Although synchronization has been extensively studied, key processes underlying its emergence in complex networks have remained hidden by the use of global order parameters. Here, we uncover how the route to synchronization unfolds through a sequential transition between two well-known but previously unconnected phenomena: chaotic itinerancy (CI) and intermittent synchronization (IS). Using a symbolic dynamics approach, we show that CI develops as a collective yet unsynchronized exploration of different domains of the high-dimensional attractor of the network, whose dimension is reduced as the coupling increases, ultimately collapsing into the reference chaotic attractor of an individual unit. At this stage, the IS emerges as irregular alternations between synchronous and asynchronous phases. These phenomena are mutually exclusive, each dominating a distinct coupling interval and governed by different mechanisms. Furthermore, network structural heterogeneity enhances itinerant behavior since access to different domains of the attractor depends on the nodes’ topological roles. The CI-IS crossover occurs within a consistent coupling interval across models and topologies. Experiments on electronic oscillator networks confirm this two-step process, establishing a unified framework for understanding the route to synchronization in complex systems.

How can we perform a metrological task if only limited control over a quantum system is given? Here, we present systematic methods for conducting nonlinear quantum metrology in scenarios lacking a common reference frame. Our approach involves preparing multiple copies of quantum systems and then performing local measurements with randomized observables. First, we derive the metrological precision using an error-propagation formula based solely on local unitary invariants, which are independent of the chosen basis. Next, we provide analytical expressions for the precision scaling in various examples of nonlinear metrology involving two-body interactions, like the one-axis twisting Hamiltonian. Finally, we analyze our results in the context of local decoherence and discuss its influences on the observed scaling.

We study the emergence of the nonlocal Josephson effect in a system composed of three laterally coupled minimal Kitaev chains and exploit it to realize the nonlocal Josephson diode effect. We find that an imbalance between crossed Andreev reflections and electron cotunneling in the middle Kitaev chain gives rise to an asymmetric $2\pi$-periodic phase-dependent Andreev spectrum, controlled by the superconducting phases across the left and right junctions. We then show that the asymmetric Andreev spectrum, formed by hybridized Andreev bound states at the left and right junctions, enables a supercurrent across one junction via the phase difference at the other junction, thereby signaling the nonlocal Josephson effect. Notably, these nonlocal Josephson supercurrents exhibit distinct positive and negative critical currents, demonstrating the realization of the nonlocal Josephson diode effect with highly tunable polarity and efficiencies exceeding 50%. The nonlocal Josephson diode effect requires breaking local time-reversal and local charge-conjugation symmetries, with the latter being unique to minimal Kitaev chains. Our results establish minimal Kitaev chains as a highly controllable platform for engineering nonlocal Josephson phenomena.

We present the diagrammatic theory of the irreducible self-energy and Bethe-Salpeter kernel that naturally arises within the Green’s function formalism for a general $N$-body non-Hermitian interaction. In this work, we focus specifically on the coupled-cluster (CC) self-energy generated by the similarity transformation of the electronic structure Hamiltonian. The main result of this work is a Green’s function formalism for non-Hermitian many-body quantum systems. We develop the biorthogonal quantum theory to construct dynamical correlation functions where the time dependence of operators is governed by a non-Hermitian Hamiltonian. We extend the Gell-Mann and Low theorem to include non-Hermitian interactions and to generate perturbative expansions of many-body Green’s functions. We introduce the single-particle coupled-cluster Green’s function and derive the perturbative diagrammatic expansion for the non-Hermitian coupled-cluster self-energy in terms of the “noninteracting” reference Green’s function, $\tilde{\mathrm{\Sigma }}\left[G_0\right]$. From the exact equation of motion of the single-particle coupled-cluster Green’s function, we derive the self-consistent renormalized coupled-cluster self-energy, $\tilde{\mathrm{\Sigma }}\left[\tilde{G}\right]$, and demonstrate its relationship to the perturbative expansion of the self-energy, $\tilde{\mathrm{\Sigma }}\left[G_0\right]$. Subsequently, we show that the usual electronic self-energy can be recovered from the coupled-cluster self-energy by neglecting the effects of the similarity transformation. We show how the coupled-cluster ground-state energy can be obtained from the coupled-cluster self-energy and provide an overview of the relationship between approximations for the coupled-cluster self-energy, ionization potential/electron affinity equation-of-motion coupled-cluster theory, and the $G_0{W}_0$ approximation. As a result, we introduce the CC-$G_0{W}_0$ self-energy by leveraging the connections between Green’s function and coupled-cluster theory. Finally, we derive the diagrammatic expansion of the coupled-cluster Bethe-Salpeter kernel.

