Papers

Phase change Ge_Sb_Te (GST) materials exhibit pronounced optical contrast and tunability driven by structural transformations, enabling a diverse range of photonic and optoelectronic applications. GST materials undergo reversible amorphous crystalline phase transitions during which the refractive index and extinction coefficient increase significantly in the crystalline phase across a broad spectral range. However, a systematic correlation between local composition, crystalline microstructure, and broadband optical response within as deposited crystalline GST films has not been established, particularly for films spanning various compositions within a single growth process and in the absence of amorphous-crystalline transitions. Here, we report a systematic study of composition resolved optostructural property relationships in as-deposited crystalline GST films spanning Ge3Sb2Te6, Ge2Sb2Te5, and GeSb2Te4 within a single CVD process, avoiding intermediate phase transitions. This enables direct correlations between composition, microstructure, morphology, and broadband optical response across 400-1700 nm. Specifically, the compositional gradient results in a shift of the absorption minimum from 815.9 nm to 889.8 nm, accompanied by a 5.9 fold change in the intensity, reflecting the strong dependence of optical behavior on composition and microstructure. We further show that femtosecond laser irradiation enables spatially selective tuning of the optical response. These findings establish crystalline GST films as a platform for broadband-tunable, spatially programmable photonic elements, controllable through both compositional design and localized laser processing.

We investigate the non-equilibrium Casimir pressure in an isothermal binary liquid mixture maintained in a spatially constant and stationary concentration gradient parallel to gravity and confined within a three-dimensional slab of thickness $L$, bounded by two infinite plates parallel to both the gravitational field and the imposed gradient. We assume that the liquid mixture, under the same non-equilibrium conditions, occupies both the interior and the exterior of the slab. Using fluctuating hydrodynamics, we show that the resulting finite-size excess pressure on the plates is described by a scaling function of the dimensionless variable $k_{\mathrm{RO}}L$, where $k_{\mathrm{RO}}$ is the gravity-induced roll-off wavevector. At large separations, this Casimir pressure decays as $1/(k_{\mathrm{RO}}L)$. Depending on the thermodynamic properties of the mixture, the corresponding force can be either attractive or repulsive, while it vanishes for ideal solutions. Since the mixture is assumed to be far from its consolute critical point, the Casimir pressure investigated here is entirely of non-equilibrium origin and it vanishes in the absence of the imposed concentration gradient. Finally, we propose an experimental setup where this force might be measured, consisting of two optically trapped colloidal particles immersed in a dense aqueous colloidal suspension diffusing into an overlying layer of pure water, estimating the expected magnitude of the resulting force.

Proximity effects in layered heterostructures are usually represented by static parameters fitted to first-principles bands, which discards the energy dependence of the virtual hybridization, the momentum transfer, and the spatial structure. We overcome this limitation by deriving a dynamical proximity operator $\mathcal{V}(\mathbf{k},\mathbf{k}';\omega)$ directly from density functional theory, downfolding the Kohn-Sham Hamiltonian of the heterostructure onto a fixed low-energy target Wannier subspace and reproducing its spectrum exactly within that subspace. The construction separates direct matrix elements from virtual hybridization through all remaining states. In graphene on hBN/Co(0001), virtual hybridization generates more than $99\%$ of the proximity exchange and gives it a resonant frequency dependence set by the Co $d$ states. In graphene/PtSe$_2$ it resolves a sublattice-selective intervalley coupling with a $\sqrt{3}\times\sqrt{3}$ charge modulation, and in graphene/WSe$_2$ a bond-resolved Rashba coupling of $0.24$~meV, against below $1$~$\mu$eV for the direct projection alone. Our results expose the limitations of static projections and establish a fitting-free microscopic foundation for low-energy modeling, spin-relaxation theory, and transport calculations.

We study the quantum mechanics of a charged particle confined to the surface of a cube enclosing a magnetic monopole. The magnetic field is chosen to have a constant magnitude on each face and to point along the outward normal, preserving the rotational symmetry of the cube. We formulate the continuum problem using two gauge patches on the cube surface and show that consistency of the wavefunction gives the Dirac quantization condition. Since an explicit vector potential does not remain invariant under ordinary rotations, we construct gauge-modified rotation operators and use them to classify the eigenstates. Even monopole charges are described by the irreducible representations of the cubic rotation group O, while odd monopole charges require the spinorial representations of the binary octahedral group 2O. We compute the spectrum with a gauge-covariant finite-difference discretization and find Landau-level-like manifolds whose degeneracies are split by the discrete cubic symmetry. We also study the corresponding tight-binding Hofstadter problem on the discretized cube. The resulting spectrum contains the usual magnetic subband structure together with additional gap states localized near the cube corners.

