The temporal decay of triggered seismicity is commonly described by the Omori law $r\left(t\right)\sim {(t+c)}^{-p}$. I introduce a minimal phenomenological framework that relates this temporal decay to two concurrent processes: the spatial spreading of a triggering perturbation and the progressive depletion of elements that remain susceptible to failure. The model yields the scaling relation $p=1-\alpha d/2+\gamma$, where $\alpha$ characterizes spreading, $d$ is an effective spatial dimension, and $\gamma$ describes depletion or healing. This relation provides a joint consistency test rather than a unique inversion of the Omori exponent for material healing. Numerical simulations recover the predicted scaling. A comparison with published earthquake-pair statistics illustrates that slow spatial spreading can be identified, but also that spatial and temporal exponents cannot be combined unless their underlying observables and event selections are compatible. The main implication is that the Omori exponent alone cannot generally be interpreted as a direct measure of fault or reservoir healing; testing the proposed relation requires compatible estimates of spatial spreading, event-rate decay, effective geometry, and, where possible, an independent recovery observable.

We introduce the popularity-driven random walk graph convolutional network (PDRW-GCN), a topology-aware graph neural network that incorporates degree-biased diffusion to exploit the heavy-tailed connectivity of scale-free networks. By incorporating a structural bias parameter, $\beta$, the model dynamically reweights neighborhood propagation based on node degree. We identify a topology-dependent diffusion transition in heterophilic graph learning: Sparse heterophilic networks benefit from hub-amplified transport ($\beta >0$), whereas dense heterophilic networks require hub-suppressed diffusion ($\beta <0$) to prevent noisy neighborhood overmixing. Experiments across homophilic and heterophilic benchmark networks demonstrate consistent improvements in node classification performance measured by F1 score and receiver operating characteristic—area under the curve. Moreover, the model exhibits diminishing performance gains on non-scale-free topologies, indicating that $\beta$ acts primarily as a topology-dependent routing mechanism rather than a generic regularizer.

A theoretical model is presented for the reacceleration process of the bubble and the spike that follows after the velocity saturation phase in the nonlinear, single-mode, two-dimensional Rayleigh-Taylor instability in ideal media. A previous irrotational model is extended to include the vorticity effects consistently with the existing evidence that vorticity drains momentum from the translational motion. Contradictions and paradoxes arising from the current paradigm based on the acceleration by the vortices centrifugal force are solved. The model shows that the time when the reacceleration occurs depends on the density ratio between both fluids, and that it is determined by achieving the corresponding final widths of the bubble and the spike, which thereafter remains constant.

An exact microcanonical analysis of the one-dimensional Ising model is presented with emphasis on the emergence of negative temperatures. The number of states of the system is obtained as a function of the energy, the magnetization, and the number of spins. The Boltzmann and Gibbs entropy is computed, and the results are compared in the thermodynamic limit and for finite systems as well. According to the Boltzmann scenario, negative temperatures naturally appear as a consequence of the energy bounded spectrum. In this case, the Boltzmann entropy is not symmetric with the energy as soon as the magnetization is different from zero and does not vanish at the maximum allowed value of the energy. Along with entropy, the specific heat and magnetic susceptibility are analyzed as functions of the temperature. Although the specific heat is always positive, the symmetry is also broken in both branches of positive and negative temperatures for finite values of the magnetization. The susceptibility, in its turn, changes sign in the negative sector. In addition, the phase transition, which is present when the temperature goes to zero from the right, is totally suppressed when the temperature tends to zero from the left. Finite-size effects are also studied to understand the equivalence of the microcanonical and canonical formulations for this interacting model. Negative temperatures are not allowed according to the Gibbs formulation.

Perfect LOCC (local operations and classical communication) discrimination of locally indistinguishable quantum states usually requires maximally entangled states as a resource. Whether nonmaximally entangled resources can enable perfect LOCC discrimination of locally indistinguishable states remains an interesting area of research. The states in the three-qubit Greenberger-Horne-Zeilinger (GHZ)-SLOCC (stochastic local operation and classical communication) class can display various entanglement distribution patterns, including cases with no bipartite entanglement in any reduced subsystems, or instances where bipartite entanglement occurs across one, two, or all three reduced subsystems. Significant research has explored how such states can be used in entanglement-assisted discrimination tasks. In this paper, we investigate the distinguishability of orthogonal product states using GHZ-SLOCC class entangled states, and we identify two nonmaximal GHZ-SLOCC states that facilitate perfect distinguishability. Additionally, we analyze the relationship between the probability of error and the amount of bipartite and multiparty entanglement. Our analysis focuses on how the distribution of entanglement affects the accuracy of state discrimination.