We develop a framework to describe collective buckling in metal-organic frameworks (MOFs). Starting from the microscopic structure of a single organic linker, we define a buckling coordinate governed by an effective double-well potential. Coupling between linkers is introduced within a dipole-dipole approximation, resulting in an effective lattice Hamiltonian. We analyze the transition between ordered and disordered phases within a mean-field approximation and estimate the critical temperature. As an illustrative example for our theory, we discuss the collective buckling instability for the prototypical cubic framework MOF-5 under different values of uniaxial strain. Our approach provides a quantitative description of collective buckling in framework materials.

Nonstabilizerness, or magic, constitutes a fundamental resource for quantum computation and a crucial ingredient for quantum advantage. Recent progress has substantially advanced the characterization of magic in many-body quantum systems, with stabilizer Rényi entropy (SRE) emerging as a computable and experimentally accessible measure. In this work, we investigate the spreading of SRE in terms of single-qubit reduced density matrices, where an initial product state that contains magic in a local region evolves under brickwork random Clifford circuits. For the case with Haar-random local Clifford gates, we find that the spreading profile exhibits a diffusive structure within a ballistic light cone when viewed through a normalized version of single-qubit SRE, despite the absence of explicit conserved charges. We further examine the robustness of this nonballistic behavior of the normalized single-qubit SRE spreading by extending the analysis to a restricted Clifford circuit, where we unveil a superdiffusive spreading. Finally, we discuss that a similar nonballistic spreading within the light cone is also observed for another indicator of the magic, i.e., the robustness of magic.

We investigate the influence of subcycle laser pulses on holographic and nonholographic intracycle interferences by analyzing the photoelectron momentum distributions of helium using time-dependent Schrödinger equation simulations supported by classical-trajectory calculations. The results show that the forward-scattering holographic (FSH), backward-scattering holographic (BSH), and time double-slit (TDS) interference structures are found to be highly sensitive to the pulse duration, carrier-envelope phase (CEP), and temporal envelope in the subcycle regime. Subcycle pulses with CEP values of $0^{\circ }$ and ${90}^{\circ }$ selectively enhance or suppress distinct features, isolating holographic patterns and enhancing BSH fringes. Classical analysis reveals that the intrinsic chirp inherent to subcycle fields shortens the recollision time for scattering trajectories, thereby increasing the fringe spacing in FSH and BSH patterns, while simultaneously enlarging the above-threshold ionization peak spacing associated with TDS interference. Pulse envelope variations, even at fixed FWHM duration, further reshape the fringe spacings by modifying the instantaneous frequency and vector potential slope near ionization times. These results demonstrate that subcycle pulses enable precise temporal control of holographic interference, offering opportunities for probing and manipulating attosecond electron dynamics.

Heat exchanged between an open quantum system and its environment exhibits fluctuations that carry crucial signatures of the underlying dynamics. Within the well-established two-point measurement scheme, we identify a “heat operator,” whose moments with respect to the vacuum state of a thermofield-doubled Hilbert space correspond to the stochastic moments of the heat exchanged with a bath. This recasts heat statistics as a unitary time evolution problem, which we solve by combining chain-mapped reservoirs with tensor-network propagation. In a multibath setup, all total and bath-resolved heat moments then follow from a single pure state evolution. We employ this approach to compute transient and steady-state heat fluctuations in Ohmic spin-boson models in and out of equilibrium, accessing the challenging low-temperature and long memory time regimes of the environment. In the nonequilibrium case, we show a crossover in the Fano factor from super-Poissonian to nearly Poissonian statistics under strong coupling asymmetry, corresponding to thermal rectification behavior. The method applies to noninteracting (bosonic or fermionic) nonequilibrium environments with arbitrary spectral densities, offering a powerful, nonperturbative framework for understanding heat transfer in open quantum systems.

Bayesian inference and kernel methods are well established in machine learning. The neural network Gaussian process in particular provides a concept to investigate neural networks in the limit of infinitely wide hidden layers by using kernel and inference methods. Here, we build upon this limit and provide a field theoretic formalism that covers the generalization properties of infinitely wide networks. We systematically compute generalization properties of linear, nonlinear, and deep nonlinear networks for kernel matrices with heterogeneous entries. In contrast to currently employed spectral methods, we derive the generalization properties from the statistical properties of the input, elucidating the interplay of input dimensionality, size of the training dataset, and variability of the data. We show that data variability leads to a non-Gaussian action reminiscent of a ${\phi }^3+{\phi }^4$ theory. Using our formalism on a synthetic task and on MNIST, we obtain a homogeneous kernel matrix approximation for the learning curve as well as corrections due to data variability that allow the estimation of the generalization properties and exact results for the bounds of the learning curves in the case of infinitely many training data points.

