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.

Many complex systems—be they financial, natural, or social—are composed of units—such as stocks, neurons, or agents—whose joint activity can be represented as a multivariate time series. An issue of both practical and theoretical importance concerns the possibility of inferring the presence of a static relationship between any two units solely from their dynamic behavior. The present contribution aims at tackling such an issue within the framework of traditional hypothesis testing: Briefly speaking, our suggestion is that of linking any two units if behaving in a sufficiently similar way. To achieve such a goal, we project a multivariate time series onto a signed graph by (1) comparing the empirical properties of the former with those expected under a suitable benchmark and (2) linking any two units with a positive (negative) edge in case the corresponding series shares a significantly large number of concordant (discordant) values. To define our benchmarks, we adopt an information-theoretic approach that is rooted into the constrained maximization of Shannon entropy, a procedure inducing an ensemble of multivariate time series that preserves some of the empirical properties on average, while randomizing everything else. We showcase the possible applications of our method by addressing one of the most timely issues in the domain of neurosciences, i.e., that of determining whether brain networks are frustrated or not, and, if so, to what extent. As our results suggest, this is indeed the case, with the major contribution to the underlying negative subgraph coming from the subcortical regions (and, to a lesser extent, from the limbic ones). At the mesoscopic level, the minimization of the Bayesian information criterion, instantiated with the signed stochastic block model, reveals that brain regions gather into modules aligning with the statistical variant of the relaxed balance theory.

Ponderomotive electron optics has attracted attention because structured optical fields provide round-lens functionalities, including negative lens power and negative spherical aberration, that are difficult to achieve with conventional Einzel and solenoid lenses. How ponderomotive lenses disperse with electron energy and whether that dispersion can be engineered for achromatization have remained largely unexplored. Here, we show that the transverse and longitudinal components of a vector optical field exhibit distinct energy dispersions because a relativistic correction modifies the effective lens action of the component polarized parallel to the electron velocity. In a radially polarized Bessel field coaxial with the electron beam, the two components form spatially colocated $J_1^2$- and $J_0^2$-type ponderomotive potentials whose relative weights depend on the electron energy, the Bessel cone angle, and the propagation direction of the light relative to the electrons. Using a local Abbe number defined in the energy domain, we find that this single field can operate as a self-achromatic round lens. We further construct zero-separation doublets—with a magnetic objective-lens model or an azimuthally polarized Bessel lens—that simultaneously cancel the first-order axial chromatic- and third-order spherical-aberration coefficients at a fixed electron-optical focal length, with the useful solutions occurring for counterpropagating light. Finite-aperture calculations at optical wavelengths of $1064\mathrm{nm}$ and $10.6\mu \mathrm{m}$ relate the achievable probe size to the required optical power, and at $10.6\mu \mathrm{m}$ they identify a low-energy, large-energy-spread regime in which the corrected doublets outperform the magnetic objective-lens model. The required optical power is compatible with demonstrated near-infrared ultrashort-pulse sources, so a single-pass proof-of-principle experiment is within reach.

The isomorphic property of strongly coupled three-dimensional (3D) Yukawa liquidlike fluids under steady shear is systematically investigated using nonequilibrium molecular dynamical simulations. It is discovered that, as the shear rate increases substantially, the shear viscosity $\eta$ and the radial distribution function $g\left(r\right)$ both exhibit excellent isomorphic scaling properties. The isomorphic scaling of shear viscosity is attributed to the dominant role of neighboring particles, whose averaged local configuration of $g\left(r\right)$ is invariant, even though 3D Yukawa fluids are continuously deformed and rearranged by the applied shear. Furthermore, it is found that the Stokes-Einstein relation is violated at higher shear rates because the diffusion coefficient $D$ is directional dependent and sensitive to the applied shear, i.e., not an isomorph invariant anymore.

