Papers

Noise sets the fundamental limits of resolution and sensitivity in Dynamic Atomic Force Microscopy (DAFM). While thermal fluctuations are conventionally assumed to be the dominant noise source, this work demonstrates that tip–sample interactions in ambient conditions introduce a non–thermal noise component that significantly exceeds the thermal background. Using a model system of sodium dodecyl sulfate (SDS) on graphite, we characterize this noise through force spectroscopy, 3D imaging modes, and Kelvin Probe Force Microscopy (KPFM). This interaction–induced noise arises from the stochastic formation and rupture of nanoscopic liquid necks, serving as a direct fingerprint of local wettability and dissipative dynamics. Crucially, we find that this “noise channel” provides chemical contrast that is distinct from and complementary to the electrostatic potential mapped by KPFM. By deciphering the physical origin of these fluctuations, we establish that noise is not merely an instrumental artifact but a rich spectroscopic signal, and we propose that Frequency Modulation (FM–DAFM) offers a superior approach to decouple these dissipative effects for high–resolution imaging.

Diagnosing hidden local orders at buried interfaces remains a central challenge in the design and characterization of quantum materials. Second-order electrical responses, such as the nonlinear Hall effect, probe inversion-symmetry-breaking terms invisible to linear transport, offering a direct window into these nanoscale environments via the quantum geometry of Bloch electrons. Here, we utilize $\text{KTaO}_3$, a complex oxide driven by strong tantalum $5d$ spin-orbit coupling and interfacial inversion symmetry breaking, to demonstrate that second-harmonic resistivities exhibit large, reproducible mesoscopic fluctuations. Remarkably, these fluctuations persist in macroscopically large ($200\,\mu\text{m}$) devices and are ubiquitous across all studied surface orientations, even where macroscopic conductivity strictly adheres to underlying crystal symmetries. We propose that these robust, magnetic-field-driven interference patterns arise from local structural symmetry breaking, driven by incipient ferroelectric polarization pinned to the interfacial impurity landscape. This defect-pinned polar mechanism is firmly supported by the signal's suppression above $10\text{ K}$ due to phase decoherence, and a complete loss of mesoscopic memory upon thermal cycling above $40\text{ K}$. By linking quantum geometry to dynamic lattice ordering, our findings establish nonlinear mesoscopic transport as a powerful new characterization tool, capable of revealing local polar tendencies and hidden structural orders in complex materials that remain fundamentally invisible to conventional probes.

A new family of high-temperature superconductors was recently discovered in the $n=2,3$ Ruddlesden-Popper nickelates, where superconductivity emerges concomitant with suppression of parent density waves and structural octahedral rotations under hydrostatic pressure. Intriguingly, compressive strain mimics the structural effects of pressure in the $n=2$ phase, yielding ambient-pressure superconductivity. However, analogous strain-stabilized superconductivity has not been realized in the $n=3$. Here, we use atomically-precise synthesis, transport, picoscale electron microscopy, and synchrotron X-ray diffraction to probe $n=3$ La$_4$Ni$_3$O$_{10}$ thin films. Although compressive strain suppresses density wave order, we do not observe superconductivity even under the largest strain state. Importantly, we identify a structural distortion unique to strained $n=3$ thin films that may inhibit superconductivity: persistent, layer-inequivalent octahedral rotations around the $c$-axis. Our results highlight key differences between the $n=3$ and $n=2$ systems, suggesting that ambient-pressure superconductivity in the $n=3$ may require new methods beyond epitaxial strain engineering.

Strong coupling between molecules and electromagnetic fields has emerged as a powerful strategy to modify the physical and chemical properties of molecules, enabled by the formation of hybridized energy levels through strong light-matter interactions. Rather than purely photonic or plasmonic modes, hybrid cavity fields that integrate plasmonic and photonic contributions provide versatile platforms with distinct advantages for tailoring light-matter interactions. Here, we present hybrid modes formed through the coupling between localized surface plasmon resonances of Au nanoparticles and Fabry-Perot microcavity modes. Furthermore, by using this hybrid platform, we demonstrate that the cavity field can give rise to cooperative coherent coupling between the spatially separated plasmonic nanoparticles and the molecules by mediating long-range dipole-dipole interactions. As we show, this cavity-mediated coupling also enhances the plasmon-exciton mixing, as compared to their direct interaction. This configuration opens new avenues for tailoring light-matter interactions at the nanoscale by supporting novel hybrid plexcitonic states that incorporate contributions from plasmons, excitons, and extended cavity fields.