Squeezed thermal reservoirs, characterized by thermal noise with anisotropic fluctuations, have profound implications in quantum thermodynamics and serve as powerful resources for quantum information. However, their experimental realizations remain challenging. Existing schemes typically rely on injected squeezed light, time-dependent modulation, or driven nonlinear interactions, which introduce complexity and limit experimental feasibility. Using only time-independent linear coupling to a lossy mode within a normal thermal environment, we identify a general and experimentally accessible framework for squeezed-reservoir engineering, applicable across platforms such as circuit and cavity quantum electrodynamics as well as coupled cavity systems. We illustrate the framework through two experimentally relevant cases: directional phase coherence extension in two-level systems like qubits or atoms, and dissipative quadrature squeezing in bosonic modes like photons or phonons. By eliminating the need for active control or squeezed input, our passive linear-coupling approach provides a resource-efficient and practical pathway to dissipative squeezing, decoherence suppression, entanglement stabilization, quantum simulation, and the exploration of unconventional quantum thermodynamics and phase transitions.

The study of active matter system has critical importance in revealing the physical essence of biological collective behavior. Dense bacterial suspension—a typical biological active matter, exhibits a wide range of phenomenona, among which bacterial turbulence has received extensive interest in recent years. This seemingly chaotic motion is widely studied in Newtonian fluid. However, studies based on complex fluids have predominantly focused on viscoelastic effects, leaving the role of shear-thinning viscosity largely unexplored despite its prevalence in natural bacterial environments like mucus and gastric fluids. Here, we experimentally employed Ficoll and Methocel polymers to study the impacts of various viscosities by Newtonian fluid and shear-thinning effects by non-Newtonian fluids on bacterial turbulence. We analyzed various physical properties, including energy, enstrophy, etc., and observed that the shear-thinning effect is significantly suppressed in high-concentration bacterial suspensions. While the ordered arrangement of polymer chains under shear flow leads to the microscopic anisotropic viscosity, the suppression is largely attributed to the disruption of polymer chains caused by strong interbacterial interactions in dense suspensions. To validate this hypothesis, we conducted experiments at a lower bacterial concentration and verified the findings using theoretical calculations based on the modified resistive force theory.

Decoherence in macroscopic quantum systems arises mainly from interactions with the environmental bath, offering key insights into the quantum-classical boundary. In this paper, we study the acoustic-environment-induced effects in a circuit quantum electrodynamics system, where an LC oscillator is optomechanically coupled to a long mechanical strip and capacitively coupled to a superconducting qubit. The mechanical strip functions as an acoustic environment, comprising a continuum of bath modes. The qubit population, serving as a probe of acoustic-environment-induced dephasing (AEID), exhibits collapse and revival dynamics in its Rabi oscillations. The AEID effect is extracted using a Ramsey-like interference scheme, manifesting as a dynamical decay in amplitude and a modification in the oscillation frequency. Our scheme opens avenues for studying the mechanisms of decoherence introduced by acoustic environments and to explore the optomechanically induced nonlinearity by collective acoustic bath modes.

Entanglement generation between distant nodes is a fundamental process in distributed quantum information processing. Qudits, high-dimensional quantum states, are promising candidates for enhancing entanglement distribution capabilities. However, the success probability of qudit entanglement distribution using Bell measurements is typically lower than that of conventional qubit-based protocols. In this paper, we propose an entanglement swapping protocol specifically designed for qutrits (three-dimensional quantum states). Our protocol employs photon-number encoding combined with an additional mode basis, such as polarization, effectively increasing the success probability. We show that the proposed qutrit protocol can achieve higher entanglement generation rates compared to conventional two-photon detection-based qubit protocols, especially under conditions of limited photon generation probability. Furthermore, we evaluate our protocol under realistic experimental imperfections, including photon loss and threshold detection, and show that it achieves high fidelity with probabilistic photon sources.