Scattering processes are essential for understanding the structure of matter, yet their real-time dynamics remain challenging to simulate classically. Quantum computers offer a promising path toward efficient simulation of such physical systems. Here, we present a general and scalable framework for simulating meson scattering in lattice gauge theories on digital quantum hardware. Our approach addresses two key challenges: First, we introduce a symmetry-preserving quantum subspace expansion method for constructing high-fidelity meson creation operators across a wide range of coupling and momenta. Second, we design a quantum circuit for meson wave packet preparation using Givens rotations, improving accuracy while reducing circuit depth compared to existing approaches. We demonstrate the method in a ($1+1$)-dimensional ${\mathbb{Z}}_2$ gauge theory and explore meson scattering dynamics with tensor network simulations. We study both elastic and inelastic scattering and provide a comprehensive characterization of the scattering process in terms of energy transfer, entanglement entropy, and heavier particle production during the dynamics. Our work provides a scalable, nonvariational approach for simulating meson scattering on near-term quantum devices and offers a concrete strategy for probing nonperturbative dynamics in confining gauge theories.

We present a general framework for extracting conformal data from critical two-dimensional classical lattice models using finite-size tensor-network flow. The central idea is to identify, from transfer-matrix spectra, a self-consistent finite-size window together with a crossover scale that separates the finite-size-scaling regime from the finite-entanglement-scaling regime induced by bond-dimension truncation. Within this window, the central charge, scaling dimensions, and conformal spins can be estimated without requiring a unique critical fixed-point tensor or detailed prior knowledge of the underlying conformal field theory. We benchmark the framework using three tensor-network renormalization schemes for the critical two-dimensional Ising and three-state clock models. Across schemes, we find robust universal behavior below the crossover scale, enabling accurate extraction of conformal data up to relatively high conformal levels. The analysis also yields a natural operational definition of entanglement scaling for classical tensor-network calculations and, in turn, a complementary estimator of the central charge.

We propose and implement a quantum-informed reduction algorithm for the maximum independent set problem that integrates classical kernelization techniques with information extracted from quantum devices. Our larger framework consists of dedicated application, algorithm, and hardware layers, and easily generalizes to the maximum weight independent set problem. In this hybrid quantum-classical framework, which we call qReduMIS, the quantum computer is used as a coprocessor to inform classical reduction logic about frozen vertices that are likely (or unlikely) to be in large independent sets, thereby opening up the reduction space after removal of targeted subgraphs. We systematically assess the performance of qReduMIS based on experiments with up to 231 qubits run on Rydberg quantum hardware available through Amazon Braket. Our experiments show that qReduMIS can help address fundamental performance limitations faced by a broad set of (quantum) solvers including Rydberg quantum devices. We outline implementations of qReduMIS with alternative platforms, such as superconducting qubits or trapped ions, and we discuss potential future extensions.

Recent advances in time-resolved cathodoluminescence have enabled ultrafast studies of single emitters in quantum materials with femtosecond temporal resolution. Here, we develop a quantum theory modeling the dynamics of free electrons interacting with quantum emitters in arbitrary initial states. Our analysis reveals that a free electron can induce transient coherent oscillations in the populations when the system is initially prepared in a coherent superposition of its states. Moreover, the electron energy spectrum exhibits a clear signature of the quantum coherence and sensitivity to the transition frequency of the emitter. These coherence effects manifest themselves as oscillations in the zero-loss peak of the spectral energy loss probability. Our findings pave the way for characterization of quantum-coherent dynamics of individual quantum emitters by electron probes.

We report time-resolved x-ray diffraction measurements of lead (Pb) subjected to laser-driven shock compression up to the melt on nanosecond timescales. Along its Hugoniot, Pb exhibits a sequence of structural transitions markedly different from those observed under static compression. The conventional fcc-to-hcp transition is suppressed. Instead, the stacking fault probability in the fcc phase increases with compression up to $\sim 20\mathrm{GPa}$, and the high-pressure bcc phase appears at 27 GPa, i.e., $\sim 60\mathrm{GPa}$ below the static hcp-bcc boundary at the same temperature. At 45.4 ($\pm 2.1$) GPa and a calculated temperature of 2695 K, partial melting is evidenced by diffuse scattering, in excellent agreement with previous diamond anvil cell (DAC) melting data. Our results demonstrate that the dynamical response of Pb involves a distinct solid-state pathway, likely associated with stacking faults probability increase. These findings highlight the need to revisit phase diagrams under shock compression, particularly when coupled with time-resolved in situ microscopic diagnostics.