Segregated states based on particle size emerge in granular materials from the competition between segregation and diffusive remixing. Here, we show that quantum coherence can enhance segregation beyond this classical limit. We introduce an open quantum cellular automaton for bidisperse mixtures that combines coherent transport and dissipative segregation. The automaton reproduces experimental and continuum-theory segregation dynamics, with segregation degrees collapsing onto a theoretical Péclet-dependent relationship. However, weakly decohering systems exhibit a coherence-driven transport regime that produces more strongly segregated steady states than classical predictions. Across a broad parameter range, the steady-state degree of segregation collapses onto two dimensionless numbers governing the competition between segregation, diffusion, and decoherence. These results identify quantum coherence as a mechanism for enhancing particle-size segregation and establish a framework for studying transport phenomena in open many-body systems.

Superconducting resonators are finding increasing applications in designing advanced quantum circuits for ongoing sensing, metrology, and computing technological revolution. A detailed knowledge of microscopic electromagnetic properties of superconducting resonators is directly relevant for their further improvements on circuitry design and device performance. Here, we introduce scanning-probe quantum microscopy to report nanoscale sensing of microwave and static magnetic field environment of an on-chip niobium (Nb) superconducting resonator. Taking advantage of Rabi oscillation measurements, we show that microwave magnetic fields generated by the superconducting resonator mode can be utilized to achieve coherent control of a quantum spin sensor. We further visualize static electromagnetic field response of the Nb resonator, showing magnetic field-induced formation, evolution, and depinning of superconducting vortices. Our results provide insights into future design, testing and evaluation of solid-state superconducting resonators, highlighting the potential of quantum sensors as a local probe to investigate electromagnetic properties of superconducting quantum circuits.

Silicon has a unique combination of properties that makes it one of the best material choices for biosensor platforms: it is inexpensive, its native oxide is atomically smooth, its fabrication processes are CMOS-compatible and have been refined for more than three decades, and it can support many transduction mechanisms in biosensor design. Over the past thirty years, researchers and engineers have used silicon nanostructures to produce ion-sensitive transistors, ultrasensitive nanowire field-effect biosensors, refractive-index-based porous silicon films, microring photonic resonators, suspended cantilevers, luminescent quantum dots, and solid-state nanopores. These device families have demonstrated successful sensing capabilities at the single-molecule, single-virus, or sub-femtomolar level under laboratory conditions; however, they have rarely been widely deployed in clinical assays. This gap is mainly caused by several well-characterized bottlenecks: for nanowire BioFETs, device variability and Debye screening; for porous silicon, fouling, pore wetting, and surface stability; for silicon photonics, thermal drift, spectral readout, and packaging; and across all platforms, calibration, reproducibility, and validation in real biofluids. In this review, we trace the development of silicon biosensors from their early stages to their current state, search and organize the literature focusing on the three most mature platforms and a set of emerging directions, summarize and compare the performance and bottlenecks of different platforms, and argue that progress over the next decade will come primarily from integrated readout, interface engineering, and systematic benchmarking rather than from the discovery of new silicon nanostructures.

Magnetic materials with square-net sublattices are of great interest due to its potential to realize magnetic frustration. Here we report the crystal growth and structural, magnetic, thermodynamic and electronic transport properties of a new rare-earth-based intermetallic compound, Er3Pt2Sb4.55(5). The new material possesses a distorted square-net framework of Er. Magnetic properties measurements suggest anisotropic behavior, long-range antiferromagnetic ordering and metamagnetic transitions based on a Jeff = 1/2 Er3+ motif. A magnetic structure is proposed based on the observed magnetic and thermodynamic properties. This new material expands the R3Pt2Sb4+x family with distorted square-net lattice of rare-earth elements and offers a new opportunity to study the relationship between magnetic ordering, crystal-electric field effect and crystal structure in rare-earth-based compounds.

The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics – such as superdiffusion – in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying $U(1)$ charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.

