We uncover a previously unrecognized hierarchical algebraic structure in the Bose-Hubbard model that enables a systematic construction of its spectrum without relying on integrability. We develop a recursive framework in which, within each fixed particle-number sector, the eigenproblem of a $p$-site system is reduced to a closed set of algebraic relations determined entirely by the eigenpairs and single-particle transfer amplitudes of the $(p-1)$-site subsystem. This reduction yields two complementary sets of Bethe-type equations whose solutions exhaust the spectrum. The underlying structure originates from the locality of the Hamiltonian, which constrains the coupling between subsystems and gives rise to an emergent sparse, near-tridiagonal representation of the many-body problem. As an explicit demonstration, we construct the complete spectrum of the three-site Bose-Hubbard model from that of the two-site system for particle numbers $n\le 3$, obtaining exact agreement with direct diagonalization. The resulting formulation substantially reduces computational cost and reveals a form of hierarchical solvability in a nonintegrable quantum many-body system. More broadly, our results suggest that recursive algebraic constructions may provide a general framework for analyzing lattice models beyond the conventional integrable paradigm.

In $s$-wave superconductors with a small concentration of magnetic impurities, the only electronic excitations that remain available at low temperatures are the excitations of the system of localized spins. We discuss a mechanism of interaction between electromagnetic waves and the localized spins in disordered superconductors. A supercurrent induces randomly distributed spin density of the itinerant electrons, which couples to the impurity spins by exchange interaction. Acceleration of the Cooper pair condensate by the external $\text{ac}$ electric field of frequency $\omega$ creates a strong, time-dependent exchange field acting on the localized spins, which is inversely proportional to $\omega$. As a result, at low frequencies the dissipative conductivity saturates to a nonzero value. We also predict that, in the presence of a $\text{dc}$ magnetic field parallel to the superconducting film, the system exhibits a large positive magnetoconductance. Using the fluctuation-dissipation theorem, we evaluate the spectrum of equilibrium current fluctuations induced by the spin fluctuations.

We theoretically investigate supercurrents of ultracold atoms in angularly ac-shaken ring lattices subjected to external rotation. Our results demonstrate how these supercurrents can be harnessed for the development of high-precision atomtronic angular accelerometers. Using both analytical and numerical approaches within the Bose-Hubbard model framework, we demonstrate that a significant net atomic current arises when the lattice driving frequency is tuned to an integer fraction of the Bloch frequency, while the current averages to nearly zero away from such a resonance. In the single-particle regime, the resonance width scales inversely with the averaging time, thereby setting a fundamental Fourier-limited bound on the measurement's sensitivity. Strikingly, our numerical simulations demonstrate that this Fourier limit—a fundamental barrier in the noninteracting system—can be surpassed by introducing weak interactions between atoms. In the interacting regime, the sensitivity surpasses the Fourier-limited scaling with the averaging time achieving an improvement of at least 2 orders of magnitude over the single-particle scenario, and exceeding the performance of previously proposed ultracold-atom-based angular accelerometers. These findings pave the way for developing new atomic-current-based inertial sensors with interaction-enhanced sensitivity.

In the brain, neural activity undergoes directed flows between states, thus breaking time-reversal symmetry. At the same time, animals also exhibit irreversible flows between behavioral states. Yet it remains unclear whether—and how—irreversibility in the brain relates to irreversibility in behavior. Here, we explore this connection in the hippocampus, where neural activity encodes physical location. We show that hippocampal irreversibility can be quantified using the time-delayed cross-correlations between neurons. As a mouse moves along a virtual track, we find that physical flows through the animal's environment generate neural flows through its cognitive map. Strikingly, this neural irreversibility is reproduced by a minimal sensory-representation model with only three parameters: the average velocity of the mouse, the variance in this velocity, and the resolution of the neural encoding. Together, these results provide a mechanistic understanding of irreversibility in the hippocampus and shed light on the links between symmetry breaking in the brain and behavior.

Billiards tables—a minimal model for particles moving in a confined region—are known to present different classical (and quantum) features according to their shape, ranging from strongly chaotic to integrable dynamics. Here, we consider the role of a stochastic perturbation of the elastic reflection law and show that while chaotic billiards maintain their key statistical feature, the behavior for integrable billiard tables is completely different: It can be linked, for tiny perturbations, to the Evans stochastic billiard, where at each collision the reflected angle is a uniformly distributed stochastic variable on $(-\pi /2,\pi /2)$. The resulting spatial stationary measure has peculiar aspects, like being typically nonuniform along the boundary, differently from any chaotic billiard table.

