Optimization of computational efficiency and improving predictive stability remain key challenges in reservoir computing (RC) research. Building on the principle of Poincaré recurrence theorem, we propose a dynamic structural bias RC algorithm, significantly improving the prediction stability. Our framework refines the conventional training process by introducing a two-step mechanism. First, a reference state library is constructed from the training time series. Second, this library is used in conjunction with a dot-product similarity calculation to generate a structural, dynamic bias term. This dynamic bias introduces high-fidelity historical information into the reservoir's state update equation. The benefit is that the bias in the prediction phase acts as a dynamic constraint guiding the reservoir evolution toward the true known trajectory. We prove that our algorithm enhances the model's ability to maintain generalized synchronization with the target system's attractor in the autonomous prediction phase. Consequently, our method achieves two key advantages: predictive stability is dramatically improved, and the model's sensitivity to network hyperparameters is reduced. We demonstrate the effectiveness of our method through the reconstruction and long-term prediction of various low-dimensional chaotic systems, showing a substantially increased prediction horizon and a more stable, faithful reproduction of the attractor's structural geometry.

Synthesizing intense terahertz (THz) waveforms with user-defined electric field profiles represents a pivotal challenge for controlling matter at ultrafast timescales. While relativistic electron beams can serve as a versatile source of coherent radiation, conventional schemes lack the ability to deterministically sculpt the temporal structure of the emitted light. Here, we experimentally demonstrate a paradigm for generating tailored THz waveforms by manipulating the longitudinal phase space of the electron beam. By controlling the nonlinear longitudinal correlation of an energy-chirped electron beam, we generate a microbunch train with a chirped density modulation. When coupled to a tapered undulator, this structured beam produces coherent radiation, whose spectral-temporal properties are tunable via adjustment of the undulator taper. Autocorrelation measurements confirm the emission of chirped pulses spanning 8–13 THz, with spectral characteristics that align with simulations of the beam structure. Our approach, establishing a direct link between beam dynamics and light-field synthesis, opens a pathway toward customizable high-field waveforms for advanced coherent control experiments.

Quantum systems with strong long-range interactions are thought to robustly resist thermalization because their energy spectra organize into a discrete number of multiplets. We show that this nonthermal behavior is surprisingly fragile to an experimentally ubiquitous perturbation: a staggered magnetic field. Using self-consistent mean-field theory and exact diagonalization, we reveal that the energy spectrum, while composed of discrete subspaces or multiplets, collectively forms a dense spectrum. The equilibration time is independent of system size and depends only on the fluctuations in the initial state. For initial states at low to intermediate energies, the long-time average aligns with the $S^z$ sector-weighted microcanonical ensemble. However, for states in the middle of the spectrum, the long-time average depends on the initial state due to quantum scarlike eigenstates localized at unstable points in classical phase space. Our results can be readily tested on a range of experimental platforms, including Rydberg atoms or optical cavities.

The on-demand manipulation of triplet states in closed-shell single molecules is still out of reach due to a lack of information about the energy of those triplet states. Yet, the access to triplet states would open up a route toward an all-optical single-molecule photonic switch/transistor and, moreover, would provide a way of performing coherent spin operations from the spinless ground state. In this work, we take an important step toward those aims by measuring the triplet energy from the weak phosphorescence signal of perdeuterated perylene, embedded as a guest molecule in a dibenzothiophene host matrix, which well preserves the coherence properties of the perylene guest. We find that perylene’s phosphorescence can be enhanced in this host matrix, when acting as an intermediary for the generation of triplet excitons. The triplet energy that we find can be used to significantly narrow down the search for the ultraweak spin-forbidden transitions from the ground singlet to the triplet states of a single molecule.

We investigate the critical behavior and real-time scattering dynamics of the interacting ${\varphi }^4$ quantum field theory in ($1+1$) dimensions using uniform matrix product states (uMPS) and the time-dependent variational principle (TDVP). A finite-entanglement scaling analysis at $\lambda =0.8$ bounds the critical mass-squared to ${\mu }_c^2\in ]-0.2595,-0.2594[$ and provides a quantitative map of the symmetric, near-critical, and spontaneously broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}\left(E\right)$ and Wigner time delay $\mathrm{\Delta }t\left(E\right)$ using a sandwich geometry protocol. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11}\simeq 0.712, \mathrm{\Delta }t\simeq -158$ for ${\mu }^2=+0.2$) and almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11}\simeq 1, \mathrm{\Delta }t\simeq -108$ for ${\mu }^2=-0.1$ and $P_{11\to 11}\simeq 1, \mathrm{\Delta }t\simeq -177.781$ for ${\mu }^2=-0.5$). Crucially, the scattering protocol exhibits a distinctive divergence near the critical coupling; we show that this behavior serves as a dynamical signature of the quantum critical point, arising directly from the closing of the mass gap. These results demonstrate that TDVP-based uMPS can effectively probe nonperturbative scattering and critical dynamics in lattice field theories with controlled entanglement truncation.