Magic-angle twisted trilayer graphene(MATTG) hosts versatile displacement-field-tuned correlated phenomena. MATTG consists of a dispersive Dirac cone which hybridizes with the flat band from a twisted bilayer graphene (TBG) sector. The hybridization strength increases with the displacement field $D$ and naively one may expect D-driven heavy fermion physics. However, the TBG Hubbard bands have a momentum-selective Mott gap, which is small at the $\Gamma$ point due to the band topology, and a rigid local moment description as in the familiar Kondo lattice model is invalid. Here we show that the dominant effect of the displacement field is to induce an energy shift of the Dirac cone and self-doping into the TBG sector. We illustrate this picture in a concrete calculation using a slave-particle theory at the filling $\nu=\pm 2$. We find that increasing $D$ drives a transition from a semimetal into a superconducting state. We also discuss the enhancement of the superconductivity by $D$ near $\nu=\pm2$ and the particle-hole asymmetry of the phase diagram. Our results provide a unified picture for electric-field-tunable superconductivity, Mottness, and heavy-fermion-like behavior in MATTG.

Motivated by the surge of interest in statistics of non-Hermitian random matrices as a framework for description of universal characteristics of dissipative chaotic quantum many-body systems, we address the problem of characterizing the parametric correlations of spectral densities. Considering parameter-dependent ensemble of complex Ginibre matrices we derive an explicit, closed-form expression for the parametric number covariance in the systems of symmetry class $\mathbf{A}$ for eigenvalues in a circular domain containing on average a finite number of eigenvalues in the spectral bulk. This behavior is expected to be universal, as further supported by numerical evidence for the real Ginibre ensemble, non-Hermitian Bernoulli Wigner matrices and bi-unitarily invariant ensembles. We also discuss a relation between parametric correlations of spectral densities and the distribution of the so-called eigenvector non-orthogonality factor, which attracted considerable interest in recent years.

A systematic method to find the Yang-Lee partition function zeros of quantum many-body systems based on perturbation theory at finite temperatures was recently introduced in arXiv:2504.01880. This method identifies wave-vector and temperature-dependent complex virtual energies obtainable from the thermal electronic Greens function. The collection of virtual energies over all $\vec{k}$ yield the Yang-Lee zeroes. We apply this approach to the one-dimensional Hubbard model for different boundary conditions. We compare the results obtained by this method up to second-order in perturbation theory with the results found by exact diagonalization. We also propose a quantity that could be used for experimental detection of these zeros of a Hubbard ring. An example of the detection method is presented using exact diagonalization of the 8-site Hubbard ring.

In non-Markovian systems, distinct dynamical phases arise from the competition between internal memory and external forcing, encompassing thermalization, persistent ergodicity breaking, and runaway energy growth. This study shows that the scaling parameter $\eta$ governs the emergent phase diagram within a system described by the Generalized Langevin Equation, particularly when subjected to external drives with asymptotic power-law tails. Three universal regimes for diffusive processes are delineated by this parameter: thermalization ($\eta > 0$), non-ergodic saturation ($\eta = 0$), and a force-dominated runaway phase ($\eta < 0$). The fluctuation-dissipation theorem, within this framework, is shown to be independent of external force and determined by the integral of noise density of states. A selective breaking of ergodicity is revealed by this formulation; microscopic fluctuations are decoupled from the drive, yet the relaxation completely encodes it, which in turn controls the kinetic effective temperature. Direct Langevin simulations in the Markovian limit quantitatively confirm this classification, capturing the non-thermal plateau at the critical point.

Motivated by the role of the holographic entropy cone in constraining the entanglement structure of states with classical gravitational duals, we investigate combinations of subsystem complexities associated with reduced density matrices in multipartite quantum systems. Focusing on subsystems composed of three disjoint regions, we introduce two quantities: a tripartite complexity, inspired by the tripartite information, and a complexity gap, designed to characterize emergent complexity in the full quantum state beyond that of its constituents. We study the sign structure of these quantities in three selected approaches to subsystem complexity. In holography, we employ the complexity=volume proposal in AdS spacetimes; for Gaussian many-body states, we use Fisher-Rao subsystem complexity; and we further develop a Krylov-space inspired, effective framework for reduced density matrices, which we test in few-qubit systems and coherent-state dynamics. Across all three approaches, we find that the tripartite complexity is not sign-definite in general. By contrast, the complexity gap exhibits a definite sign in every example we analyze, although the sign itself depends on the underlying notion of subsystem complexity. Our results suggest that the complexity gap could be a natural candidate building block for a prospective hierarchy of subsystem complexity inequalities.

