In this study we investigate the ground-state phase diagram of the quantum spin-$\frac{1}{2}$ anisotropic $\mathit{XZ}$ chain using the infinite time-evolving block decimation algorithm. The model exhibits four distinct phases: ${\mathrm{FM}}_x, {\mathrm{FM}}_z, {\mathrm{AFM}}_z$, and $\mathrm{PM}$. In terms of the transverse magnetic field $h$ and anisotropy parameter $J$, our analysis focuses on the lines $h=0$ and $0.5$ with $J\ge 0$, where different types of quantum phase transitions (QPTs) occur. We compute the bifurcation behavior of the ground-state fidelity per lattice site. On the line $h=0$, continuous behavior at the bifurcation point identifies a continuous QPT between the ordered ${\mathrm{FM}}_x$ and ${\mathrm{FM}}_z$ phases at the critical point $J_{c1}$, with bifurcations on both sides reflecting $Z_2$ symmetry breaking in both phases. On the line $h=0.5$, a continuous bifurcation indicates a QPT between the ordered ${\mathrm{FM}}_x$ and disordered $\mathrm{PM}$ phases at $J_{c2}$, with bifurcation occurring only on one side, corresponding to $Z_2$ symmetry breaking in a single phase. We further compute the ground-state fidelity susceptibility per lattice site. When the ground state is obtained from random initial states, the fidelity susceptibility exhibits oscillatory behavior in the symmetry-broken phase, providing a clear signature of ground-state degeneracy. These fidelity-based measures serve as effective tools for identifying critical points and characterizing the nature of symmetry breaking. To complement these results, we evaluate the two-spin Wigner-Yanase skew information and local quantum uncertainty (LQU) as indicators of quantum correlations. While both detect QPTs, we find that not all nonanalytic features in the LQU correspond to genuine phase transitions. A critical behavior analysis is carried out at $J_{c1}$ and $J_{c2}$ to extract the critical exponents ${\eta }^I, {\eta }^C, {\eta }^x$, and ${\eta }^z$, associated with mutual information $\mathcal{I}\left(r\right)$, classical correlation $\mathcal{C}\left(r\right)$, and spin-spin correlations $\langle {\sigma }_i^x{\sigma }_j^x\rangle , \langle {\sigma }_i^z{\sigma }_j^z\rangle$. Our results demonstrate that ${\eta }^{\mathcal{I}}={\eta }^C$ and ${\eta }^{x/z}={\eta }^{\alpha }/2$ for $\alpha =I,C$, consistent with known universal scaling relations. We also extract the order parameter exponent $\beta$, correlation length exponent $\nu$, dynamic exponent $z$, and the central charge $c$. A transition at $J_{c1}$ between the ${\mathrm{FM}}_x$ and ${\mathrm{FM}}_z$ phases is identified as a Gaussian transition with central charge $c=1$, involving the breaking of two $Z_2$ symmetries and lying beyond the conventional Landau-Ginzburg-Wilson symmetry-breaking paradigm. The transition at $J_{c2}$ between the ${\mathrm{FM}}_x$ and $\mathrm{PM}$ phases belongs to the quantum Ising universality class, characterized by $c=\frac{1}{2}$ and breaking of a single $Z_2$ symmetry.

For disordered systems within the random first-order transition (RFOT) universality class, such as structural glasses and certain spin glasses, the role played by activated relaxation processes is rich to the point of perplexity. Over the last decades, various efforts have attempted to formalize and systematize such processes in terms of instantons similar to the nucleation droplets of first-order phase transitions. In particular, Kirkpatrick, Thirumalai, and Wolynes proposed in the late 1980s an influential nucleation theory of relaxation in structural glasses. Already within this picture, however, the resulting structures are far from the compact objects expected from the classical droplet description. In addition, an altogether different type of single-particle hopping-like instantons has recently been isolated in molecular simulations. Landscape studies of mean-field spin-glass models have further revealed that simple saddle crossing does not capture relaxation in these systems. We present here a landscape-agnostic study of rare dynamical events, which delineates the richness of instantons in these systems. Our work not only captures the structure of metastable states, but also identifies the point of irreversibility, beyond which activated relaxation processes become a fait accompli. An interpretation of the associated landscape features is articulated, thus charting a path toward a complete understanding of RFOT instantons.

