesses, and displacement constraints on the particles. The paper describes eight aberrant conditions (pathologies) of granular systems, in the forms of various bifurcations and instabilities. When placed in the context of an LCP, the eight conditions are unambiguously defined. These pathologies include three types of bifurcation: discrete, continuous-bounded (not yet reported in the literature), and continuous-unbounded. Not yet reported in the literature is an abrupt discontinuous change in movements upon a continuous change of the data. Methods and results are illustrated with examples of granular systems. Results show that instability and bifurcation are pervasive conditions near failure; that failure and softening are sensitive to the geometric contours of the particles at contacts; and that quasi-static systems can encounter states that require a dynamic transition to resolve a lack of paths consistent with loading.

We present Tomography-NMR, an open-source Python package that reconstructs quantum density matrices from spectroscopic measurement data. The package implements a complete analysis pipeline for two-qubit quantum state tomography based on the product operator formalism: raw time-domain signals are Fourier-transformed into frequency-domain spectra, spectral peak intensities are mapped to expansion coefficients of the density matrix, and the full quantum state is reconstructed. Three integration methods are provided for different use cases: direct peak height measurement and fixed-parameter numerical integration require no theoretical reference and are suited to unknown states, achieving fidelities of approximately 98% on a benchmark set of known states, while a systematic parameter optimization against a known target state achieves reconstruction fidelities exceeding 99% for the same benchmark states. While the detailed theoretical framework for quantum state tomography is well established, the practical procedures for extracting density matrices from experimental spectra are often inadequately documented in the literature and obscured within proprietary software. This package addresses that gap by providing a fully transparent, reproducible implementation of every analysis step, from spectral preprocessing to density matrix visualization. The software has been validated on experimentally prepared two-qubit states measured via nuclear magnetic resonance (NMR) spectroscopy of coupled $^{31}$P nuclei. Average reconstruction fidelities range from 0.975 to 0.995 across a benchmark set of 20 two-qubit states, including the computational basis states, Bell states, and the outputs of three fundamental quantum gates (CNOT, H, and T). Although developed for NMR, the modular architecture facilitates adaptation to other spectroscopic platforms and alternative measurement protocols.

The behavior of spin quantum in k-space is key to identifying altermagnets (AMs) as the third kind of fundamental collinear magnetism. In contrast, non-collinear magnets,though abundant in nature,lack well-defined spin quantum numbers, and the resulting spin textures are often highly complex, which limits their potential for next-generation spintronic applications. Here we propose hyperspin, which lives in a higher-dimensional space, to address these drawbacks. Through analyzing the commutation relations between spin and Hamiltonian for a class of non-collinear magnets, we reveal it is a hyperspin, rather than the usual spin, that commutes with Hamiltonian. Unexpectedly, these non-collinear magnets should also show collinear spin-split bands in k-space like collinear AMs. We therefore classify such non-collinear magnets as hyperspin altermagnets (HAMs), as opposed to the usual collinear AMs. Our theory elucidates the fundamental physics of AMs and HAMs and provides a framework for exploring the wide range of non-collinear magnets that may possess other kinds of conserved quantities.

Altermagnetism has recently emerged as a distinct collinear magnetic phase exhibiting momentum-dependent spin-splitting despite vanishing net magnetization, as a consequence of inequivalent non-magnetic environments. Lately, it has been proposed that strong electronic correlations may yield spontaneous altermagnetism due to orbital ordering even for equivalent non-magnetic environments. While previous studies have largely focused on the electronic structure, a unified understanding of the collective excitations associated with these two different microscopic mechanisms stabilizing altermagnetism remains absent. Here, we develop an extended Kugel'-Khomskiĭ spin-orbital model on a decorated square lattice that simultaneously incorporates inequivalent non-magnetic environments and correlation-driven orbital ordering within a common theoretical framework. Employing a self-consistent mean-field spin-wave orbital-wave formalism, we demonstrate the emergence of mutually unhybridized but interdependent magnon and orbiton excitations exhibiting characteristic chiral-splitting. We show that the splitting originates from two distinct microscopic contributions: a lattice-dependent term arising from inequivalent non-magnetic environments and an orbital-order-induced exchange-anisotropy term that survives even for equivalent non-magnetic environments. The proposed framework therefore unifies the collective excitations associated with both types of altermagnetism. We further investigate the finite-temperature evolution of the coupled spin-orbital system, revealing the breakdown of spin-wave and orbital-wave approximations through spurious 1st-order transitions, while complementary classical Monte Carlo simulations recover the expected continuous 2nd-order behaviour. Our work establishes a unified microscopic framework for understanding collective magnon and orbiton excitations in altermagnets.