This note discusses zero-sum games with open-ended innovation, whereby each player may introduce new strategies. The innovation process is modelled as a draw of new strategies form a distribution. It is argued that, when the cost of innovation is vanishingly small, this setting can lead to an everlasting innovation arm-race. In particular, the introduction of new technologies of the advanced player increases the marginal utility for technological innovation of the backward one, whereas innovation of the backward player disincentivizes the more advanced one to innovate.

Global diagnostics such as Berry curvature and quantum metrics characterize the geometry and topology of an occupied Bloch subspace, leaving the microscopic sectors that carry this structure implicit. We introduce the relative hybridization coordinate $Z$ as a projector-level diagnostic connecting these global quantities to local degrees of freedom. As the Grassmann graph coordinate relative to a chosen sector, $Z$ reconstructs the local projector and retains the phase and matrix orientation absent from ordinary weight or fat-band descriptions. On valid chart patches, its momentum-space texture encodes Berry curvature, quantum metric, Berry phases, and Wilson loops, while chart obstructions appear as rank-drop defects whose balanced-chart winding of $\det Z$ gives the first Chern number. In the QWZ model this defect inventory reproduces the Chern phase diagram. In the lattice BHZ model, matrix $Z$ diagnoses the orbital $E|H$ partition as a robust matched chart for the QSH geometry, while the spin partition remains essential to the block and $\mathbb Z_2$ interpretation and shows rank deficiency as a matched chart in the spin-conserving limit. The relative hybridization coordinate thus provides a sector-resolved framework for relating band geometry and topology to microscopic structure.

We present a numerical study of subsystem distance decay following a global quantum quench in the infinite one-dimensional transverse-field Ising chain, using the mathematically rigorous Bures distance $B_A(t)$ to quantify the deviation of the time-evolved reduced density matrix from its stationary generalized Gibbs ensemble state. We show that the late-time decay follows a discrete power law $B_A(t) \sim t^{-\lambda}$, with the exponent $\lambda$ confined to discrete values: $1$, $5/4$, $3/2$, $7/4$, $2$, $5/2$, and potentially further values. The specific exponent is jointly determined by the pre- and post-quench transverse fields, as well as by properties of the symmetric excitation-fraction function $m_S(\varphi)$, defined on $\varphi\in[0,\pi]$ to characterize the pre-quench Hamiltonian eigenstates, including continuity, boundary values, and first-derivative boundary values, among others. The previously established $t^{-3/2}$ decay for the initial ground state of the pre-quench Hamiltonian is naturally recovered as a special case of this general classification. Our results reveal a universal discrete structure governing local equilibration dynamics in integrable quantum systems.

The Aharonov-Casher (AC) effect is a quantum mechanical phenomenon in which the wave function of a particle with a magnetic moment moving in a region subject to an electric field develops a phase shift due to spin-orbit interaction, even if no classical force acts on it. This phase also depends on the medium through which the particle moves. Here we focus on the AC phase of an electron moving in twisted bilayer graphene (TBG) lying in the $x$-$y$ plane, subject to a uniform electric field perpendicular to the plane of the graphene, ${\bf E}=E{\hat{\bf z}}$. The AC phase is determined by an $SU(2)$ vector potential ${\bf A}$ from which a phase factor is generated, and used to perform a gauge transformation of the Hamiltonian. We find that the AC phase for a straight line path between two points in the TBG plane is linear with $E$ and exhibits sharp peaks at the magic angles. To help demonstrate an experimental method for determining the AC phase, we examine the probability of polarized electron propagation from a source tip to a drain tip in a double-tip scanning tunneling spectroscopy configuration.