The Ising model on fractal lattices has attracted renewed interest, yet a quantitative understanding of how the critical temperature depends on the Hausdorff dimension $\left(D_{\mathrm{H}}\right)$ and connectivity $\left(Q\right)$ remains limited. We study the ferromagnetic Ising model on the one-parameter “legs-extension” family of fractal lattices originally introduced by Genzor et al. and apply the higher-order tensor renormalization group (HOTRG) method, following the tensor-network construction developed for these geometries in earlier work. By tuning a single structural parameter, we access lattices with $D_{\mathrm{H}}$ decreasing from $1.792$ to $1.260$ and connectivity $Q$ from $0.50$ to $0.131$, and obtain high-precision critical temperatures $T_{\mathrm{c}}$ and magnetization exponents $\beta$ with carefully quantified uncertainties from systematic bond-dimension and fitting-window analyses, finding that $\beta$ is strongly and almost exponentially suppressed as $D_{\mathrm{H}}$ is reduced. Along this one-dimensional trajectory in the $\left(D_{\mathrm{H}},Q\right)$ plane, $T_{\mathrm{c}}$ decreases monotonically with $D_{\mathrm{H}}$ and, when plotted against $Q$, exhibits a robust near-linear behavior within this lattice family over almost an order of magnitude in connectivity. A finite-temperature phase transition persists throughout the explored range down to our lowest Hausdorff dimension, $D_{\mathrm{H}}\approx 1.260$, implying that the lower critical dimension of this family, if it exists, lies below this value. Comparison with zero-order and first-order mean-field theory shows that HOTRG systematically incorporates fluctuation effects beyond mean-field approximations. The tabulated $T_{\mathrm{c}}$ and $\beta$ values thus provide a stringent benchmark for theories of criticality on fractal lattices and a quantitative reference for future numerical and analytical studies on other complex geometries.

In this study, we explore the geometric construction of the Klein bottle and the real projective plane $\left({\mathrm{RP}}^2\right)$ within the framework of tensor networks, focusing on the implementation of crosscap and rainbow boundaries. Previous investigations have applied boundary matrix product state techniques to study these boundaries. We introduce an approach that incorporates such boundaries into the tensor renormalization group methodology, facilitated by an efficient representation of a spatial reflection operator. This advancement enables us to compute the crosscap and rainbow free energy terms and the one-point function on ${\mathrm{RP}}^2$ with enhanced efficiency and for larger system sizes. Additionally, our method is capable of calculating the partition function under isotropic conditions of space and imaginary time. The versatility of this approach is further underscored by its applicability to constructing other (non)orientable surfaces of higher genus.

We describe in detail a mathematical framework in which statistical ensembles of hybrid classical-quantum systems can be properly described. We show how a maximum entropy principle can be applied to derive the microcanonical ensemble of hybrid systems. We investigate its properties, and in particular how the microcanonical ensemble and its marginal classical and quantum ensembles can be defined for arbitrarily small range of energies for the whole system. We show how, in this situation, the ensembles are well defined for a continuum of energy values, unlike the purely quantum microcanonical ensemble, thus proving that hybrid systems translate properties of classical systems to the quantum realm. We also analyze the relation with the hybrid canonical ensemble by considering the microcanonical ensemble of a compound system composed of a hybrid subsystem weakly coupled to a reservoir and computing the marginal ensemble of the hybrid subsystem. Lastly, we apply the theory to the statistics of a toy model, which gives some insight on the different properties presented along the article.