In a quantum walk, the first-detection return probability (FDRP) characterizes salient features, determining whether the quantum walk is transient or recurrent. We study the FDRP of quantum walks on a chain where the initial site is stroboscopically monitored by a detector and the walker performs long-range hopping between sites. We assume that the hopping strength decays with the distance $d$ as $d^{-\alpha}$ and $\alpha\geq 0$ and show that the power-law exponent $\alpha$ critically determines the behavior of the FDRP. The value $\alpha=1$ separates recurrent ($\alpha<1$) from transient ($\alpha>1$) quantum walks through a continuous phase transition in the total detection probability. For $\alpha<1$, strong long-range hopping induces localization, resulting in unit total detection probability. Instead, for $\alpha>1$ the long-range walk is transient and the return probability decays algebraically as a function of time as $t^{-\beta}$. The associated decay exponent $\beta$ features nonanalytic points as a function of $\alpha$. Such singularities are not exclusively determined by the low-energy spectrum, but are caused by the interference between infrared and ultraviolet energy modes induced by projective measurements, signalling the emergence of critical behavior intrinsic to the non-unitary dynamics. These dynamics are solely controlled by tuning the long-range exponent $\alpha$ and can thus be experimentally probed in atomic and molecular systems.

Agitated filter dryers (AFDs) are a crucial unit operation in small molecule manufacturing that enables simultaneous filtration, washing, and drying of active pharmaceutical ingredients. One of the key challenges in AFDs is associated with undesired agglomeration, where the presence of hard agglomerates results in off-spec products, equipment damage, and additional downstream processing. This article presents a novel mechanistic model that describes the formation of soft and hard agglomerates during agitated filter drying. By integrating population balance and multiphysics modeling, the model can accurately predict the evolution of the product temperature, moisture content, and particle size distribution, and hence quantify the extend and impact of undesired agglomeration across various operating conditions. Our proposed model-based framework enables the rational design and operation of AFDs for improving the product quality and process reliability.

Thermally generated magnons enable heat-driven spin transport in magnetic insulators, yet the relative importance of multiple microscopic mechanisms governing their propagation remains incompletely understood. Here, we investigate thermal magnon transport in low-damping Li$_{0.5}$Al$_{1.0}$Fe$_{1.5}$O$_4$/Pt nanodevices using a nonlocal spin Seebeck geometry that separates magnon transport from local thermoelectric effects. Thermal imaging establishes a detector region outside the thermal healing length, enabling intrinsic nonlocal measurements. We find that thermal magnon transport is strongly suppressed by magnetic fields far above saturation, and further that thermal magnon transport decreases with increasing temperature despite an increasing magnon population. Brillouin light scattering reveals the key microscopic mechanism driving this effect: increasing field reduces the group velocity of backward volume magnons, directly reducing the magnon spin diffusion length. Micromagnetic simulations reproduce this behavior only when a temperature-dependent exchange stiffness is included. These results identify magnon group velocity and exchange stiffness as key parameters governing thermal magnon transport in ferrimagnetic thin films.