Topologically polarized mechanical metamaterials enjoy a special built-in asymmetry that manifests as a preferred localization of edge states on selected edges. While this property has been shown for a few ideal Maxwell lattices, we currently lack systematic criteria to design families of structural systems exhibiting polarization. Here, we propose a framework to design polarized structural configurations enabled by topology optimization (TO), using both band and mode morphological properties as drivers of the optimization algorithm. Through the lens of TO, we are able to tap into a vast design space, unlocking geometric freedom far beyond what is achievable with canonical lattice architectures. At the same time, we elucidate important criteria that need to be satisfied, beyond the optimization outcome, to ensure robustness of the achieved polarization against perturbations of the edge morphology. These results provide the inspiration to loop back into the realm of ideal lattices in search of new configurations characterized by extreme polarization. The peculiar shape and connectivity of the TO-generated lattice offer a blueprint for identifying a new family of Maxwell trusses based on augmented kagome geometry. We demonstrate the achievement of strong polarization signatures up to a three-count edge state mismatch. For all the cases studied, we show agreement between theory, simulations, and experiments, which include laser vibrometry wave measurements on a waterjet-cut specimen and static tests on a 3D-printed prototype.

We study the statistical field-theoretic renormalization of active flocks via the Martin-Siggia-Rose-De Dominicis-Janssen (MSRDJ) formulation of stochastic dynamics, focusing on the Toner-Tu theory of Malthusian flocks, or polar-ordered, momentum non-conserving active fluids in which density fluctuations relax sufficiently rapidly to be eliminated as hydrodynamic degrees of freedom. Working in the limit of isotropic diffusion in two spatial dimensions, we perform an all orders analysis of the perturbative renormalization of propagators and interaction vertices. We show that a nonlinearly realized diagonal rotation/shift symmetry gives rise to Ward identities that protect the trigonometric structure of the convective derivative, ensuring that the sine and cosine interaction potentials retain their functional form under renormalization up to a rescaling of their overall couplings. We demonstrate that the freedom to renormalize the dynamical critical exponent in this boost non-invariant theory prevents the determination of the precise values of the critical exponents and anomalous dimensions in the theory, highlighting parallels and crucial differences with sine-Gordon and XY models. We express all anomalous dimensions as functions of the dynamical critical exponent, which remains undetermined due to the absence of a relation ordinarily forced upon boost invariant systems. We revisit and contextualize several claims and counterclaims in the recent literature in light of these results.

Translation invariance underlies all algebraic constructions of topological codes with geometrical locality. It has remained an open question whether codes that generically break this invariance can still be topological and simultaneously possess geometrical locality. Resolving this question is important both fundamentally—deepening our understanding of topological phases—and practically, as relaxing translation invariance could vastly expand the design space and potentially reduce resource overhead in fault-tolerant architectures. Here we introduce space-group codes, in which crystallographic point-group operations enter the bulk stabilizer algebra; bivariate bicycle (BB) codes arise as the translation-only limit. The key insight is that the point-group orbit resolves topology and locality together: it yields a computable algebraic criterion for topological order and a folded geometry in which point-group operations become local. We identify space-group codes whose code parameters exceed the reported same-blocklength, same-check-weight BB benchmarks. In five parameter-matched neutral-atom comparisons, reflection codes reduce the optimized movement cost in every case, by up to $60\%$, while folded placements also enable lower-overhead multilayer superconducting layouts. Treating spatial operations as a code-design variable therefore opens a route to topological codes jointly optimized for information protection and hardware geometry.

The tunability and control of topological edge/surface states are crucial for the development of new device applications. In this work, by combining first-principles calculations and Wannier-based tight-binding methods, we show the emergence of quantum spin Hall phases in van der Waals heterostructures formed by stacking two trivial quintuple layers from the Bi$_2$Te$_3$ family. We demonstrate the tunability of the edge states under interlayer strain and external electric field effects, suggesting the possibility of switching topological edge states on/off by external control. Additionally, the quantum spin Hall edge channels remain robust against interlayer twist, highlighting their stability against external perturbations. Our results provide a new way to create and manipulate two-dimensional topological phases in systems based on Bi$_2$Te$_3$ family, which can be valuable for practical applications, such as topological field effect transistors and spintronic devices.