Advanced atomic magnetometers have made it possible to acquire nuclear magnetic resonance spectra in zero to ultralow magnetic fields. This regime carries the benefit of compact, low-cost instrumentation with reduced spin relaxation effects and the ability to probe phenomena that are inaccessible in conventional high-field experiments. A trade-off is that the resulting spectra must be interpreted using simulations that are taxing for classical computation. Working by example for small-molecule and protein spectroscopy, we demonstrate that these simulations are a promising target for fault-tolerant quantum computation. Our holistic analysis spans from input selection to the construction of explicit circuits for qubitized quantum dynamics. By maintaining parity with experimental requirements, we demonstrate how certain cases might be especially promising for early fault-tolerant architectures. Notably, valuable natural products and small proteins could be simulated with a few hundred logical qubits and less than ${10}^{12} T$ gates, corresponding to days of runtime with foreseeable hardware based on spin or superconducting qubits.

Whether and how a system approaches equilibrium is a central issue in nonequilibrium statistical physics, underpinning our understanding of both thermalization and heat transport. Bogoliubov's three-stage (initial, kinetic, and hydrodynamic) evolution hypothesis provides a qualitative framework, but quantitative advances have mostly been restricted to near-integrable systems such as dilute gases. In this work, we investigate the relaxation dynamics of a one-dimensional diatomic hard-point gas and present a phase diagram that comprehensively characterizes relaxation behavior across the full parameter space, from near-integrable to far-from-integrable regimes. We first analyze thermalization (local energy relaxation in nonequilibrium states) and identify three universal dynamical regimes: (1) In the near-integrable regime, kinetic processes dominate (initial $+$ kinetic phase), local energy relaxation decays exponentially, and the thermalization time $\tau$ scales with perturbation strength $\delta$ as $\tau \propto {\delta }^{-2}$. (2) In the far-from-integrable regime, hydrodynamic effects dominate (initial $+$ hydrodynamic phase), local energy relaxation follows power-law decay, and thermalization time scales linearly with system size $N$. (3) In the intermediate regime, Bogoliubov phase emerges, marked by the transition from kinetic to hydrodynamic relaxation. The phase diagram further reveals that hydrodynamic behavior can emerge even in small systems when the system is sufficiently far from the integrable regime, challenging the conventional view that such effects are only significant in large systems. In the thermodynamic limit, the system's relaxation behavior depends on the order in which the limits ($N\to \infty$ or $\delta \to 0$) are taken. We then turn to heat transport (decay of heat-current fluctuations in equilibrium) and demonstrate that its behavior is fully consistent with the thermalization process, leading to the first unified theoretical description of thermalization and heat transport. Our results establish a comprehensive view of relaxation in classical many-body systems and suggest a route for studying similar dynamics in quantum systems, highlighting universal scaling laws and the interplay of kinetic and hydrodynamic processes across integrability regimes.

We study the dynamics and intervention strategies of a rumor using the modified Maki-Thompson model. A key challenge in social networks is distinguishing between natural increases in transmissibility and artificial injections of rumor spreaders, such as through broadcast events or astroturfing. Using stochastic simulations, we compare two scenarios: one with organic growth in transmissibility and another with externally injected spreaders. Although both lead to high autocorrelation, only the organic growth produces oscillatory patterns in autocorrelation at multiple lags, an effect we can analytically explain using the $N$-intertwined mean-field approximation. This distinction offers a practical tool to identify the origin of rumor virality and also infer its transmissibility. Our approach is validated analytically and tested on real-world data from Twitter during the announcement of the Higgs boson discovery. In addition to detection, we also explore control strategies. We show that the average lifetime of a rumor can be manipulated through targeted interventions: placing spreaders at specific locations in the network. Depending on their placement, these interventions can either extend or shorten the lifespan of the rumor.

One of the fundamental questions in population dynamics is how biological populations respond to environmental perturbations. In population dynamics, the mean fitness and the fraction of a trait in the steady state are important because they indicate how well the trait and the population adapt to the environment. In this study, we examine the parallel mutation–reproduction model, which is one of the simplest models of an evolvable population. As an extension of the Markov chain tree theorem, we derive diagrammatic expressions for the static responses of the mean fitness and the steady-state distribution of the population. For the parallel mutation–reproduction model, we consider self-loops, which represent trait reproduction and are excluded from the Markov chain tree theorem for the linear master equation. To generalize the theorem, we introduce the concept of rooted 0/1 loop forests, which generalize spanning trees with loops. We demonstrate that the weights of rooted 0/1 loop forests yield the static responses of the mean fitness and the steady-state distribution. Our results provide exact expressions for the static responses and the steady-state distribution. Additionally, we discuss approximations of these expressions in cases where reproduction or mutation is dominant. We provide numerical examples to illustrate these approximations and exact expressions. We also demonstrate how our results can be used to design control strategies for harmful populations.