We present an extensive molecular dynamics (MD) study of the dynamical properties of a binary hard-sphere fluid over a wide range of packing fractions, $\phi \approx 0.357-0.582$. The self-diffusivity, $D$, and shear viscosity, $\eta$, are computed using an efficient implementation of the Einstein–Helfand method. The finite-size effects in $D$ scale as $1/N^\alpha$, with $\alpha$ increasing from approximately $1/3$ to $3/4$ with increasing $\phi$, whereas those in $\eta$ are negligible except for $\phi \gtrsim 0.554$, where they scale as $1/N$. The data are then extrapolated to the thermodynamic limit to obtain $D_{\infty}$ and $\eta_{\infty}$. Both coefficients show a super-Arrhenius dependence on $\phi$ for dense states, accompanied by a breakdown of the Stokes–Einstein relation. Although both $D_{\infty}(\phi)$ and $\eta_{\infty}(\phi)$ data are well described by an exponential form, we demonstrate that these fits do not provide reliable estimates of the critical packing fraction, $\phi_0$, owing to the substantial extrapolation required beyond the accessible equilibrium range. We find the commonly assumed proportionality between $\eta$ and the structural relaxation time, $\tau_\alpha$ , to not hold for this system. For $\phi\gtrsim 0.570$, the van Hove self-correlation function $G_s(r, \tau)$ exhibits a spatial exponential decay at intermediate times, $\tau$, signaling dynamic heterogeneity. The characteristic decay length scales as $\lambda \sim \tau^\nu$, with $\nu \approx 1/3$, in contrast to the conventional square-root scaling. We also investigate temporal heterogeneity through the four-point dynamic susceptibility, $\chi_4(\tau)$, and its peak time, $\tau_4$. These findings provide rigorous benchmark MD data for computational studies of glassy dynamics and establish a reference for testing theoretical models in dense disordered systems.

The Charge Density Wave (CDW) state is a perfect example of a combined structural and electronic state, both characterized by a periodic lattice distortion and an electronic modulation of condensed electrons, resulting from electron-phonon coupling. They are thus prone to be tuned by lattice strain. NbSe3 is a prototypical example of CDW states, with a chain-like structure displaying two CDWs at 145K and 59K, with wavevectors along and inclined with respect to the chain axis b. Here, we report on the evolution of the lattice structure and CDW properties in the quasi-one-dimensional charge-density-wave system NbSe3 under tensile stresses applied along and perpendicular to the chains axis b by a combination of X-ray diffraction and transport measurements. We find that the lattice structure show exotic Poissons coefficients and strongly anisotropic Youngs moduli while the evolution of the electrical resistance demonstrates shifts of both charge-density-wave critical temperatures that are strongly correlated with the lattice parameters. The two CDW transitions display different behaviours under applied stresses, and suggest that a modification of the band curvature leads to the observed transport signatures.

We develop a microscopic phase-space description of the quantum Calogero model in the presence of an external harmonic confining potential. Building on the quantum Lax-pair structure, we construct a Hermitian Wigner operator whose expectation value obeys the exact phase-space evolution equation d_t rho + lambda d_x rho - Omega^2 x d_lambda rho = 0 for arbitrary initial states and to all orders in the interaction strength. The resulting dynamics is a rigid rotation in phase space with period 2 pi/Omega, providing a microscopic realization of the isochronous dynamics of the trapped Calogero model. We further show that the moments of the phase-space density form rotating multiplets rather than independent conserved quantities. In particular, within the quadratic sector, the unique conserved combination is proportional to the trapped Hamiltonian, providing a nontrivial consistency check of the construction. In the limit Omega -> 0, the equation reduces to the exact free-streaming equation of the untrapped model.