To date, the laser cooling of rubidium atoms has inevitably relied on 780 nm cooling light corresponding to the first excited state $5{\mathrm{P}}_{3/2}$. Here, we demonstrate diffuse laser cooling of ${}^{87}\mathrm{Rb}$ atoms using the 420 nm $5{\mathrm{S}}_{1/2}\to 6{\mathrm{P}}_{3/2}$ transition without a preceding 780 nm cooling stage. A high-power $420\mathrm{nm}$ laser is used as the cooling light to produce cold atoms in a 1-m-long diffuse-cooling cell. Absorption spectroscopy yields a cold-atom density of approximately $1.4\times {10}^{11}{\mathrm{m}}^{-3}$. We compare the cooling performance of the 420 nm and conventional 780 nm diffuse-cooling schemes and verify the feasibility of using the high-excited-state transition as an independent cooling channel in this large-volume diffuse-cooling system. This approach provides an alternative cooling/pumping pathway for continuous cold-atom active optical clocks, where compatibility with the clock-lasing process and reduced cooling-light-induced perturbations are important. It is also expected to open up research directions and application prospects in frontier fields such as Rydberg atoms, quantum information, and so on.

The Lieb-Robinson correlation function can be used to characterize the propagation of quantum information in Ising chains. Considerable work has been done to establish bounds on this correlation function in various circumstances. To actually calculate the value of the correlation function directly typically requires a state space that grows exponentially with system size, and so is intractable for all but relatively small systems. We employ a recently developed method that enables direct calculation of the Lieb-Robinson correlation function and that scales linearly with system size. This enables the computation for systems with more than a thousand qubits, revealing the propagation of quantum information down the chain. We extend this technique to the problem of Ising chains with randomly disordered coupling strengths. Increasing disorder causes localization of the quantum correlations and halts propagation of quantum information down the chain. We see light-cone isocontours therefore becoming vertical. The decay of correlations down the chain is characterized by a correlation length that in the paramagnetic phase increases quadratically with mean coupling strength and inverse quadratically with disorder level. The correlation length peaks at the phase transition. We map our general expression for the correlation function in the Ising system onto the probability density in the single-particle tight-binding Su-Schrieffer-Heeger model for a specific initial condition.

For the BCS theory of superconductivity, the electron-phonon interaction is transformed to an attractive electron-electron interaction in the vicinity of the Fermi energy only. At the same time, its formal derivation using a unitary transformation reveals that the electrons attract one another whenever their energies do not differ by more than the phonon energy ${\omega }_{\mathrm{D}}$, independent of closeness to the Fermi energy. Consequently, the order parameter becomes finite even away from the Fermi level. Yet, for small interactions, its magnitude is usually small and can be safely ignored, justifying the BCS approximation. Intriguingly, we find that an accumulation of density of states at an energy ${\varepsilon }_{\mathrm{peak}}$ in proximity to the Fermi energy induces a significant order parameter magnitude around ${\varepsilon }_{\mathrm{peak}}$, which exceeds the one at $E_{\mathrm{F}}$ for moderate coupling strengths. This strong enhancement is heralded by the softening of an additional collective mode, which resembles a second phase transition. We predict measurable signatures in the thermodynamic and spectroscopic responses to this unexpected phenomenon, guiding future experimental searches for it. Finally, we demonstrate that these signatures remain robust upon including a phenomenological Coulomb repulsion, indicating that the enhancement is not an artifact of the idealized model.

Resolving the ultrafast decay of metastable electronic states into channels associated with spin-orbit-split ionization thresholds is a long-standing goal of attosecond photoelectron spectroscopy. Here, we use a variant of the rainbow reconstruction of attosecond beating by interference of two-photon transitions technique to study, experimentally and theoretically, the ultrafast dynamics, resolved in photoelectron energy and emission angle, of the autoionizing states comprised in the narrow 177 meV energy gap between the $3p^{-1} {}^{2}P_{3/2}^o$ and ${}^{2}P_{1/2}^o$ thresholds in argon. The scheme employs three pulses: an XUV attosecond pulse train (pump), generated as odd harmonics of a fundamental IR frequency $\omega$; a weak replica of the IR field (driver) that copropagates phase-locked with the pump; and a second IR pulse (probe) with controllable delay $\tau$ with respect to the pump. Two harmonics excite bound states below the ${}^{2}P_{3/2}^o$ threshold and the continuum above the ${}^{2}P_{1/2}^o$ threshold, and their overlapping sideband populates even-parity resonant states between the two thresholds, giving rise to resonant signals beating at both $\omega$ and $2\omega$. From the photoemission cross section and the ${\beta }_2$ and ${\beta }_4$ asymmetry parameters, we resolve both the $nf$ and the $np$ resonant series. In both theory and experiment, the relative weight of the $\omega$ and $2\omega$ beatings changes significantly across the interthreshold gap, an evolution that we trace back to higher-order probe-photon processes. The resonant photoelectron emission is found to be strongly localized in small spots within the $({\beta }_2,{\beta }_4)$ region admissible for two-photon transitions.