Local detailed balance (LDB) is a central guiding principle for modeling nonequilibrium stochastic dynamics, yet it only constrains the ratio of forward and backward transition rates and does not fix the steady state. Although the functional form of rates under the same LDB has been shown to affect steady-state correlations and transition temperatures, whether it can qualitatively reshape phase behavior in strongly interacting systems, such as the morphology and stability of phase-separated patterns, remains unclear. Here, for a two-dimensional driven lattice gas with attractive nearest-neighbor interactions, we consider hopping rates with a parameter that preserves the same LDB but tunes asymmetry along the driving force. We find that this parameter controls qualitative phase behavior: In the homogeneous phase, it reverses the sign of the structure-factor discontinuity and hence the anisotropy in long-range density correlations; in the phase-separated regime, it switches the orientation of anisotropic patterns and their long-time stability. Both effects are coherently captured by an approximate fluctuating hydrodynamic equation. The results demonstrate that, in contrast to equilibrium systems, qualitative features of nonequilibrium phases are controlled by the specific choice of dynamical rules even under the same LDB.

Quantum entanglement is defined as nonseparability of density operators, yet experimental phase-space statistics alone cannot distinguish classical from quantum sources, so classical data can be used to violate entanglement inequalities. Imposing uncertainty bounds, or full tomography, can map the same data onto positive, entangled density operators, yielding a hybrid regime in which classical and quantum models coincide. Thus, certifying genuine quantum entanglement requires additional tests, such as Wigner negativity, incompatibility beyond phase-space measurements, or nonlinear dynamics.

From numerical simulations, it is known that the barrier-crossing time of a non-Markovian one-dimensional reaction coordinate with a single exponentially decaying memory function exhibits a memory turnover: For intermediate values of the memory decay time, the barrier-crossing time is reduced compared to the Markovian limit, and for long memory times, it increases quadratically with the memory time when keeping the total integrated friction and the mass constant. The intermediate memory acceleration regime is accurately predicted by Grote-Hynes theory; for the asymptotic long-memory slowdown behavior, no systematic analytically tractable theory is available. Starting from the Green's function for a general inertial (i.e., finite-mass) non-Markovian Gaussian reaction coordinate in a harmonic well, we derive by an exact mapping a generalized Fokker-Planck equation with a time-dependent effective diffusion constant. To first order in a systematic cumulant expansion, we derive an analytical Arrhenius expression for the barrier-crossing time with the preexponential factor given by the energy relaxation time, which can be used to robustly predict barrier-crossing times from simulation or experimental trajectory data of general non-Markovian inertial systems without the need to extract memory functions. For a single-exponential memory kernel, we give a closed-form expression for the barrier-crossing time, which reproduces the Kramers turnover between the high-friction and high-mass limits as well as the memory turnover from the intermediate memory acceleration to the asymptotic long-memory slowdown regime. We also demonstrate that a non-Markovian system with single-exponential memory is singular in the zero-mass limit and that the long-memory barrier-crossing slowdown reflects the interplay between mass and memory effects. Thus, physically sound models for non-Markovian systems should include a finite mass.

In active matter and living matter, such as clusters of migrating cells, collective dynamics emerges from the underlying interactions. A common assumption of theoretical descriptions of collective cell migration is that these interactions are pairwise additive. It remains unclear, however, whether the dynamics of groups of cells is solely determined by pairwise interactions or whether higher-order interaction terms come into play. To investigate this question, we use time-lapse microscopy to record the dynamics of three cells interacting together in a linear three-site geometry. We collect a large number of cellular trajectories and develop an inference scheme to infer both pairwise and potential three-body cell-cell interactions. Our results reveal evidence of three-body interactions in one of the two cell lines tested. However, these three-body interactions only introduce minor corrections to the overall dynamics. Our work provides a methodology to infer the existence of three-body interactions from trajectory data and supports the commonly assumed pairwise nature of cell-cell interactions.