We report a neutron diffraction study of the structural and magnetic properties of a family of ferro- and ferrimagnetic Prussian blue analogues (PBAs), $A_4$[Fe(CN)$_6$]$_{2.7}$ ($A$ = Co, Mn, Ni), Rb$_2$Ni$_4$[Fe(CN)$_6$]$_{3.3}$, and Mn$_4$[Cr(CN)$_6$]$_{2.7}$, as a function of temperature (2–450~K) and applied magnetic field. All bimetallic compounds of the Fm$\overline{3}$m family exhibit a broad diffuse feature at low scattering angle, which we identify, through comparison with the cation-stabilized Rb$_2$NiFe framework, as an intrinsic signature of correlated vacancies and their associated interstitial water. High-temperature diffraction reveals a continuous crossover from positive to negative thermal expansion in CoFe and MnFe upon dehydration, while NiFe remains structurally robust up to 450~K. At low temperature, all compounds order in a collinear ferrimagnetic state with propagation vector $\mathbf{k}=(0,0,0)$, except MnFe, which adopts a partially frustrated magnetic structure with $\mathbf{k}=(1,0,0)$. A moderate magnetic field of $B_c = 1.3$~T drives a spin reorientation in MnFe toward the collinear $\mathbf{k}=(0,0,0)$ ferrimagnetic state common to the other compounds; the same transition is independently induced by dehydration. A minimal Heisenberg model shows that this transition results from a near-compensation between antiferromagnetic Mn–Fe coupling and a geometrically frustrated antiferromagnetic Mn–Mn interaction on the face-centered-cubic Mn sublattice, placing MnFe in the vicinity of a magnetic compensation point. These results resolve a longstanding ambiguity in the interpretation of the Fe $K$-edge XMCD response of MnFe-based PBAs, and establish water content as a key parameter controlling both the structural and magnetic stability of this family of materials, with direct relevance to their use as battery electrodes.

The paper presents a broad thermomechanic framework for the isothermal rate-independent constitutive behavior of dense granular materials. The essential quantities in this framework are directly measurable in discrete element (DEM) simulations: free energy, dissipation, stress, and strain. The paper proposes that energy and dissipation are governed by two sets of internal variables: fabric variables that control the reversible stiffness and structure variables associated with internal sliding. The relevant fabric variables are identified and measured with simulations. Two hypotheses are considered for the structure variables: the macro-scale irreversible strain and an aggregate measure of the micro-scale frictional forces among sliding contacts. Both hypotheses are tested with simulations, which allow direct calculation of the internal variables. The paper then demonstrates the manner in which the measured variables are applied in incremental constitutive models. Among other findings are the following. (1) Dissipation from contact sliding is pervasive and occurs in all directions of incremental loading. (2) Contact motions are not reversed by a reversal of the strain direction, and contacts continue to slide when loading is reversed. (3) The free energy can not be assumed smoothly differentiable; instead, Gâteaux derivatives must be used with irreversible effects. (4) Basic assumptions of elastoplasticity are contravened: no region of purely reversible strain exists, no uniform yield direction exists, no uniform flow direction exists, and irreversible strain is not proportional to the projected total strain. A three-mechanism elastoplasticity model, however, closely fit the DEM results, and methods are demonstrated for quantifying the model. The results emphasize that advanced constitutive models are needed for capturing the general incremental behavior of granular materials.

In this work, we investigate the electronic, topological, and transport properties of a Creutz-Su-Schrieffer-Heeger (CSSH) ladder. Using a tight-binding model within the Green's function formalism, we calculate the energy spectrum, local density of states (LDOS), and electronic transmission. We first determine the energy spectrum of the CSSH ladder and analyze the different topological phases present in the system, identifying one trivial phase and three distinct nontrivial regions. We then study electronic transport and show that the transmission reproduces the different topological phases through characteristic transport signatures. Finally, we derive the conditions for the emergence of non-topological flat bands and demonstrate that these bands also provide the necessary conditions for the formation of bound states in the continuum (BICs). Our results establish a direct connection between the topological properties, flat-band formation, and electronic transport in the CSSH ladder.