Fluctuation theorems establish that thermodynamic processes at the microscale can occasionally result in negative entropy production. At such scales, another distinct possibility becomes more likely: processes in which no entropy is produced overall. In this work, we explore the constraints imposed by such null-entropy events on the fluctuations of thermodynamic currents. By incorporating the probability of null-entropy events, we obtain tighter bounds on finite-time thermodynamic uncertainty relations derived from fluctuation theorems. Our results are directly applicable to both quantum and classical systems that satisfy the fluctuation theorem. We validate our framework using an example of a qudit SWAP engine.

Bulges in the plasma membrane of cells known as blebs can form spontaneously in a wide range of biological processes, but what controls their shape and stability remains incompletely understood. To address this we introduce a dual phase-field model with coupled order parameters representing the cell cortex and plasma membrane that can quantitatively model blebbing in three dimensions. Simulations and sharp-interface analyses reveal that, depending on whether blebbing occurs by detachment of the plasma membrane or rupture of the actin cortex, blebs can form discontinuously through a saddle-node bifurcation or continuously with increasing cortical tension. The model predictions are in good quantitative agreement with existing experimental data for laser-induced cortex rupture.

We introduce a time-embedded convolutional neural network (TCNN) for modeling spatiotemporal heat transport in plasmas, particularly under strongly nonlocal conditions. In our earlier work, the Luciani-Mora-Virmont (LMV) Informed Neural Network (LINN) (Luo et al., Phys. Rev. Res. 7, L042017 (2025)) combined prior knowledge from the LMV model with kinetic Particle-in-Cell (PIC) data to improve kernel-based heat-flux predictions. While effective under moderately nonlocal conditions, LINN produced physically inconsistent kernels in strongly time-dependent regimes due to its reliance on the quasistationary LMV formulation. To overcome this limitation, TCNN is designed to capture the coupled evolution of both the normalized heat flux and the characteristic nonlocality parameter using a unified neural architecture informed by underlying physical principles. Trained on fully kinetic PIC simulations, TCNN accurately reproduces nonlocal dynamics across a broad range of collisionalities. Our results demonstrate that the combination of time modulation, coupled prediction, and convolutional depth significantly enhances predictive performance, offering a data-driven yet physically consistent framework for multiscale plasma transport problems.

We propose a neural network model, which, with appropriate assignment of the stability of its equilibrium points (EPs), achieves Hopfield-like associative memory. The oscillator Ising machine (OIM), based on Kuramoto-like dynamics, is an ideal candidate for such a model, as all its $0/\pi$ binary EPs are structurally stable with their dynamic stability tunable by the coupling weights. Traditional Hopfield-based models store the desired patterns by designing the coupling weights between neurons. The design of coupling weights should simultaneously take into account both the existence and the dynamic stability of the EPs for the storage of the desired patterns. For OIMs, since all $0/\pi$ binary EPs are structurally stable, that is, any of these EPs remains an EP regardless of the values of the coupling weights or the system parameters, the design of the coupling weights needs only to focus on assigning appropriate dynamic stability for the $0/\pi$ binary EPs according to the desired patterns. In this paper, we establish a connection between the stability and the Hamiltonian energy of EPs for OIMs, and, based on this connection, provide a Hamiltonian-regularized eigenvalue contrastive method (HRECM) to train the coupling weights of OIMs for assigning appropriate stability to their EPs. Finally, numerical experiments are performed to validate the effectiveness of the proposed method.