The encounter of diffusing entities underlies a wide range of natural phenomena. The dynamics of these first-passage dynamics are strongly influenced by confining geometries. Confinement modifies microscopic diffusion through conservative and hydrodynamic interactions, making it essential for realistic modeling. In this article, we investigate how confinement affects the first-passage statistics of a diffusing particle. Using state-of-the-art holographic microscopy combined with advanced statistical inference, we probe this motion with nanometric precision. Our experimental and numerical results show that confinement can either hinder or enhance first-passage kinetics, depending on the spatial direction. In particular, a wall-normal target finding is accelerated by confinement-induced non-Gaussian displacement statistics—which increases the probability of rare, large displacements—compared to an analogous situation relying on a Gaussian process. The results presented hereafter carry implications for confined chemical reactions and biological winners-take-all processes near boundaries.

Actin flow in the cortical cytoskeleton underneath the cell membrane generates mechanical stresses that shape the cell surface. We study this mechanism using a hydrodynamic model of a compressible active gel polymerizing at the membrane and undergoing turnover. We determine how actin flow, density relaxation, and friction of actin with the membrane generate stress on a corrugated membrane at the linear order in deformation. Analytical solutions in limiting regimes, combined with finite element methods in the general case, provide a map of normal and tangential stresses as functions of compressibility, interfacial friction, and actin turnover, and determine the conditions under which actin polymerization can render the membrane linearly unstable. The nonlinear regime is also briefly discussed.

The emergence of functional connectivity between distant brain regions that lack a direct structural link remains a long-standing question in neuroscience. Remote synchronization (RS) offers a promising framework for uncovering the underlying mechanisms. So far, RS has been well studied in artificial network topologies such as star or starlike graphs but little attention has been paid to realistic brain networks with complicated topologies, due to their completely different synchronization pathways. In this study, we address this gap by introducing an efficient method, termed the noncompletely overlapping path algorithm, to detect RS using empirical structural and functional brain network data. Under this approach, two nodes are considered to exhibit RS if they are functionally synchronized despite being structurally disconnected. That is, they share neither a direct structural link nor an indirect path composed of synchronized nodes. We demonstrate that the proportion of RS nodes in a brain network strongly depends on the thresholds used to define both structural and functional connectivity, with optimal threshold values existing for each. Furthermore, we show that the method can be generalized: It applies not only to empirical time series but also to oscillator-based network models, and it admits a theoretical interpretation. This indicates that the algorithm offers a general framework to detect RS in complex networks.

In quantum computations of gauge theories at finite temperature and finite density, enforcing Gauss's law for all states contributing to the thermal ensemble is a nontrivial challenge. In this work, we adapt the quantum minimally entangled typical thermal states (QMETTS) algorithm to ${\mathbb{Z}}_2$ gauge-constrained systems and propose a method for computing finite-temperature and finite-density expectation values without eliminating redundant gauge-field degrees of freedom. In QMETTS, the thermal ensemble is sampled via a Markov chain of pure states generated by imaginary-time evolution and projective measurements. To preserve gauge invariance while maintaining efficient sampling, we introduce measurement bases that are gauge invariant and mutually unbiased within the physical subspace. We show that such measurement bases can be constructed efficiently for ${\mathbb{Z}}_2$ lattice gauge theories in arbitrary spatial dimensions and arbitrary boundary conditions by exploiting the correspondence between ${\mathbb{Z}}_2$ lattice gauge theories and the stabilizer formalism. Furthermore, since expectation-value estimation on quantum hardware is inherently affected by shot noise, we explicitly incorporate shot noise into the analysis. By formulating a finite-shot version of QMETTS, we show that the resulting estimator remains unbiased and that using one observable-measurement shot per sampled state is nearly optimal in terms of variance when the total number of circuit executions used to generate the Markov chain and measure observables is fixed. This result indicates that it is often more efficient to generate more QMETTS samples than to accurately estimate the expectation value for each individual pure state. We validate the proposed method numerically in a $(1+1)$-dimensional ${\mathbb{Z}}_2$ lattice gauge theory coupled to staggered fermions. Our results provide a gauge-invariant sampling framework for finite-temperature and finite-density quantum algorithms for lattice gauge theories.