We investigate the nature of memory effects in the non-Markovian dynamics of spin-boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We focus on two such criteria, one based on the dynamical map and the other on single-intervention process tensors, and discuss their connection. We apply these criteria to quench dynamics in spin-boson and two-spin-boson models, computed using a numerically exact method for non-Markovian open-system dynamics based on matrix product operator influence functionals. This method is ideally suited to simulate quantum multitime processes in spin-boson models across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, it is still possible to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.

The Hubbard model has occupied the minds of condensed matter physicists for most part of the last century. This model provides insight into a range of phenomena in correlated electron systems. We wish to examine the paradigm of quantum algorithms for solving such many-body problems. The focus of our current work is on the one-dimensional model that is integrable, meaning that there exist analytical results for determining its ground state. In particular, we demonstrate how to perform a gate-based quantum computer simulation of quantum annealing for the Hubbard Hamiltonian. We perform simulations for systems with up to 40 qubits to study the scaling of required annealing time for obtaining the ground state. We find that for the half-filled cases considered, there is a polynomial quantum speedup over algorithms based on the Bethe-ansatz equations.

We study the quantum relaxation dynamics for a lattice version of the one-dimensional $N$-flavor Gross-Neveu model after a Hamiltonian parameter quench. Allowing for a system-reservoir coupling $\gamma$, we numerically describe the system dynamics through a time-dependent self-consistent Lindblad master equation. For a closed ($\gamma =0$) finite-size system subjected to an interaction parameter quench, the order parameter dynamics exhibits oscillations and revivals. In the thermodynamic limit, our results imply that the order parameter reaches its postquench stationary value in accordance with the eigenstate thermalization hypothesis. However, time-dependent finite-momentum correlation matrix elements equilibrate only if $\gamma >0$. Our findings are consistent with the system being described by a pertinent generalized Gibbs ensemble and, accordingly, highlight subtle yet important aspects of the postquench relaxation dynamics of quantum many-body systems.

We report the formation of a soliton—termed “event soliton”—in nonlinear photonic spacetime crystals (STCs). In these media, simultaneous spatiotemporal periodic modulation of the dielectric constant generates mixed frequency ($\omega$) and wave vector ($k$) gaps. Under Kerr nonlinearity, the event solitons emerge as fully localized entities in both spacetime and energy-momentum domains, providing a tangible demonstration of the concept of “event” in relativity. The $\omega k$-gap mixture arises from the coexistence and competition between time-reflected and Bragg-reflected waves due to the spatiotemporal modulation. We propose a partial differential equation to capture various spatiotemporal patterns and present numerical simulations to validate our theoretical predictions, reflecting a three-way balance among $k$-gap opening, $\omega$-gap opening, and nonlinearity. Our work opens avenues for fundamental studies and fosters experimental prospects for implementing spacetime crystals and pattern formation in time-varying photonics.

Stark broadening of spectral lines in plasmas is a cornerstone of opacity modeling and plasma diagnostics, with critical implications for controlled fusion and astrophysics. Despite recent advances in fully quantum-mechanical close-coupling calculations for electron-impact broadening, the impact of denser plasma environments remains largely unexplored due to theoretical bottlenecks associated with electron-ion collision processes. Based on our close-coupling theory for electron-ion collisions in plasmas, which resolves the problem of extracting short-range scattering phase shifts, we introduce a fully relativistic close-coupling approach for the Stark broadening that incorporates plasma screening effects. Systematic investigations of hydrogenic radiators reveal distinct patterns of line broadening dependence on plasma conditions, offering valuable insights for plasma diagnostic applications. Furthermore, we provide a quantum-mechanical interpretation of the screening factor commonly introduced in semiclassical impact theories. This work establishes a robust foundation for future studies on complex atomic systems in high-density plasmas.

Flat-band states in topological systems provide a unique platform for investigating strongly correlated phenomena and many-body physics. However, in two-dimensional (2D) static tight-binding systems, perfectly flat bands can only exist in the topologically trivial phase, as characterized by a zero Chern number. Here, we show that by introducing periodic driving into a 2D photonic Lieb lattice composed of coupled microring resonators, the resulting Floquet topological insulator can host perfectly flat bands with nontrivial topology. In particular, by tracking the evolution of the flat-band modes over each cycle, we show that the non-Abelian displacements of the flat-band modes are characterized by a nontrivial quantized helicity even though the quasienergy bands have zero Chern number. The helical motion of the flat-band modes can be described by a braiding of the world lines of their trajectories, with a nontrivial winding number directly connected to the helicity. We also propose a scheme to experimentally measure the quantized non-Abelian helicity in a microring lattice subject to a synthetic magnetic field. These results suggest that Floquet topological photonic insulators based on coupled microring resonators can provide a versatile platform for investigating non-Abelian topological physics and strongly correlated phenomena in photonic flat-band systems.