Resolving the mean-squared displacement (MSD) and velocity autocorrelation function (VACF) of interacting Brownian particles remains a central challenge in simulations of soft-matter systems, especially at low densities where particle-particle interactions are sparse and signals are dominated by thermal noise. A recently proposed noise-cancellation (NC) algorithm [Mandal et al., Phys. Rev. Lett. 123, 168001 (2019)] addressed this by decomposing particle trajectories into two components: free Brownian motion and interaction-induced displacements. The NC approximation enhances signal clarity by neglecting cross-correlations between the total particle displacements and the extracted interaction-induced contributions of the trajectories—an assumption that has so far lacked rigorous theoretical justification. In this work, we establish an exact theoretical relation between the VACF, the force autocorrelation function (FACF) characterizing the interaction-induced contributions, and these cross-correlations, which is valid for Brownian systems. We show that in thermal equilibrium, the cross-correlations vanish for Brownian systems because the VACF is strictly proportional to the negative FACF, which establishes the NC algorithm as an exact method. In contrast, for Brownian nonequilibrium systems, the cross-correlations remain finite, providing a direct fingerprint of nonequilibrium physics in such systems and a criterion to distinguish equilibrium from nonequilibrium states. Here, suitable corrections must be applied for the NC method to remain accurate. Our results expand the scope of the NC algorithm to a broad range of soft-matter systems in and out of equilibrium, where it has the potential to strongly enhance the resolution of VACF data obtained through simulations in future studies.

In this work, we develop an operator learning augmented physics-informed neural network (OL-PINN) framework for solving partial differential equations with sharp solution features and singular behaviors. The method combines the standard PINN architecture with a pretrained deep operator network (DeepONet), which is trained on a related class of smooth problems and serves as an operator prior to provide reliable extrapolations. This integration acts as a regularization mechanism that enhances stability, improves efficiency, and reduces the reliance on large numbers of residual points. The proposed OL-PINN is systematically validated on several benchmark problems, including the nonlinear diffusion–reaction equation, Burgers equation, lid-driven cavity flow, and the two-dimensional Navier-Stokes equations in vorticity form. Numerical experiments demonstrate that OL-PINN achieves higher predictive accuracy and more stable convergence than vanilla PINNs and DeepONet extrapolations, even when trained with only a small number of residual points. Importantly, OL-PINN proves effective in addressing ill-posed problems with incomplete boundary conditions, which are intractable for classical numerical methods. Furthermore, OL-PINN is able to predict new small-scale flow structures, such as emergent vortices at higher Reynolds numbers, highlighting its potential as a promising tool for simulating turbulent or near-turbulent flows.

Unlike classical elasticity, where stresses arise from deformations relative to a stress-free reference configuration, rigidity in amorphous systems is maintained by disordered force networks that generate internal prestress. Previously, we introduced a “stress-only” formulation, where mechanical equilibrium resembles Gauss's law in a rank-2 tensor electrostatics with vector charges, and demonstrated that the mechanical response of jammed solids is described by the dielectric response of this gauge-theoretic formulation. Here, we extend this framework by incorporating scale-dependent screening that captures both dielectric and Debye-type behavior. This introduces a characteristic length scale in stress correlations as well as in the response to external forces. Through numerical simulations of soft-sphere packings, we show that this length scale is set by the particle size, thus providing a natural ultraviolet cutoff while preserving long-wavelength emergent elasticity. We show that this length scale remains finite for all pressures, with no evidence for an emergent Debye-like screening near the frictionless unjamming transition. We demonstrate that, although individual realizations show strong fluctuations, disorder averaging at fixed macroscopic conditions yields a robust dielectriclike response that persists up to unjamming. Finally, we also provide a physical interpretation of the gauge field within the electrostatic mapping: relative grain displacements in response to localized external perturbations correspond to difference in the gauge field, linking the field-theoretic description to particle-level mechanics.

We construct a mathematical model for a diffusiophoretic motion of a deformable droplet, which is floating at a liquid surface and is driven by the surface tension gradient originating from the surface concentration field of the chemicals that are emitted from the droplet. We define the free energy of the system by including the surface and line energies. From the calculation of the functional of the free energy, we obtain a mathematical model for the diffusiophoretic motion with deformation. By only considering the deformation of the second mode, we explicitly derive the time-evolution equations for the translational motion and the elliptic deformation. There are three stable states: an immobile circular droplet, an immobile elliptically deformed droplet, and a mobile droplet with the elliptic deformation in which the minor axis meets the motion direction, and we discuss the transition between these three stable states.