The discrimination of quantum states is fundamental to quantum information processing. Inverse-squeezing Kennedy (IS-Kennedy) receivers can outperform the coherent-state binary phase-shift-keyed Helstrom benchmark at the same energy by converting transmitter-side squeezing into an effective coherent-state separation gain, without violating the Helstrom bound for the squeezed-state alphabet. This work investigates how squeezing mismatch degrades this mechanism. We show that imperfect inverse squeezing transforms the ideally nulled output into a residually squeezed state, thereby altering the photon-number statistics before detection. This residual-squeezing picture reveals a strong physical asymmetry between squeezing-magnitude and squeezing-phase mismatches. Magnitude mismatch produces an energy-independent error floor in the high-signal-energy regime, whereas phase mismatch generates a residual-squeezing term that grows with signal energy. In the small-residual-squeezing regime, this leads to a polynomial growth of the leading error contribution and a rapid collapse of the standard quantum limit advantage. We also identify a parity-step effect in photon-number-resolving detection: Because the nulled residual squeezed vacuum contains only even photon numbers, increasing detector resolution improves the high-energy robustness only when the effective saturation threshold crosses the next even photon number. These results identify phase locking as the dominant bottleneck for IS-Kennedy-type non-Gaussian receivers under unitary squeezing mismatch and provide design guidelines for robust squeezed-state quantum receivers.

Governed by the Nielsen-Ninomiya theorem, Weyl points (WPs) function as topological monopoles that cannot exist in isolation but must form charge-neutral assemblies in the momentum space of crystals. While these WPs are locally characterized by quantized chiral charges, the finite generating family governing their global assembly into a Weyl semimetal (WSM) phase remains undiscovered. Here, we resolve this by identifying “irreducible Weyl molecules” (IWMs) as the elementary, charge-neutral topological building blocks of WSMs. By rigorously imposing the constraints of 1651 magnetic space groups on minimal zero-sum chiral-charge sequences, we obtain exactly 16 crystallographically realizable IWMs. We establish a universal linear-combination principle, demonstrating that any crystallographically realizable charge-neutral chiral-node configuration $Y$ within $\left|C\right|\le 4$ is constructed from a linear superposition of these 16 generators $X_i$ with non-negative integer coefficients $n_i$, governed by $Y={\sum }_{i=1}^{16}{n}_i{X}_i$. Utilizing first-principles calculations on a predicted family of boron allotropes, we reveal that this superposition principle organizes the bulk nodal configurations and constrains the admissible end point connectivity of Fermi arcs, while the realized surface geometry remains dependent on termination, energy, and allowed inter-IWM reconstruction. Our work establishes a “periodic table” for WSMs, offering a general theoretical framework for the classification and rational design of Weyl complexes.

High-harmonic generation in solids enables probing of strong-field electron dynamics in condensed matter and the development of compact ultrafast light sources. Whereas most studies have focused on above-bandgap high-order harmonics, which are usually interpreted through short electron-hole trajectories that recombine within one optical cycle, the microscopic origin of low-order emission near the bandgap remains poorly understood. Here, we investigate near-bandgap harmonic generation in ZnO by combining semiconductor Bloch equations with a complex-time quantum-trajectory analysis. Our results indicate that these harmonics are not a continuation of the short trajectory. Rather, they originate from multiple-scattering trajectories, in which the electron-hole pair undergoes repeated Bragg scattering at the Brillouin-zone boundary and electron-hole reencounter near the $\mathrm{\Gamma }$ point before the actual recombination occurs. We identify that the imaginary part of the electron-hole displacement provides a practical diagnostic of the residual tunneling memory. Real-space electron-hole overlap alone does not imply coherent recombination unless the full complex displacement vanishes. These results clarify the microscopic picture of near-bandgap harmonic emission in ZnO and offer a framework for interpreting phase-resolved strong-field dynamics in solids.

We develop the semiconductor Wannier equations (SWEs), a real-time, real-space formulation of ultrafast light-matter dynamics in crystals, by deriving the equations of motion for the electronic reduced density matrix in a localized Wannier basis. Working in real space removes the structure-gauge ambiguities that hinder reciprocal-space semiconductor Bloch equations. Electron-electron interactions are included at the time-dependent Hartree plus static screened-exchange level. Decoherence is modeled with three complementary channels: pure dephasing, population relaxation, and distance-dependent real-space dephasing, providing physically grounded damping for strong-field phenomena such as high-harmonic generation. Conceptually, the SWEs bridge real-space semiclassical intuition with many-body solid-state optics, offering a numerically robust and gauge-clean alternative to reciprocal-space approaches for nonlinear optical response and attosecond spectroscopy in solids.