Analytic continuation from imaginary-time Green’s functions to real-frequency spectra is a central ill-posed inverse problem in quantum many-body physics. We show that the thermal kernel admits an analytical generalized singular-value structure once its purely dynamical part is separated from the statistical weight imposed by the heat bath. The dynamical kernel is the imaginary-bandwidth continuation of Slepian’s finite Fourier transform and is governed by the same Sturm-Liouville algebra that yields prolate spheroidal wave functions. Fermionic and bosonic statistics then enter as gauge transformations of the frequency-space inner product, giving a generalized singular system and self-adjoint effective potentials in the corresponding weighted space. The Shannon number, $N_c=\beta {\omega }_{\max }/\pi$, fixes the upper information capacity of this pure Laplace channel. Finally, the optimal sampling points are obtained as eigenvalues of a Legendre colleague matrix, giving a deterministic compressed-sensing grid without iterative root searches.

The actin cytoskeleton is an inherently disordered active system. The actomyosin cortex and reconstituted actomyosin systems are globally disordered, yet undergo transitions between distinct disordered states as parameters like motor and crosslinker concentration and filament length and rigidity change. In cells, these changes are related to genetic mutations or differences in cell state and dictate fundamental biological processes. However, we do not have well-established methods to detect and classify differences in disordered polymer networks. Image-based morphology techniques provide a noninvasive, high-throughput method of extracting information about a system. In this work, we simulate biopolymer networks under varying conditions and develop and use morphological descriptors to construct trajectories in morphospace. Using statistical analysis, we find that morphological descriptors are able to distinguish between different trajectories of the system, including differences not apparent to the eye. However, no single descriptor alone is able to capture all the differences in the simulated trajectories. Nematic order parameters typically perform the worst for our simulations, while curvature and texture descriptors can collectively distinguish between dynamic trajectories. This work helps develop quantification of cytoskeleton dynamics for classification and data-driven modeling.

The realization of spin-based devices remains one of the central goals of spintronic research. Single-molecule magnets constitute an important class of nanoscale magnetic systems with significant potential for spintronic applications, where individual molecules can serve as fundamental building blocks of functional devices. In this work, we systematically investigate a family of $4d$ and $3d$ transition-metal metallocenes using first-principles density functional theory. Among the seven $4d$ metallocenes considered, only Mo and Rh metallocenes undergo Jahn-Teller distortions and exhibit uniaxial anisotropy with energy barriers of approximately 20 K. Similarly, among the $3d$ metallocenes studied in this work, only Cr and Co metallocenes undergo Jahn-Teller distortions and display uniaxial anisotropy, although with smaller barriers below 10 K. All remaining metallocenes exhibit easy-plane anisotropy. We find that the magnetic anisotropy energy does not increase monotonically with the number of $d$ electrons; instead, it is governed primarily by the orbital ordering of the transition-metal $d$ states. Our calculations further show that the Jahn-Teller distortion induces transverse anisotropy, leading to zero-field magnetization tunneling across the energy barrier, with the weakest tunneling rate for Mo metallocene. For the Mo metallocene, the magnetic anisotropy energy increases to approximately 60 K in cationic charge states, although the magnetic anisotropy changes from uniaxial to easy plane. In this work, we also investigate the influence of ligand size on the structural stability of metallocenes and establish practical guidelines for constructing reliable molecular models for first-principles studies. Finally, we also propose that metallocenes with easy-plane anisotropy could serve as magnetic sensing elements, highlighting their potential beyond memory applications.

We employ the polar decomposition of the Dirac field to describe it as an effective spinorial fluid. We then construct a $(1+1+2)$ covariant formalism for the Dirac field that avoids the introduction of tetrad fields and Clifford matrices. Within this framework, we analyze the conditions under which a self-gravitating Dirac field can be consistently embedded in locally rotationally symmetric (LRS) space-times of types I, II, and III. In accordance with the LRS symmetry requirements, we extend a previous work by assuming that the velocity and spin vector fields of the Dirac field lie in the planes defined pointwise by the generators of the timelike and spacelike congruences, which underlie the $(1+1+2)$ decomposition. We present some analytical and numerical solutions to illustrate the applicability of the proposed framework.

Half-metallic ferromagnets exhibit a gap in the density of states for one spin projection while remaining gapless for the opposite spin. We show that in helimagnets an unusual half-metallic state can exist, where the spin projection that experiences the gap is determined by the direction of the wave vector. This state originates from the nontrivial topology of the band structure, specifically from the dispersion forming a multisheeted covering over the Brillouin zone. We present two-dimensional tight-binding models for $p$-wave and $f$-wave half metals. These structures can be realized in crystalline and van der Waals systems. The complex band structure of the unusual $p$-wave half metal in nanostructures is also discussed. In a quantum well, a standing wave with a helical spin structure is formed, and a persistent spin current exists.