We analyze the dynamic properties of dissipationless generalized Langevin equations in the presence of fluid inertial kernels possessing power-law tails, $k\left(t\right)\sim t^{-\kappa }$. For $\kappa >1$ no thermalization occurs, and particle motion is ballistic. Since the long-term statistical properties of velocity depend on the initial preparation of the system, this case falls in the realm of nonergodic behavior as momentum transfer is concerned. Conversely, new phenomena arise for $0<\kappa <1$. In this case, a form of weak thermalization appears in the presence of thermal/hydrodynamic fluctuations and attractive potentials. However, the absence of dissipation clearly emerges once an external constant force is applied: an asymptotic settling velocity cannot be achieved as the expected value of the particle velocity diverges.

We apply the theory of Resonance-Assisted Tunneling (RAT) to a many-body quantum kicked system with a well-defined semiclassical limit. Using a quantum resonant condition, we identify eigenstates associated with classical resonances and compute their quasienergy splitting semiclassically. We distinguish two regimes: the first, where RAT predictions show excellent agreement with exact quantum results, and a second, where the splitting coincides with that of a harmonic oscillator with frequency determined by the classical oscillation of the resonance. We quantify the perturbation strength above which RAT theory is no longer valid and analyze its scaling in the semiclassical limit, providing analytical expressions to estimate this upper bound.

Nonequilibrium spatiotemporal patterns have been extensively studied. However, a single oscillator or cyclic loop of states is typically employed at each site in theories and simulations. Here, we investigate how competition among multiple identical cyclic loops at each site alters patterns. We simulate active Potts models with standard Potts interactions between neighboring sites in two-dimensional square lattices. When multiple three-state cycles exist in state flips, such as in octahedral and square-antiprism networks, all types of spiral waves comprising the three states are formed simultaneously at high flip energies. However, at lower energies, only one or a few types emerge and switch stochastically into different types. At even lower energies, cyclic changes in single-state dominant homogeneous phases emerge [homogeneous cycling (HC) mode]. At intermediate flip energies, the spiral wave and HC modes temporally coexist in small systems but do not switch between each other in large systems. Conversely, when multiple four-state cycles exist in six-state and cubic networks, one state remains dominant for the entire range of flip energies, whereas the other states occasionally form domains at intermediate flip energies. Therefore, the number of spatially coexisting states can be controlled using flip networks and energies.

We investigate the processes of plasma formation and phase transitions occurring during the explosion of metal point emitters made from copper and tungsten wires approximately 1 mm in length and $\sim 10$ $\mu \mathrm{m}$ in diameter. The experiments were performed under vacuum-to-forevacuum discharge conditions using nanosecond current pulses of up to $\sim 1$ kA. It was found that an extended region of the copper emitter, with a length of $\sim 200$–300 $\mu \mathrm{m}$, remains intact for tens of nanoseconds and even after the discharge ends, while the emitter's base explodes completely, and its explosion products become stratified. A transition zone is observed between the base and end regions of the emitter, characterized by a smooth or sharp expansion of the degraded metal without stratification in the explosion products. During the copper emitter explosion, ejections of dense plasma with an electron concentration of at least ${10}^{20}{\mathrm{cm}}^{-3}$ can occur. The expansion velocity of the exploded copper emitter material can reach $(1–3)\times {10}^5$ cm/s at residual air pressures of ${10}^{-4}$ to ${10}^{-1}$ Torr. An increase in air pressure to $\sim 1$ Torr leads to a decrease in both the specific energy input and the expansion velocity of the explosion products. The explosion dynamics of copper and tungsten point emitters differ. In the structure of the tungsten emitter's explosion products, no striations are observed, and the length of the exploded region almost entirely coincides with the emitter's total length. Analysis of the point emitters' explosion dynamics and the discharge's electrophysical parameters indicates that the transition of the emitter to the explosion regime is based on two key stages: first, the achievement of the explosive electron emission mode over an extended part of the emitter's end region, followed by the development of a shunting breakdown through the expanding explosion products along the emitter surface.