We investigate the magnetic ground states and transverse spin excitations of bilayer and trilayer nickelates within a multi-orbital itinerant framework. For the bilayer system, although Hartree-Fock calculations slightly favor a double-stripe order, the calculated excitation spectrum of the single-stripe state, characterized by an anisotropic low-energy cone at $Q_{\text{BL}}$ and isotropic high-energy excitations near $\Gamma$, exhibits good qualitative agreement with recent RIXS and neutron scattering experiments. We further identify mirror-even optical interlayer modes at $Q_{\text{BL}}$ whose energies match the mirror-odd modes at $\Gamma$. For the trilayer system, both mirror-odd and mirror-even spin-density-wave states can be stabilized near $Q_{\text{TL}}$, with the mirror-odd state lower in energy in the parameter regime studied. The mirror-odd state hosts an additional nearly gapless mode dominated by the middle layer, while the mirror-even state contains only one acoustic branch together with two gapped optical modes. Comparison with available RIXS data favors the mirror-odd spin-density-wave scenario. Our results show that magnetic excitations provide a sensitive probe of the magnetic order and support a common itinerant origin of magnetism in multilayer nickelates.

Variational infinite matrix product state (iMPS) calculations usually make Hamiltonians with algebraically decaying interactions compatible with standard MPO algorithms by first replacing the target Hamiltonian with a finite-pole sum-of-exponentials surrogate, thereby introducing a Hamiltonian-representation residual. We formulate the fixed-$D$ variational energy without introducing such a surrogate. For a fixed finite-$D$ MPS, the algebraic tail can be summed directly through the connected transfer matrix: the tail $e^{\mathrm{i} Qr}/r^\alpha$ is represented by the matrix function $F_{\alpha,Q}(\widetilde{T}_A)$, with $F_{\alpha,Q}(z)=\operatorname{Li}_\alpha(e^{\mathrm{i} Q}\,z)/z$. We evaluate the resulting matrix-function action using a Krylov method and obtain stable gradients by combining a Fréchet adjoint with implicit fixed-point differentiation. Benchmarks on long-range free fermions and the inverse-square Heisenberg family, including the Haldane–Shastry point, validate the transfer-matrix-function formulation. A long-range Ising-chain calculation illustrates a practical consequence of avoiding a finite-pole Hamiltonian representation. At a fixed, independently known critical field, finite-pole surrogate Hamiltonians can bias a critical diagnostic away from criticality, whereas the matrix-function calculation retains the expected critical signatures of the target algebraic Hamiltonian.

We consider protocols for control of dipolar Bose-Einstein condensates where the critical role is played by the long-range anisotropic interatomic magnetic dipole-dipole interaction. The phase diagram of such a condensate has been explored theoretically and experimentally with certain values of the interatomic scattering length corresponding to superfluid and supersolid phases, where supersolidity appears as a modulation in the ground state density. Preparation of this modulated ground state is challenging, since excitations appear as a result of a finite-time evolution required to produce qualitative changes in the wavefunction density. To solve this problem we consider the time-dependent control of a dipolar Bose-Einstein condensate using shortcuts to adiabaticity techniques, concentrating on design of the time-dependent scattering length, a parameter of the system easily tunable by contemporary experiments. The first technique is the variational approach based on the Euler-Lagrange equations for a separable ansatz describing the evolution of the superfluid state. Secondly, we study the transition from superfluid to supersolid using a direct optimization protocol. We discuss the fidelity of the developed protocols in terms of the evolution time.

Amorphous silicon (a-Si) is understood to be the canonical continuous random network material, ideally defined by fully fourfold coordination. Here, we show that a defect-free ('ideal') model of a-Si from machine-learning-driven molecular-dynamics simulations [L. A. M. Rosset et al., Nat. Commun. 16, 2360 (2025)], subsequently evaluated with hybrid-level density-functional theory computations, can accurately reproduce the experimentally observed electronic bandgap. We compare this model with one resulting from the Wooten-Winer-Weaire (WWW) bond-switching approach and with other recent approximants to ideal a-Si. More broadly, our work provides a platform for studies of band tails, optical properties, and transport in a-Si.