Designing machine-learning interatomic potentials involves achieving the precise representation of complex many-body interactions alongside the efficiency required for scalable molecular dynamics. We introduce Transformer Atomic Cluster Expansion (TRACE), an energy-conserving architecture that combines atomic cluster expansion density correlations with local multihead cross-attention. The correlations form an O(3)-equivariant state for each center, which queries tensorial neighbor features that remain fixed functions of species and geometry. No learned state is passed between atoms. On a laptop MacBook-M1, we train and test TRACE for polymorphic cesium lead iodide, liquid water, and intramolecular methyl migration against experiments. For cesium lead iodide, TRACE reproduces the r$^2$SCAN+rVV10 ordering of four polymorphs and gives a classical edge-sharing hexagonal non-perovskite($\delta$) to corner-sharing cubic perovskite($\alpha$) Gibbs-free-energy crossing $\simeq$580K near the experimental observations of $\simeq$600K. By employing enhanced sampling to cross high energy barriers, the same TRACE potential successfully captures the $\delta$-to-$\alpha$ perovskite transformation without any reinforcement learning. A water potential trained on a reduced set of CCSD(T) configurations places the first oxygen–oxygen maximum at 2.85~Å, compared to the experimental value of 2.80~Å. For the gas-phase methyl migration in 2,2-dimethylisoindene, umbrella sampling yields an activation free energy of $27.92\pm0.03$~kcal~mol$^{-1}$, in close agreement with the experimental measurement of $29.2\pm1.1$~kcal~mol$^{-1}$. Across these diverse benchmarks, a single unified architecture successfully captures multi-species crystallization, liquid structures, phase diagrams, and chemical reactivity.

The entanglement asymmetry measures how strongly a symmetry is broken inside a subsystem. Analytic results at equilibrium have so far covered free theories and, perturbatively, the critical XXZ chain. We compute the Rényi entanglement asymmetries of a large interval in the gapped, $U(1)$-breaking phase of the interacting XYZ chain. The calculation combines three ingredients. A charged-moment identity, which we prove for fermionic Gaussian and for injective matrix-product ground states, ties the asymmetry to the static susceptibility of the broken charge. A non-conservation sum rule then evaluates the susceptibility from sine-Gordon form factors, its two-kink and one-breather channels providing a lower bound on the universal amplitude. The Baxter–Johnson–Krinsky–McCoy solution supplies the kink mass for different couplings. Infinite-system density-matrix renormalization group simulations built on these masses reproduce the master formula.

The ferroelectric instability in superstructures, superlattices, quantum wires, and disordered solid solutions in the BaS–PbS system with the NaCl structure has been discovered and investigated using first-principles calculations within the density functional theory. The emergence of ferroelectricity in these structures is associated with the instability of TO phonons in linear –Pb–S–Pb–S– chains, which arises as a result of stretching of the structures upon the introduction of large barium atoms. Additionally, it has been discovered that, alongside ferroelectric phases, the structures also exhibit stable, competing antiferroelectric phases and those with a mixed ferroelectric–antiferroelectric ordering (ferroelectrically polarized one-dimensional Pb–S chains arranged in an ordered or disordered manner in the perpendicular direction). These phases often become the ground state of the studied systems. The closeness of the energies of the ferroelectric, antiferroelectric, and mixed states indicates the emergence of a multi-minimum potential with an infinite number of wells separated by potential barriers in the configuration space. This suggests a possible emergence of nonergodicity in the structures at low temperatures.

Lanczos concepts are often realized on supercomputers. In view of modern architectures of high-performance computing triple-hybrid schemes employing MPI, CPU-openMP as well as GPU-openMP should be utilized. The present article sketches how such a scheme could be utilized in order to meet the demands of the finite-temperature Lanczos method for anisotropic spin systems.

Using three-point bending, this study investigates surface-crack formation in photo-aged polypropylene (PP) that has a depth-dependent aging gradient. PP undergoes embrittlement under ultraviolet (UV) irradiation, and because the photo-oxidation proceeds inward from the irradiated surface, the embrittlement develops non-uniformly across the specimen thickness. PP specimens were mildly photo-aged by UV irradiation and had not yet developed visible surface cracks. Each specimen was bent in two configurations: with the UV-irradiated ("aged") surface on the tensile side, and with the opposite ("reverse") surface on the tensile side. When the aged surface was on the tensile side, the stress-strain curves exhibited several discrete stress drops, and in-situ side-view observation confirmed that the formation of each new surface crack coincided with a stress drop. In contrast, no clear stress drops were observed when the reverse surface was on the tensile side. These results show that the through-thickness gradient of embrittlement is directly reflected in the bending stress-strain response. Uniaxial tensile testing, the standard method for evaluating mechanical properties, formally assumes a nominally uniform deformation across the cross-section and therefore reflects the spatially averaged response. Three-point bending, by contrast, imposes the largest tensile strain at the specimen surface and thus selectively probes the embrittled surface layer, making it an effective method for detecting the surface embrittlement of photo-aged polymers.

