We show that anisotropic spin interactions do not merely break spin-space group (SSG) symmetries, but instead twist them through cohomology invariants, yielding symmetry classes beyond subgroups of $\mathrm{O}\left(3\right)\times Isom\left({\mathbb{R}}^3\right)$. This requires redefining the spin-only group ${\mathcal{S}}_0$ in terms of proper spin rotations. Based on this unitary ${\mathcal{S}}_0$, we formulate a twisted SSG (tSSG) theory that captures the complete set of spin-space symmetries. We then study a spin-1 model with tSSG symmetry using linear flavor wave theory and find ${\mathbb{Z}}_2$ topological quadrupolar excitations defined on a spin Brillouin Klein bottle. Specifically, the quadrupolar excitations possess a momentum-space glide-reflection symmetry and the edge states exhibit a nonlocal momentum twist. These results establish the symmetry language required for interacting spin systems, whether realized in magnetic materials or on programmable quantum simulators, and open a route to unconventional magnetism.

Efficient optomechanical cooling typically requires high photon occupancy to maximize cooling power, a constraint that generally limits the degree of coherent quantum control available in the few-photon regime. Here, we investigate this trade-off by considering a strongly nonlinear cavity operated as a discrete quantum system. In the weak-coupling limit, we derive a general connection between the optomechanical damping rate and the cavity's dressed-state manifold. This framework reveals that the damping rate (determined by the population imbalance across dressed states) is directly tunable via the coherent manipulation tools, which are standard in circuit quantum electrodynamics. We illustrate this framework using a Josephson photonics architecture, where a dc-biased junction induces a photon blockade that truncates the cavity to an $N$-level system. By sacrificing raw cooling (or heating) power, this platform enables full quantum mechanical control over optomechanical properties, offering a versatile avenue for the quantum manipulation of mechanical modes.

The Eigen model is a prototypical toy model of evolution that is synonymous with the so-called error catastrophe: When mutation rates are sufficiently high, the genetic variant with the largest replication rate does not occupy the largest fraction of the total population because it acts as a source for the other variants. Here, we show that, in the stochastic version of the Eigen model, there is also a fidelity catastrophe. This arises due to the state-dependence of fluctuations and occurs when rates of mutation fall beneath a certain threshold, which we calculate. The result is a type of noise-induced multistability in which the system stochastically switches between short-lived regimes of effectively clonal behavior by different genetic variants. Most notably, when the number of possible variants—potentially $\sim 4^L$, with $L\gg 1$ the length of the genome—is significantly larger than the population size, there is only a vanishingly small interval of mutation rates for which the Eigen model is neither in the fidelity- nor error-catastrophe regimes.

We investigate the singular behavior of information flow near the Hopf bifurcation point by analyzing the learning rate as a specific measure of information flow. We study the Brusselator, a model system exhibiting the Hopf bifurcation. We first numerically compute the learning rate in the stationary regime and find that it remains finite even in the deterministic limit, suggesting that the learning rate can be quantified in deterministic dynamics through probabilistic descriptions. Linear analysis accurately reproduces the numerical results in the stationary regime but fails near the bifurcation point. To overcome this limitation, we employ the singular perturbation method, well known in deterministic bifurcation theory, and carry out the corresponding calculation explicitly for a stochastic system described by a Langevin equation. This allows us to evaluate the learning rate near the bifurcation point. We then theoretically derive its nonsmooth behavior in the deterministic limit. Our results demonstrate that changes in dynamical behavior are reflected in the learning rate and provide a basis for analyzing information processing in biochemical oscillations.

The evolution of a charged lepton in the field of an electromagnetic plane wave can be described as a superposition of Volkov states. Here, we demonstrate that imposing specific momentum correlations among Volkov states produces a spatiotemporally structured wave packet whose probability-density peak, evaluated on fixed-light-cone slices, travels at an arbitrary tailored velocity. This velocity can be chosen independently of both the field amplitude and the velocity expectation value. The imposed momentum correlations modify the expectation-value trajectory, providing a measurable signature of the arbitrary velocity within a physical observable.

The spatial distribution of cloud droplets is relevant for various microphysical processes, such as condensational growth, collision coalescence, riming and aggregation, and radiative transfer. Cloud droplets and other hydrometeors exhibit clustering at dissipation scales and above due to turbulence-induced preferential concentration. Here, we investigate the role of entrainment in modulating the scale-dependent clustering of cloud droplets and explore how this mechanism differs from inertial clustering. We have performed experiments in the Pi convection-cloud chamber, and imaged 2D droplet fields in the cloud-top region where dry-air entrained through an open cylindrical flange leads to an entrainment-mixing process. Captured images are processed to retrieve instantaneous two-dimensional velocity fields using particle image velocimetry, scale-dependent clustering is explored using the radial distribution function, and spatial nonuniformity is quantitatively identified through the Kolmogorov-Smirnov test. The analysis reveals that the observed droplet clustering is scale dependent and occurs intermittently with enhanced magnitude in the region influenced by entrainment. Furthermore, the strength of clustering and spatial nonuniformity increases with mean entrainment flow. Using a novel bias-mitigation method, we estimate that the strength of clustering (pair-correlation function) roughly doubles in the presence of entrainment (downdraft), compared to no-entrainment (updraft) regimes. Such an entrainment-clustering relationship could be used to help identify and decipher the role of entrainment in modulating localized clustering in natural atmospheric clouds.

Multiple phenotypic protein expressions arise from one genome represent variations in the protein relative abundance and their stoichiometry. A lack of definite compositional parts challenges the modeling of protein megacomplexes and cellular architectures. Despite the advance in protein structural predictions with Artificial Intelligence (AI), the mechanism of protein interactions and the emergence of megacomplexes they assemble remains unclear. Here, we present a statistical-physics framework of grand canonical ensemble to explore the protein interactions that drive the emergent assembly of a megacomplex using the observational mass spectrometry datasets including protein relative abundance and the cross-linked connections. Using chromatin remodeler megacomplex, INO80, as an example, we discovered a class of “divergent” protein that plays a critical role in orchestrating the assembly beyond nearest neighbors, dependent on the excluded volumes exerted by others. With the constraints of the excluded volumes by varying the volume fraction of INO80 subunits, these divergent subunits orchestrate and form clusters with selective components growing into configurationally distinct architectures. We propose a machinery view for the INO80 chromatin remodeler complex where each loosely associated subunits can be occasionally recruited for parts as attachment into a core assembly driven by excluded volumes. Our computational framework provides a mechanistic insight into taking the volume fractions as necessary physicochemical variables representing cell states to remodel the configurations of protein megacomplexes with structurally loose modules.

We present a theoretical scheme for a family of fast and high-fidelity two-qubit iswap gates between neutral atoms separated by more than $20\mu \mathrm{m}$, enabled by resonant dipole-dipole spin-exchange interactions between Rydberg states. The protocol harnesses coherent excitation-exchange-deexcitation dynamics between the qubit and the Rydberg states within a single and smooth laser pulse, in the presence of strong dipole-dipole interactions. We utilize optimal control methods to achieve theoretical gate fidelities and durations comparable to blockade-based gates in the presence of relevant noise, while extending the effective interaction range by an order of magnitude. This enables entanglement well beyond the blockade radius, offering a route toward fast, high-connectivity quantum processors.

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.