Navigating the vast space of synthetically accessible molecules demands surrogate models that are interpretable and capable of handling multiple competing objectives at the same time. Deep learning approaches struggle to satisfy them under the computational constraints of quantum-level chemistry. Here, we introduce a modular pipeline that combines interpretable linear meta-learning models and adaptive-confidence uncertainty quantification into an Efficient Global Optimization (EGO) framework for multi-objective molecular discovery. For the first time, linear meta-learning is deployed in a multi-objective chemical search setting: by training across chemical objectives and cheap auxiliary properties, the meta-learned surrogates acquire transferable chemical knowledge that adapts rapidly to new objectives from limited data. Evaluated empirically on a real large scale search for spin-crossover metal-organic complexes, the baseline performs 78% worse in Pareto sense than the meta-learning alternative. We also address the calibration challenges inherent to active search. Since optimal candidates typically lie precisely in the distributional tails, standard uncertainty estimates fail. We introduce an adaptive confidence-tuning algorithm that dynamically recalibrates the exploration-exploitation trade-off as the molecular search evolves. Empirically, dynamic confidence tuning further dominates over 50% of the statically calibrated front.

A defining feature of chirality is the distinction between a system and its mirror image. Despite extensive experimental observations of chiral phases and theoretical advances, a quantum-information theoretic characterization of chirality based solely on the entanglement structure of many-body quantum states remains elusive. Here, we introduce the notion of many-body chirality by formulating it as an obstruction to transforming a quantum state into its complex conjugate through finite-depth local operations. We rigorously establish many-body chirality for stabilizer realizations of $\mathbb{Z}_d^{(k)}$ anyon theories, proving that complex conjugation can be implemented by local quantum channels if and only if the underlying anyon data are mirror invariant. This reveals forms of chirality that evade conventional diagnostics, including examples with vanishing modular commutator, vanishing chiral central charge, and commuting-projector realizations. We further show that this obstruction is intrinsically four-partite, while invisible to tripartite entanglement structure. Finally, we prove that $\mathbb{Z}_d^{(k)}$ states with $d>2$ possess intrinsic many-body imaginarity: their complex phase structure cannot be removed by finite-depth local unitaries. Remarkably, this includes states that are not many-body chiral.

The topological heavy-fermion model provides a minimal framework for describing the coexistence of localized moments and itinerant Dirac electrons in magic-angle twisted bilayer graphene (MATBG). Several analytical and numerical methods have been applied to this model; however, whether they provide a realistic description of MATBG remains incompletely understood. In this work, we develop an Hubbard operator approach that incorporates non-local correlations beyond the single-site limit. We benchmark the approximate calculations against numerically exact determinant quantum Monte Carlo simulations of a lattice-regularized model. We show that commonly used local approximations, such as Hubbard-I, fail to capture the coupling between localized and itinerant degrees of freedom, leading to incorrect spectral properties in the local-moment regime. In contrast, the Hubbard operator method provides a controlled description of both correlation functions and spectral features over a regime of parameters, in good agreement with exact numerical methods.

Many industrial applications and biological scenarios involve the interdiffusion of two polymeric species. Motivated by biological subcellular source-driven processes, we study polymer-polymer interdiffusion problems in the absence or the presence of a polymeric source, for both unentangled and entangled scenarios. Utilizing a two-fluid formalism, we arrive at scaling relations, self-similar reductions, and analytical solutions, which are confirmed with one- and two-dimensional numerical simulations. The introduction of a source term breaks the self-similar structure, modifying the boundary conditions and the domain of integration. Nevertheless, we show that the front characteristics of the diffusing droplet exhibit similar spatial structures as in the absence of a source. Our results allow deeper understanding of polymer-polymer interdiffusion and nonlinear transport, especially in the presence of a source.