The paper presents a consistent thermomechanical framework for strongly nonlocal continua, a type of generalized media in which a material's response at a point depends on deformation and temperature gradients within its neighborhood. Such dependence is responsible for localization phenomena having an intrinsic size, and nonlocal modeling also serves as a practical regularization tool to prevent mesh dependence. Nonlocality is of the integral type, using a kernel function that gives the relative influence of neighboring points on a central point. The paper develops three sources of nonlocality: (1) nonlocal momentum balance equations; (2) nonlocal conservation laws (including the first and second laws of thermodynamics); and (3) a material's nonlocal constitutive structure. Balance equations are derived using the principle of virtual power, permitting non-smooth force and displacement fields and non-smooth boundary surfaces with indistinct normal directions. The balance equations differ from those of classical local continua. Conservation laws also differ from those of local continua, with the mechanical power and heating at a point being averaged over its neighborhood. These laws are developed for processes that are sufficiently slow to minimize additional meso-scale kinetic energy due to internal turbulence. Stress, entropy, and dissipative forces are obtained as averaged derivatives of the free energy function with respect to strain, temperature, and internal variables. An example is presented of a stretched elastoplastic bar with a small defect, and nonlocality is shown to impart a characteristic size to the deformation pattern.

Crystallisation of liquids often occurs at solid surfaces, via heterogeneous nucleation or prefreezing. Understanding this process is crucial for controlling crystal morphology in thin films and developing efficient nucleating agents - especially for polymers, typically processed in a molten state. However, the efficiency of nucleation and prefreezing with respect to crystallisation kinetics and semicrystalline polymer morphology has not been well studied and remains unclear. Here, we address this challenge by conducting a systematic study of substrate-induced crystallisation in dewetted droplets of the model polymer poly($\varepsilon$-caprolactone) (PCL) on various crystalline and amorphous substrates. Using polarized light optical microscopy, droplet crystallisation temperature was monitored and varied across the substrates, revealing three scenarios: close-to-homogeneous nucleation on glass and silicon; heterogeneous nucleation on ordered and disordered carbon-rich substrates; and prefreezing on graphene. The temperature-dependent nucleation rate was analysed and found to obey classical nucleation theory for all systems except PCL on graphene, where it diverges as all the droplets crystallise simultaneously. The highest in- and out-of-plane PCL crystal orientation is found on graphene, where the epitaxially grown lamellae extend vertically over several hundred nanometres. These results demonstrate that prefreezing has a superior influence on crystallisation kinetics and crystal morphology, making prefreezing substrates perfect nucleating agents.

We report the results of an experimental search for ultralight axion-like dark matter in the mass ranges 19.5–20.5 and 21.5–22 neV. The Cosmic Axion Spin Precession Experiment-electric probes the axion-nuclear electric dipole moment coupling. We perform solid-state nuclear magnetic resonance on $^{207}$Pb spin ensembles which reside in a polarized ferroelectric crystal. The background axion-like dark matter field induces an oscillating torque on the $^{207}$Pb spins via the electric dipole moment coupling $g_{d}$. The experiment is calibrated with pulsed magnetic resonance measurements covering two frequency bands (4.6–5.0 and 5.2–5.3 MHz) that correspond to the axion Compton frequencies associated with the identified axion mass ranges. By sweeping the leading magnetic field applied to the sample, we are able to detect the $^{207}$Pb nuclear magnetic resonance in these frequency ranges using a superconducting quantum interference device, inductively coupled to the sample with a broadband circuit. We establish the upper bounds $|g_{d}| < 4\times 10^{-4}$ GeV$^{-2}$ with 95% confidence in these frequency bands. Our results demonstrate the detection and small-tip angle calibration of low-field $^{207}$Pb nuclear magnetic resonance, allowing for sensitivity to axion-like dark matter in the nanoelectron-volt axion mass range.

The system of electrons bound by a charged atom chain is studied within the Dirac theory. The general analytical solution of the Dirac equation is obtained. Analytical expression for electron energy is derived from which it follows that the principal quantum number can be introduced for electron states in such a system, similar to the case of a hydrogen atom. We prove that electrons bound by the atomic chain, are fully collectivized and the energy can be calculated as a function of the occupation number. The spectral band with the principal quantum number $n$ is shown to be split into $n$ subbands forming the fine structure. The scale of the fine structure splitting is calculated.