Living systems display organized, context-dependent dynamics through a restricted repertoire of persistent functional states. At mesoscopic scales, where biological motion is classical, dissipative, and noisy, such discreteness cannot be attributed to microscopic quantum effects alone. Here, we formulate a mesoscopic theory of functional closure for thermodynamically open episodes in which regulatory organization confines the dynamics to an approximately invariant informational class. Within a constrained open Hamilton-Jacobi framework, exact dissipative composability requires the complete irreversible realization of a biological act—including bulk, interfacial, regulatory, composite, and unresolved internal contributions—to admit an exhaustive, nonredundant thermodynamic partition. In an approximately isothermal regime, causal accumulation of the total irreversible power defines a unique positive dissipative-action scale, ${\hslash }_{\mathrm{B}}$. This act-dependent scale sets the resolution of distinguishable functional realizations, while closure defines the domain on which a global additive action invariant can be constructed. If the nontrivial closure spectrum has a least positive action scale, its admissible values form an exact lattice. Quantization in biological dissipative-action units occurs only when this primitive closure scale saturates the independently constructed thermodynamic resolution, so that the spectrum is resolved in integer multiples of ${\hslash }_{\mathrm{B}}$. Coherent functional modes are the closure-compatible, persistent, and action-resolved realizations of these discrete classes. The theory predicts clustering of completed trajectories in actionlike observables and separates state correlation, hidden dissipation, and information-geometric distinguishability from the exact composability of irreversible physical cost.

In strongly correlated multiband systems, such as intermetallics, heavy fermions, and Kondo insulators, electron-electron interactions lead to the damping of electronic quasiparticles at finite temperatures. This phenomenon results in an effective dehybridization between the electrons in the large conduction band and those in the narrow, correlated band. The dehybridization effect has been employed to explain the temperature dependence of several physical properties of intermetallics, heavy fermions, and actinide compounds. Recent insights from the theory of non-Hermitian systems provide a novel perspective on this problem. In this work, we adopt this viewpoint through a renormalization group (RG) approach. We derive RG equations for a one-dimensional two-band model to identify the exceptional points of this system and to characterize its topological properties. Our findings reveal that for a topological, non-Hermitian particle-hole-symmetric chain, dehybridization can be interpreted as a topological phase transition, characterized by critical exponents that we calculate. We discuss the nature of the energy scale for dehybridization in the context of the phase diagram of heavy fermions.

We provide an operational interpretation of the multivariate Rényi divergence in terms of economic-theoretic tasks based on betting, risk aversion, and multiple lotteries. Specifically, we show that the multivariate Rényi divergence $D_{\underline{\alpha }}\left({\vec{P}}_X\right)$ of probability distributions ${\vec{P}}_X=(p_X^{\left(0\right)},...,p_X^{\left(d\right)})$ and real-valued orders $\underline{\alpha }=({\alpha }_0,...,{\alpha }_d)$ quantifies the economic-theoretic value that a rational agent assigns to $d$ lotteries with odds $o_X^{\left(k\right)}\propto {\left(p_X^{\left(k\right)}\right)}^{-1}$ ($k=1,...,d$) on a random event described by $p_X^{\left(0\right)}$. In particular, when the odds are fair and the rational agent is allowed to maximize over all betting strategies, the economic-theoretic value (precisely, the isoelastic certainty equivalent) that the agent assigns to the lotteries is exactly given by $w_{\underline{R}}^{\mathrm{ICE}}=exp\left[D_{\underline{\alpha }}\left({\vec{P}}_X\right)\right]$, where $\underline{R}=(R_1,...,R_d)$ is a risk-aversion vector with $R_k=1+{\alpha }_k/{\alpha }_0$ being the risk-aversion parameter associated with lottery $k$. Furthermore, we introduce a conditional multivariate Rényi divergence that characterizes a generalized scenario where the rational agent is allowed to have access to side information. We prove that this quantity satisfies a data processing inequality that can be interpreted as the increment in the economic-theoretic value provided by side information; crucially, we show that such a data processing inequality is a consequence of the agent's economic-theoretically consistent risk-averse attitude toward every lottery and vice versa. Moreover, we demonstrate the applicability of these results to the resource theory of informative measurements within the operational framework of general probabilistic theories encompassing quantum theory. By establishing quantitative connections between information theory, physical theories, and theories from economics, our framework provides an operational foundation for quantum state betting games with multiple lotteries in the realm of quantum resource theories.