Statistical methods are essential for understanding thermodynamic systems with many degrees of freedom. For systems in equilibrium, a very useful method is that of correlation functions, which establish a correlation between a field phi(x), which depends on the spatial position x, and the same field evaluated at another position, phi(x0). Fisher [Journal of Mathematical Physics 5, 944322 (1964)] introduced the autocorrelation function for fluctuations of the order parameter, which has been an important mathematical tool for understanding second-order phase transitions in equilibrium. However, his analysis is restricted to a Euclidean space of dimension d, and an exponent eta is introduced to correct the spatial behavior of the correlation function at T = Tc. In a recent work, Lima et al. [Phys. Rev. E 110, L062107 (2024)] demonstrated that a modern fractional differential analysis is necessary for a complete description of the correlation function at Tc. In this study, we highlight the deep connection among scaling behavior, critical exponents, and fractal geometry. Our results provide a unified geometric interpretation of critical exponents and fractal dimensions, broadly applicable to thermodynamic phase transitions. However, the approach does not apply to topological phase transitions, which lack local order parameters and the associated scale-invariant fractal geometry. We verify its predictions for several cornerstone thermodynamic models: the Ising, Potts, XY, and Heisenberg systems.

Characterising the universal aspects of non-equilibrium quantum many-body dynamics is one of the key goals of this century's physics research. Progress, however, is hindered by the lack of general theoretical frameworks for studying interacting quantum matter far from equilibrium. A recent breakthrough has been the realization that several key non-equilibrium quantities, such as the rate of growth of entanglement or the fluctuations of conserved charges within finite subsystems, can be related to equilibrium properties through a space-time duality that effectively exchanges the roles of space and time. This observation effectively enables the study of non-equilibrium phenomena using tools and concepts borrowed from equilibrium statistical mechanics and thermodynamics. A first proof of principle of this framework, dubbed space-time duality approach (SDA), was provided by interacting integrable systems, where thermodynamic properties can often be characterized exactly, while dynamical quantities typically remain beyond analytical reach. Subsequent developments, however, revealed that the SDA suffered from an intrinsic ambiguity, restricting its applicability to homogeneous quenches and to charge fluctuations arising from symmetric initial states. Here we resolve this ambiguity from first principles and derive closed-form predictions for entanglement growth and charge fluctuations after general quantum quenches. We benchmark our results against the exact analytical solution of the Rule 54 quantum cellular automaton and extensive TEBD simulations of the XXZ chain. Moreover we show that, when specialised to the entanglement entropy, our framework naturally reproduces the predictions of the quasiparticle picture.

The Bose polaron problem of an impurity immersed in a Bose-Einstein condensate (BEC) has been predicted to feature strong correlations arising from bound states of multiple bosons with the impurity. While direct experimental evidence has so far remained elusive, here we observe clear signatures of three-body correlations in Bose polarons. We perform radiofrequency spectroscopy on $^{40}$K impurities in a BEC of $^{23}$Na and identify polaronic hybrid states that can be understood as superpositions of the bare atom, a NaK dimer and a Na$_2$K trimer, coupled through coherent particle exchange with the condensate. We show that the main spectroscopic features are captured by a simple three-level model without free parameters. Our work shows how a condensate environment can coherently hybridize bound states of different composition and mass, reminiscent of quark-flavor mixing described by the Cabibbo-Kobayashi-Maskawa (CKM) matrix in particle physics.

We show that the non-Hermitian skin effect (NHSE) can enhance pairing correlations in moiré Hubbard systems through a channel-selective mechanism: skin-induced localization amplifies the boundary density of states, strengthening local pairing tendencies within an intermediate “golden window” of non-reciprocity $\gamma\in[0.5,1.2]\,t$. Using exact diagonalization of the non-Hermitian Hubbard model on triangular lattices with open boundaries, we map the $(U,\gamma)$ phase diagram. The double occupancy $D(\gamma)$ exhibits non-monotonic behavior – rising by up to 21% then declining – reflecting a competition between NHSE-enhanced boundary pairing and over-localization. A decomposition of the pairing susceptibility $\chi_{\mathrm{SC}}$ on the $3\times3$ cluster reveals that the NHSE acts channel-selectively: it enhances on-site pairing ($+21\%$) while simultaneously suppressing competing antiferromagnetic correlations (22% reduction), so that the total pairing susceptibility, dominated by the on-site channel, grows by $+98\%$ on that cluster. These trends are corroborated by an independent non-Hermitian DMRG calculation and establish an enhancement of finite-cluster pairing correlations rather than trivial density redistribution. We do not claim long-range superconducting order. A BCS scaling estimate converts the same pairing-response signal into a dome-shaped $T_c(\gamma)$ fingerprint, suggesting an experimentally distinguishable response in coherent-drive versus reservoir-dominated moiré devices.