We investigate the topological and collective radiative properties of a one-dimensional diatomic chain of identical quantum emitters with alternating spacing, coupled to the electromagnetic vacuum. The system realizes an extended, non-Hermitian Su-Schrieffer-Heeger-type model with vacuum-mediated long-range interactions and collective dissipation. We focus on the single-excitation manifold, where the dynamics are described by an effective Hamiltonian. For an infinite chain, the complex band structure reveals subradiant modes associated with wave vectors outside the light line, as well as parameter regimes where real-part band crossings occur. The bulk topology is characterized by a complex Berry phase, which remains quantized in the presence of inversion symmetry and a spectral gap. For finite chains, using exact diagonalization, we identify superradiant, subradiant, and edge states with distinct decay rates and spatial profiles. Edge states emerge in the topologically nontrivial regime when a bulk gap in the real part of the energy spectrum is present, while subradiant states exhibit strongly suppressed decay with system-size dependence. Finally, we analyze the far-field radiation patterns associated with different classes of eigenstates and show that the emission characteristics reflect the decay properties, spatial localization, and the parity of the unit-cell amplitudes.

The paper presents the brief overview of known isothermal equations of state for solids and of theoretical background to construct them, focusing on widely used Murnaghan equation. Since the latter has a limited range of application, failing to reproduce reliably both near-equilibrium and high-pressure regions simultaneously, the paper proposes simple, but rather efficient way to improve it. The suggested modification favors its applicability at high pressures, allowing to expand considerably the region of reliable reproducing of experimental or computational data. The proposed improved equation has been tested in fitting of U(V) data, obtained within ab initio computations, as well as of experimental V-P data for a representative selection of solids. In comparison with ordinary Murnaghan equation, it has found significant advantages, extending the range, where the computational data may be reproduced trustworthy (from the equilibrium state to the pressures, appreciably higher, the ordinary equation could). As for the fitting of experimental data, the proposed improved Murnaghan equation reproduces them, in the presented examples, at least not worse than other well-known equations (Vinet, Birch-Murnaghan, Mao) do. Some aspects of fitting process, as well as some alternative approaches to obtain the proposed equation of state in various forms are also discussed.

The paper concerns computation of average stress within small sub-regions of a larger static granular assembly, where the sub-region's boundary is allowed to pass through the assembly's particles. An exact average is computed for certain stress components and for certain categories of sub-regions. The paper also identifies those choices of sub-regions for which exact stress components may be exactly computed, but when these conditions are not met, provides reasonable bounds on the error.

We investigate the geometric structure of a Hermitian two-level mixing Hamiltonian motivated by neutral meson oscillations and its connections with qubit, fermionic, and topological descriptions. Mapping the Hamiltonian to an effective qubit representation, we analyze the geometric phase associated with cyclic parameter evolution on the Bloch sphere. Without identifying the complex mixing phase with a physical CP-violation observable, we interpret it as a CP-like geometric parameter controlling the azimuthal orientation of the Hamiltonian vector and its reversal under phase conjugation. Third-order Bargmann invariants constructed from the eigenstates yield an associated discrete phase whose dependence on the mixing parameters is examined alongside the continuous geometric construction. The cyclic evolution is also represented as a single-qubit $R_z$ phase operation and expressed through Majorana bilinears. Extending the construction to the momentum-dependent Bogoliubov-de Gennes Hamiltonian of the Kitaev chain, we relate momentum-space winding to the topological regimes and the quantized Berry (Zak) phase in the real-parameter model, while the corresponding Bargmann construction approaches the global phase in the continuum limit. Together, these results provide a geometric perspective connecting phase structure, qubit operations, fermionic representations, and momentum-space topology within related two-level Hamiltonians.