We have introduced PT-symmetry to a central spin model by adding a PT-symmetric interaction with a tunable hermiticity parameter $\gamma$. Using the pseudo-Hermitian formalism, we applied a Dyson map to transform the non-Hermitian Hamiltonian to its Hermitian representation. We have found that the decoherence slows down as $\gamma$ increases, eventually ceasing at $\gamma=1$. We define a pseudo-Hermitian observable that commutes with the metric operator to add as the self-Hamiltonian. Einselection gradually forced the system to select the eigenstates of the self-Hamiltonian as $\gamma\rightarrow1$. The steady-state purity of the central spin states in the strong environment regime exhibits a paradoxical decrease as $\gamma$ increases. However, a turning point (minimum) corresponding to a maximum information dissipation to the spin bath is found. Finally, the Breuer-Laine-Piilo (BLP) measure, which is used to quantify the non-Markovianity of a quantum system, was evaluated for a finite time. The BLP measure in the strong environment regime exhibited similar turning point behavior, which means that the information backflow reaches a saturation point before declining. This decline signifies the point where PT-symmetry starts shielding the central spin from the environment.

Lipids and liquid crystals provide a useful platform for addressing how molecular-scale organization is translated into mesoscale shape transformation. Variations in hydrocarbon-chain packing can modify interfacial order, anchoring conditions, and elastic stresses, potentially coupling molecular organization to droplet morphology. Here, we investigate the temperature-dependent structural evolution of monoolein-doped 4-octyl-4'-cyanobiphenyl (8CB) droplets dispersed in aqueous phospholipid solutions. Using polarized optical microscopy, we show that the internal monoolein concentration and the external lipid environment jointly regulate phase transitions, thin filamentation, and larger deformations during heating. The droplets undergo coupled smectic-nematic-isotropic transitions, with extended thin filaments observed exclusively in the smectic regime. At the smectic-to-nematic transition, we observe an abrupt and discontinuous onset of droplet shape deformation, revealing a shape-change transition coupled to the bulk mesophase transition. To our knowledge, this is the first report of a discontinuous droplet-shape-change transition coincident with a smectic-to-nematic phase transition. Varying the internal and external lipid contents redirects the reconfiguration pathway between filament-dominated smectic responses and more amorphous nematic shape changes. Interfacial tension measurements further show that stronger reductions in liquid-crystal-aqueous interfacial tension do not necessarily produce filamentation or deformation. Instead, the observed morphodynamics arise from the coupling between bulk elasticity, mesophase structure, and lipid-mediated interfacial organization. These findings establish lipid composition and hydrocarbon-chain architecture as key parameters governing thermally induced shape transformations in liquid crystal droplets.

We study ultradilute $^{39}$K Bose-Bose bulk mixtures and droplets in an external harmonic potential that confines them in one spatial direction towards the two-dimensional (2D) limit. Equations of state for several confinements are obtained with quantum Monte Carlo (QMC) at $T=0$, using interaction potentials that include information on the $s$-wave scattering length $a$ and the effective range $r_{\rm eff}$. Performing the calculations using two different interaction potential models we have determined the range of confinements for which equations of state are universal in terms of $a$ and $r_{\rm eff}$. Based on the QMC equation of state, we develop a 2D QMC density functional for each confinement strength and use it together with the local density approximation to determine properties of the self-bound drops. For moderate squeezing, energies and droplet profiles obtained using the 2D QMC functional agree well with those obtained using 3D functionals, while offering a substantial reduction in computational cost, and a consistent approach in crossover to 2D. Noticeably, our results approach 2D mean-field (MF) + Lee-Huang-Yang (LHY) predictions only for the most strongly confined systems for which universality in terms of $a$ and $r_{\rm eff}$ is observed. This implies a very narrow range of confinements for which 2D LHY functionals are applicable, which has important consequences for the study of vortices.