We develop an age-structured hydrodynamic (HD) theory that describes the collective behavior of $N\gg 1$ anomalously diffusing particles under stochastic renewal resetting. The theory treats the age of a particle—the time since its last reset—as an explicit dynamical variable and allows for resetting rules that introduce global interparticle correlations. The anomalous diffusion is modeled by the scaled Brownian motion (sBm): a Gaussian process with independent increments, characterized by a power-law time dependence of the diffusion coefficient, $D\left(t\right)\sim t^{2H-1}$, where $H>0$. We apply this theory to three different resetting protocols: independent resetting to the origin (model A), resetting to the origin of the particle farthest from it (model B), and a scaled-diffusion extension of the “Brownian bees” model of Berestycki et al. [Ann. Probab. 50, 2133 (2022)]. In all these models, nonequilibrium steady states are reached at long times, and we determine the steady-state densities. For model A, the (normalized to unity) steady-state density coincides with the steady-state probability density of a single particle undergoing sBM with resetting to the origin. For model B, and for the scaled Brownian bees, the HD steady-state densities are markedly different: In particular, they have compact supports for all $H>0$. The age-structured HD formalism can be extended to other anomalous diffusion processes with renewal resetting protocols that introduce global interparticle correlations.

Correlation functions and correlation lengths are frequently used to describe phase transitions in quantum systems, but they require an explicit choice of observables. The recently introduced information lattice instead provides an observable-independent way to identify where and at which scale information is contained in quantum lattice models. Here, we use it to study the difference between the metallic and insulating regimes of one-dimensional noninteracting tight-binding chains. We find that the information per scale follows a power law in metals at low temperature and that Friedel-like oscillations are visible in the information lattice. At high temperature or in insulators at low temperature, the information per scale decays exponentially. Thus, the information lattice is a useful tool for analyzing the metal-insulator transition.

We study the Schrödinger equation with $1/r^3$ and attractive $1/r^2$ potentials. Using the quantum defect theory, we obtain analytical solutions for both repulsive and attractive $1/r^3$ interactions. The obtained discrete-scale-invariant energies and wave functions, validated by excellent agreement with numerical results, provide a natural framework for describing the universality of Efimov states in mixed dimension. Specifically, we consider a three-body system consisting of two heavy particles with large dipole moments confined to a quasi-one-dimensional geometry and resonantly interacting with an unconfined light particle. With the Born-Oppenheimer approximation, this system is effectively reduced to the Schrödinger equation with $1/r^3$ and $1/r^2$ potentials, and manifests the Efimov effect. Our analytical solution suggests that, for repulsive dipole interactions, the three-body parameter of the mixed-dimensional Efimov states is universally set by the dipolar length scale, whereas for attractive interactions it explicitly depends on the short-range phase. We also investigate the effects of finite transverse confinement and find that our analytical results are useful for describing the Efimov states composed of two polar molecules and a light atom.

Marine organisms manipulate their surrounding flow through their swimming dynamics, which affects the transport of their own odor cues. We demonstrate by direct numerical simulations how a group of swimmers, moving at intermediate Reynolds numbers, immersed in a turbulent flow, alter the shape of the odor plume they release in the water. Odor mixing is enhanced by increased velocity fluctuations and a swimmer-induced flow circulation that widens the odor plume at close range while speeding up dilution of the chemical trace. Beyond a short-range increase in the likelihood of being detected, swimming considerably reduces detections with effects that can persist at distances on the order of ten times the size of the group or more. We find that pullerlike swimmers are more effective at olfactory shielding than pusherlike swimmers. We trace this difference back to the dynamics at the swimmer location, which tends to trap odor at the source for pushers and to dilute it for pullers. Olfactory shielding is robust to changes in the conditions, and is more pronounced for weak turbulent Reynolds numbers and large swimmer Reynolds numbers. Our results suggest that olfactory shielding may play a role in the emergence of different swimming modalities by marine organisms.

Effective-medium approaches, such as the coherent potential approximation, are commonly used to describe the rigidity transition of disordered elastic networks. While successful in capturing the universal critical behavior of these systems near the onset of rigidity, its traditional formulation neglects spatial correlations in the underlying disorder. Here, we propose a multipurpose generalization of the coherent potential approximation to describe the mechanical behavior of elastic networks with spatially correlated disorder. We apply our theory to a simple rigidity-percolation model for colloidal gels and study the effects of correlations on both the critical point and the overall scaling behavior. We find that although the presence of spatial correlations (mimicking attractive interactions in gels) shifts the critical packing fraction to lower values, suggesting subisostatic behavior, the critical coordination number of the associated network remains isostatic. More importantly, we discuss how our theory can be employed to describe a large variety of systems with spatially correlated disorder.

Tensor network formalisms have emerged as powerful tools for simulating quantum state evolution. While widely applied in the study of optical quantum circuits, such as boson sampling, existing tensor network approaches fail to address the complexity mismatch between tensor contractions and the calculation of photon-counting probability amplitudes. Here, we present an alternative tensor network framework that exploits the input-output relations of quantum optical circuits encoded in the unitary interferometer matrix. Our approach bridges the complexity gap by enabling the computation of the permanent—central to boson sampling—with the same computational complexity as the best known classical algorithm based on a graphical representation of the operator-basis matrix product states that we introduce. Furthermore, we exploit the flexibility of tensor networks to extend our formalism to incorporate partial distinguishability and photon loss, two key imperfections in practical interferometry experiments. This work offers a significant step forward in the simulation of large-scale quantum optical systems and the understanding of their computational complexity.