We propose a method to measure the interaction between an ultracold gas of neutral atoms and a surface. This solution combines an optical dipole trap reflected by the surface, a magnetic trap formed by current carrying wires embedded below the surface, and a rotation of the surface itself. It allows to adiabatically transport a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate from few micrometers to few hundred nanometers of the surface. At such distances, atom-surface interaction strongly affects the trapping potential, causing an increase of the tunneling rate toward the surface. In this paper, we show that the measurement of the lifetime of the cloud and its comparison to a tunneling model will allow to extract the Casimir-Polder force coefficient in the retarded regime ($c_4$). Our model includes noise-induced heating, calibration biases of experimentally controlled parameters, and accuracy of the atom lifetime measurement. Using typical trapping parameters and experimental uncertainties, we numerically estimate the relative uncertainty of $c_4$ to be 10%. This method can be implemented with any atomic species that can be magnetically and optically trapped.

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here, we establish a link between mixed unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions 3 and 4, and show how the method can detect non-mixed-unitary behavior based on incomplete channel tomography.

Data assimilation (DA) optimally fuses observational data with mathematical models, serving as a core computational framework for forecasting complex dynamical systems like the weather. Because manipulating large-scale high-rank error covariances is classically intractable, conventional DA is forced into severe structural compromises such as artificial localization or static parametrizations that destroy genuine cross-variable correlations. Future fault-tolerant quantum computing (FTQC) could offer transformative advantages to overcome these classical computational limits. While quantum linear system solvers theoretically provide exponential speedups for matrix inversion, the practical mapping of large-scale, uncompromised DA onto quantum architectures remains largely unexplored. Our framework builds upon two emerging technologies: FTQC hardware and efficient block-encoded oracles of the error covariance and observation operators, which we envision being supplied by future artificial intelligence surrogate models. Under this premise, we identify a potential bottleneck in the quantum implementation. We show that a direct mapping of the DA equations leads to a quadratic increase in the subnormalization factor ($\alpha$) associated with block encoding when typical nonlocal observations are utilized. To mitigate this algorithmic overhead, we propose a quantum-ready, combined state-observation space formulation. By reconfiguring the DA problem into an expanded saddle-point block-matrix system, our approach avoids the explicit multiplication of nonlocal observation operators. This maintains a linear scaling of $\alpha$ and confines the conditioning of the quantum solver to that of the observation error covariance, decoupled from the severely ill-conditioned prior. Numerical verification using the chaotic Lorenz-96 model demonstrates that our formulation achieves perfect fidelity with the uncompromised DA solution. Although reading out the full analysis state reduces the exponential speedup to a polynomial one, the framework retains a substantial advantage over the classical matrix inversion. This work bridges computational geosciences and quantum information science, providing the essential algorithmic foundation for large-scale DA to become a compelling application for FTQC.

Levitated nanoparticles are being investigated as ultrasensitive quantum sensors of forces and accelerations, with applications ranging from fundamental physics phenomena such as dark matter or quantum gravity to real-world applications. Attention is now turning to multiparticle regimes, and an important question is whether collective effects offer advantages for sensing. We investigate here the spectral characteristics of collective motion of $N$ trapped nanoparticles interacting via the optical mode of a cavity. We find that the collective motion typically exhibits two generic spectral features: a broad spectral feature, the collective bright mode (CBM), which has been previously studied, and a structure of sharp peaks, the mechanical mode comb (MMC). We can describe all the detailed spectral features of the system, with a simple closed-form expression, by reducing the motion to a one-dimensional generic collective mode, which is non-Hermitian. We show that the MMC is more advantageous than the usual CBM for increased sensitivity in force sensing. We find that the mechanical comb can autonomously repair loss of “teeth” due to particle loss, a feature that may offer robustness in sensing.