Sol-gel transitions are ubiquitous in soft matter and biological systems, yet their thresholds are often poorly captured by classical Flory-Stockmayer theory because spatial organization and loop formation are neglected. Here, we combine molecular dynamics simulations with random graph and random geometric graph models to determine the respective roles of topology and geometry in reversible associative polymer solutions. We show that a coordinate-free random graph recovers the mean-field Flory-Stockmayer limit, whereas a random geometric graph quantitatively reproduces the shifted percolation thresholds observed in molecular dynamics simulations when the detection radius is chosen according to the polymer conformational size. This geometric mapping remains quantitatively valid for linear chains with regularly spaced binding sites over a broad range of chain stiffness. At the microscopic level, we identify primary loops formed already in the pre-gel regime as the dominant source of the deviation from mean-field predictions. Near the gel point, the cluster-size statistics obtained from simulations and random geometric graphs are consistent with the universality class of three-dimensional percolation. These results establish random geometric graphs as a minimal predictive framework for describing topological transitions in reversible associative polymer solutions and show that gelation and network formation can be inferred directly from single-chain conformational information.

Ultracold polar molecules have emerged as an exciting platform for experiments in quantum science, with many proposed applications seeking to leverage the existence of long-range dipolar interactions and the rich internal structure of long-lived states. However, the complexity of molecules also presents many experimental challenges. In this chapter, we review the experimental advances over the past two decades that have brought ultracold molecules under full quantum control. We focus on three key topics: control of ultracold molecular collisions, engineering dipolar interactions and nascent quantum simulations in optical lattices.

Clean, nonsplit vortex zero-bias peaks (ZBPs) can be misinterpreted as Majorana zero modes (MZMs), making static scanning tunneling microscopy intrinsically ambiguous. Here we use the STM tip coupling to drive a local boundary-renormalization-group (boundary RG) flow, turning dynamical Coulomb blockade into a falsification test for Majorana-like ZBPs. Experimentally, in a $\mathrm{SrSn}_3$ thin film, normal-state spectra establish an Ohmic dissipative environment, and a common boundary-RG/thermodynamic-Bethe-ansatz analysis of the superconducting-gap and vortex-center spectra yields consistent dissipation strengths within the $r < 1/2$ Majorana-filter regime. Lowering the tip nevertheless drives a clean, non-split vortex-center ZBP into a zero-bias dip, opposite to the protected flow of an isolated MZM, unmasking the peak as a Majorana false positive produced by a conventional vortex-core state. The same flow selectively suppresses the strongly tip-coupled channel, resolving the two-gap superconductivity. Dissipative STM thus tests dynamical protection rather than spectral appearance.

We consider a one-dimensional driven-dissipative Bose-Hubbard model subjected to incoherent pump and one- and two-body losses, and analyze it by studying its two-point space-time correlations. By employing a combination of numerical methods, such as stochastic semi-classical simulations and tensor network methods, as well as perturbation theory within the Keldysh formalism, we characterize the system at varying filling and interaction strength. We present results for two complementary regimes: i) at large filling and weak interactions, where we show that Kardar-Parisi-Zhang scaling is visible in the linewidth of the spectral function and ii) at weak filling and strong interactions, where we analyze what remains of the mean field transition and identify a change of nature of the excitations. Our study covers two important regions of the phase diagram of such a system.

Dynamic light scattering (DLS) is a versatile technique for probing microscopic dynamics in soft condensed matter. However, applying DLS to supercooled molecular liquids and glasses demands exceptional experimental performance due to weak depolarized scattering, slow relaxation near the glass transition, and the need for quantitative comparison with complementary spectroscopic techniques. In this tutorial we discuss, how a depolarized dynamic light scattering (DDLS) setup can be tailored to meet these challenges. By combining conventional fiber-optical photon correlation spectroscopy, and multispeckle photon correlation imaging with high-frequency DDLS, such a setup allows to capture rotational dynamics across more than 20 orders of magnitude in time. We detail the experimental design required for high signal-to-noise ratios and long-term optical stability, alongside the treatment of coherence and partial heterodyning effects. As we demonstrate, after proper treatment the different detection schemes yield the same electric-field autocorrelation function, enabling the construction of continuous, ultra-broadband DDLS datasets. Furthermore, multispeckle detection enables time-resolved correlation measurements without temporal averaging, extending DDLS to non-equilibrium systems such as aging molecular glasses. This methodology establishes a unified experimental framework for quantitative investigations of equilibrium and non-equilibrium molecular reorientation dynamics over an exceptionally broad time range.