High-entropy alloy superconductors, characterized by extreme chemical disorder and complex electronic environments, have attracted significant attention as model systems for exploring superconductivity in disordered materials. Here, we investigate a Cr-based equiatomic high-entropy alloy, Cr-V-Ti-Nb-Ta, which contains a magnetic $3d$ element, providing an opportunity to examine the influence of magnetic elements on superconductivity in highly disordered systems. Despite expected magnetic pair breaking, this alloy exhibits bulk type-II superconductivity with a transition temperature of $T_c=2.33\left(3\right)\mathrm{K}$ and a high upper critical field. Transverse-field $\mu \mathrm{SR}$ measurements reveal an $s$-wave superconducting gap close to the BCS value, while zero-field $\mu \mathrm{SR}$ suggests preserved time-reversal symmetry. These results establish Cr-V-Ti-Nb-Ta as a promising platform for exploring the interplay between disorder, magnetism, and superconductivity in high-entropy alloys.

Two types of coherent population transfer are developed using nonresonant intense ultrashort optical pulses. Transition-restricted wave-packet interference (WPI) achieves almost complete population transfer to the nearest state from the initial state. High-intensity optical-field population transfer between eigenstates (HOPE) also enables state-selective excitation of higher-lying states, exhibiting features of ac Stark-induced multiphoton Rabi oscillation and multipulse WPI. Experimentally, rotational excitation of nitric oxide from $J=1/2$ to $J=3/2$ via restricted WPI, and to $J=5/2, 7/2$, and $9/2$ via HOPE, was demonstrated with respective efficiencies of 90%, 85%, 70%, and 17%.

Active turbulence in overdamped chiral systems presents a complex challenge, namely, the frequent exhibition of nonuniversal spectral scaling, creating large-scale coherent structuring that seemingly defies standard inertial fluid descriptions. In this study, we investigate the hydrodynamic limit of a two-dimensional polar chiral active fluid modeled as an ensemble of locally coupled, motile Kuramoto-Sakaguchi oscillators. By introducing a renormalized fluid element (RFE) operator, we coarse-grain microscopic phase singularities, and in so doing, we isolate the macroscopic transport dynamics. We demonstrate that while the raw phase field consistently exhibit a steep, dissipative energy spectrum, associated with enstrophy injection at the microscale, the RFE-filtered field reveals a dual behavior characterized by an inverse energy cascade. When the intrinsic frequency dispersion, drawn from a scale-free power-law distribution, is broad enough to seed fluctuations at all resolved scales, this hidden cascade acts akin to a topological heat pump, driving the system toward a state of macroscopic vortex clustering, structurally analogous to supersonic shallow water dynamics. Conversely, a narrow frequency dispersion results in kinetic arrest, forming an active vortex glass. These results suggest that overdamped phase-slaved active matter can sustain effective inertial cascades, providing a mathematical framework for understanding scale-dependent energy transport in driven chiral systems.

Low-energy effective theories provide a natural description of four-dimensional physics in higher-dimensional geometries, where the imprint of the bulk geometry appears as parameters of the lower-dimensional theory. Inspired by the Damour-Esposito-Farése model of spontaneous scalarization in first-generation scalar-tensor theories of gravity, we investigate the possibility of tachyonic instability and spontaneous scalarization in braneworld scenarios. We consider the two-brane Randall-Sundrum (RS) model where the low-energy effective theory on either brane is of scalar-tensor nature with the extra-dimensional radion playing the role of the scalar. We have determined the possibilities for tachyonic (in)stability of the radion field on either brane in three scenarios: the RS model with fine-tuning conditions in which the potential of the radion field vanishes identically, the RS model without fine-tunings where the radion potential arises purely from the gravity sector, and the RS model with a bulk stabilizing field that generates a radion potential with a minimum. With the bulk stabilizing field, we have found that on-brane matter with $T>0$ changes the vacuum expectation value (VEV) of the radion, destroying the resolution of the gauge hierarchy problem, whereas on-brane matter with $T<0$ does not alter the stability and VEV of the radion. We further determined the exact condition of tachyonic (in)stability of radion field with the on-brane ${\mathrm{dS}}_4$ and ${\mathrm{AdS}}_4$ geometries.

The influence of plasma on the evolution of scattering singularities in microwave cavities remains largely unexplored, despite its importance for controlling reflectionless plasma excitation. In this work, we investigate the evolution of scattering singularities in a plasma-loaded microwave cavity. To analyze this complex interaction, a numerical model describing an experimental cavity containing a plasma tube is developed. This model enables the tracking of singularity evolution across various plasma configurations and explains the underlying physical mechanisms. Our results demonstrate that significant changes in the imaginary frequency of these singularities occur under two specific conditions: high collision frequency associated with optimal electron densities or high electron densities associated with optimal collision frequency. Furthermore, in the collisionless regime, we show that the variation of the real frequency increases due to the excitation of a transverse plasmonic resonance inside the plasma tube.