We derive all symmetry-allowed bond-current form factors generated by nearest-neighbor bond-charge interactions on square, triangular, and kagome lattices. We find that the anisotropy of the bond-current susceptibility systematically favors ordering wave vectors that support closed loop-current states, whereas symmetry-related wave vectors with weaker susceptibility generate noncirculating current textures. Near van Hove filling, this correspondence is robust across all lattice geometries considered, producing staggered flux phases on the square lattice, diamond-shaped current patterns on the triangular lattice and both chiral and nonchiral loop-current states on the kagome lattice. Our results establish a direct link between bond-current form factors, susceptibility anisotropy, and real-space current topology, providing a general framework for identifying loop-current orders and interpreting signatures of time-reversal symmetry breaking in correlated electron materials.

Colloidal semiconductor quantum dots are promising materials for numerous applications due to their tunable emission and high quantum yields. However, emission instability in the form of luminescence blinking remains a significant obstacle to their practical implementation. While recent advances in synthesis and surface engineering have demonstrated partial or complete blinking suppression, the quantitative assessment of the "quality" of this suppression remains challenging. Existing criteria typically rely on threshold-based classification into ON and OFF states, which becomes inherently ambiguous owing to the continuous distribution of emission intensities in single quantum dots. Here, we propose a threshold-free two-dimensional quantitative criterion based on the variance of the recombination rate and the relative quantum yield, both of which can be extracted from standard time-correlated single-photon counting measurements. We validate the criterion using simulated blinking trajectories covering all major blinking mechanisms and demonstrate that it cleanly separates them into distinct regions of the two-dimensional parameter space while providing a quantitative measure of the degree of suppression. This approach directly quantifies the temporal stability of emission without requiring arbitrary state definitions, thereby providing a robust metric for comparing different blinking suppression strategies.

The asymmetric expansion of magnetic bubble domains in ultrathin ferromagnets provides a powerful route to probe the interfacial Dzyaloshinskii-Moriya interaction (DMI). While conventional analyses rely on domain wall velocities measured along selected directions as a function of in-plane field, recent approaches have highlighted the additional insight contained in the angular dependence of the velocity, $v(\theta)$. Here, we develop an extended angular creep model that incorporates both the dispersive domain wall stiffness and a chirality-dependent prefactor associated with chiral damping. This generalization captures the full anisotropic dynamics of domain wall motion around a bubble domain. We show that these contributions significantly modify the angular velocity profile and can lead to features not accessible within existing models. Our results establish a more complete framework for interpreting creep-driven domain expansion and provide improved sensitivity for the quantitative extraction of DMI and chiral dynamical effects.

We explore the similarities and differences between the Gibbs phenomenon in partial Fourier representations of discontinuous signals and Friedel oscillations in the electron density of a solid near an anomaly. Inspired by the apparent similarities of the two phenomena, we perform a detailed exploration of both from the viewpoint of an engineer being introduced to a concept from solid-state physics. Focusing on the density of an one-dimensional electronic gas confined by a square potential, we show that, despite the similarities, Friedel oscillations cannot be attributed to the inability of a partial Fourier series to describe a discontinuity. Nevertheless, the two phenomena do exhibit similarities, which can be exploited to develop intuition. By adopting an educational style, we hope to establish some common language between electrical engineers and condensed-matter physicists, hoping that this can further inspire the two communities to seek intuition and further comprehension within neighbouring but different disciplines.

We develop a basis-resolved covariance framework for investigating the organization of low-energy many-body wavefunctions in the spin-$1/2$ Kitaev–Heisenberg model. By constructing covariance matrices from local-spin, bond-correlation, and plaquette-flux representations of the low-energy states, Principal Component Analysis (PCA) is employed to identify the dominant collective covariance modes. We find a systematic evolution of the covariance geometry across the phase diagram: magnetically ordered phases are described by an essentially one-dimensional covariance manifold, conventional magnetic phase boundaries exhibit competition between leading covariance modes, whereas the Kitaev regimes develop intrinsically multidimensional covariance geometry. Furthermore, the same many-body wavefunction produces distinct covariance geometries in different operator representations, demonstrating that covariance geometry is determined jointly by the quantum state and the physical observables used to probe it. Shannon entropy and the participation ratio provide quantitative measures of this evolution. The present framework establishes basis-resolved covariance geometry as a complementary statistical perspective for characterizing frustrated quantum many-body systems beyond conventional order parameters.

The problem of finding lower and upper bounds on multivariate homogeneous polynomials is both difficult and important given its applications to questions ranging from dynamical stability in complex potential landscapes to data analysis. From the standpoint of tensor eigenvalue theory, the question is equivalent to finding the smallest and the largest eigenvalues of the coefficient tensor corresponding to the given polynomial. Standard approaches outlined in the literature amount to running nonlinear iterations in search for the optimal rays along which the growth of the polynomial is fastest or slowest. Unlike the case of matrices (or their corresponding multivariate quadratic forms) convergence of such algorithms for higher-rank tensors is capricious due to the complex topography of polynomial objective functions. In this essay, a very different strategy, inspired by quantum-mechanical variational methods, is introduced for finding bounds on polynomials. The original polynomial is replaced by an operator acting in a suitably chosen (large) space of states, such that in an appropriate "classical" limit this operator approaches the original polynomial expression made of commutative variables. As a result, approximating the smallest and largest eigenvalues of the coefficient tensor, and thus finding bounds on polynomials, amounts to diagonalizing the resulting quantum operator, represented as a large matrix, and then inspecting the smallest and largest eigenvalues of this matrix. This approach is then successfully applied to standard test examples from tensor eigenvalue literature and other problems of interest in mathematical physics including Strichartz-type inequalities.

We challenge the widespread consensus that mean-field theory fails to describe long-range open quantum systems in the presence of symmetry breaking and/or when starting from strongly correlated states (e.g., macroscopic superpositions). While recent literature relies on cumulant expansions to capture such systems, this approach rests on truncations with no clear justification. Here, we show that it is, at best, conceptually redundant in the strong long-range regime. We show that the evolution can be decomposed into, and fully reconstructed from, independent mean-field dynamics. This decomposition generates the entire hierarchy of cumulants and, as a byproduct, identifies—to our knowledge, for the first time—a regime in which cumulant expansions exactly predict low-order cumulants. We illustrate the power of our findings with two applications: we compute the moment generating function for nonequilibrium $\mathcal{Z}_2$ symmetry breaking, and construct states restoring time-translation symmetry in time crystals. In both cases, our method fully reproduces the exact many-body dynamics, which is out of reach of cumulant expansions. Our results reclaim the exactness of mean-field theory, offering a transparent framework for large-scale open quantum systems.

The nonlocal Majorana polarization, defined as the product of the expectation values of the particle-hole operator at opposite halves of the system, has been shown to be a reliable topological indicator that determines the presence and quality of Majorana zero modes in Hermitian topological superconducting setups. In this work, we extend the concept of nonlocal Majorana polarization to the non-Hermitian realm by taking into account the biorthogonal eigenstates and demonstrate its utility by exploring distinct non-Hermitian superconducting systems. In particular, we show that the Majorana polarization can distinguish between Majorana zero modes, trivial zero-energy states, and exceptional points in non-Hermitian superconductors. Also, we introduce the concept of nonlocal Majorana polarization sensitiviy for characterizing the contribution of non-Hermiticity to Majorana polarization. As a byproduct, we find that non-Hermiticity enhances Majorana zero modes robustness, a property captured by the nonlocal Majorana polarization.

We demonstrate that antisymmetric Compton scattering can detect both the switching and the continuous rotation of the Néel vector in two-dimensional (2D) antiferromagnets. By probing magnetoelectric (ME) multipoles, which couple electric and magnetic dipoles, this approach overcomes the limitations of conventional techniques that rely on a finite net magnetization. Using a group-theoretical decomposition of the staggered moments in 2D MnPS$_3$ into irreducible representations, combined with first-principles calculations, we show that the antisymmetric Compton profile (ACP) is highly sensitive to the Néel vector orientation: it reverses sign under Néel vector reversal and exhibits distinct anisotropies under in-plane rotation. These results establish the ACP as a versatile probe of antiferromagnetic (AFM) order and magnetoelectric phenomena in van der Waals materials.