The spectral form factor of random matrix theory plays a key role in the description of disordered and chaotic quantum systems. While its moments are known to be approximately Gaussian, corrections subleading in the matrix dimension, $D$, have recently come to researchers' attention, with conflicting results in the literature. In this work, we investigate these departures from Gaussianity for both circular and Gaussian ensembles. Using two independent approaches—sine-kernel techniques and supersymmetric field theory—we identify the form factor statistics to next leading order in a $D^{-1}$ expansion. Our sine-kernel analysis highlights inconsistencies with previous studies, while the supersymmetric approach backs these findings and suggests an understanding of the statistics from a complementary perspective. Our findings fully agree with numerics. They are presented in a pedagogical way, highlighting pathways (and pitfalls) in the study of statistical signatures at next leading order, which are increasingly becoming important in applications.

Motivated by anomalous nonlocal correlation in the Kitaev spin liquids, we propose a quantum energy teleportation protocol between remote partners Alice and Bob on a quantum spin model, and examine how its performance is characterized by Majorana fermions that clearly depict nonlocal correlations inherent in the model. In our model, Bob's energy extraction is activated by energy injection by Alice's projective measurement and subsequent classical communication of the measurement result. We derive two formulas: one for the maximally extracted energy by the protocol, $\mathrm{\Delta }{E}_B^{\max }$, and the other for the maximum of energy reduction in a local spin system where Bob performs feedback unitary operation, $\mathrm{\Delta }{E}_{B,B}^{\max }$. The protocol aims to extract a positive amount of the former energy distinct from the latter due to the presence of an interaction between the local system and others. We find that the extracted energy becomes positive when a nonlocal correlator defined by Majorana fermions at Alice and Bob's sites is finite. We also find that the amount of the energy reduction becomes positive when another nonlocal Majorana correlator is finite. In both formulas, the correlators appear as a result of Bob's feedback unitary operation. We find that the latter formula is equal to the upper bound of energy extraction in the second law of effective information thermodynamics. We discuss the effective information-thermodynamical aspects behind the protocol at zero temperature.

We study the dynamics of a mobile impurity in a two-leg bosonic ladder. The impurity moves both along and across the legs and interacts with a bath of interacting bosonic particles present in the ladder. We use both analytical (Tomonaga-Luttinger liquid) and numerical [Density Matrix Renormalization Group (DMRG)] methods to compute the Green's function of the impurity. We find that for a small impurity-bath interaction, the symmetric mode of the impurity effectively couples only to the gapless mode of the bath while the antisymmetric mode of the impurity couples to both gapped and gapless modes of the bath. We compute the time dependence of the Green's function of the impurity, for impurity created in either the antisymmetric or symmetric mode with a given momentum. The latter case leads to a decay as a power law below a critical momentum and exponential above, while the former case exhibits both power-law and exponential decay depending on the transverse tunneling of the impurity. We compare the DMRG results with analytical results using the linked cluster expansion and find good agreement. In addition, we use DMRG to extract the lifetime of the quasiparticle, when the Green's function decays exponentially. We also treat the case of an infinite bath-impurity coupling for which both the symmetric and antisymmetric modes are systematically affected. For this case, the impurity Green's function in the symmetric mode decays as a power law at zero momentum. The corresponding exponent increases with increasing transverse tunneling of the impurity. We compare our results with other impurity problems for which the motion of either the impurity or the bath is limited to a single chain. Finally, we comment on the consequences of our findings for experiments with the ultracold gases.

We study the dynamics of entanglement asymmetry in random unitary circuits (RUCs). Focusing on a local $U\left(1\right)$ charge, we consider symmetric initial states evolved by both local one-dimensional circuits and geometrically nonlocal RUCs made of two-qudit gates. We compute the entanglement asymmetry of subsystems of arbitrary size, analyzing the relaxation timescales. We show that the entanglement asymmetry of the whole system approaches its stationary value in a time independent of the system size for both local and nonlocal circuits. For subsystems, we find qualitative differences depending on their size. When the subsystem is larger than half of the full system, the equilibration timescales are again independent of the system size for both local and nonlocal circuits and the entanglement asymmetry grows monotonically in time. Conversely, when the subsystems are smaller than half of the full system, we show that the entanglement asymmetry is nonmonotonic in time and that it equilibrates in a time proportional to the quantum-information scrambling time, providing a physical intuition. As a consequence, the subsystem-equilibration time depends on the locality of interactions, scaling linearly and logarithmically in the system size, respectively, for local and nonlocal RUCs. Our work confirms the entanglement asymmetry as a versatile and computable probe of symmetry in many-body physics and yields a phenomenological overview of entanglement-asymmetry evolution in typical nonintegrable dynamics.

Spectra of non-Hermitian systems with skin effects are sensitive to the boundary conditions. In this work, we introduce a system composed of an impurity and a nonreciprocal Su-Schrieffer-Heeger (SSH) chain with odd number of lattice sites. The shift in the energy of the zero mode can be dramatically changed by adding two vanishingly small couplings between the impurity and two ends of the chain. Here, we propose a multiple physical quantities sensor with exponential-power-law amplification mechanism. Sensitivity of the proposed sensor exhibits an exponential scaling with SSH chain size and a power-law scaling with frequency of the impurity. This system is designed for detecting two small physical quantities, i.e., the impurity-chain coupling strengths. If and only if these two physical quantities exist simultaneously, the energy of zero mode will obviously change. Moreover, sensitivity is also robust against on-site disorder or dissipation of the impurity. Sufficiently strong disorder will change the localization of the eigenstate, and this leads to device failure. We also show the parameter range of the proposed sensor, and this range accurately corresponds to a nontrivial spectral winding number. The single physical quantity sensors suffered from repeated construction and low utilization rate. Thus, our findings pave a basic way toward sensors that couple multiple physical quantities to the boundary of the non-Hermitian topological chain.

The minimal bound of the thermodynamic uncertainty relation (TUR) is modulated from that of the classical counterpart (${\mathcal{Q}}_{\min }=2$) when a quantumness is present in the dynamical process far from equilibrium. A recent study on a dissipative two-level system (TLS) subject to an external field indicates that quantum coherence can suppress the fluctuations of the irreversible current and loosens the TUR bound to ${\mathcal{Q}}_{\min }^{\mathrm{TLS}}\approx 1.25$. Here, by extending the field-driven single TLS to a quantum mechanically coupled two-qubit system (TQS), we explore how the quantum coupling between the two qubits, an additional complexity introduced to the probem of TLS, affects the photon current, fluctuations, and the TUR bound. We find that the TUR bound of the TQS depends on the strength of coupling, such that ${\mathcal{Q}}_{\min }^{\mathrm{TQS}}={\mathcal{Q}}_{\min }^{\mathrm{TLS}}\approx 1.25$ when the two qubits are effectively decoupled under weak coupling, whereas another loose bound ${\mathcal{Q}}_{\min }^{\mathrm{TQS}}\approx 1.36$ is identified for two strongly coupled qubits under strong fields. By contrasting the TQS against two coupled noisy oscillators, we illuminate the quantumness unique to the TQS and its effect on the TUR. Our findings from the study of the TQS form the basis for understanding the TUR of more general $N$-qubit systems.

Accurate computation of local atomic virial stress is crucial for predicting materials’ mechanical response in large-scale molecular dynamic simulations, but conventional methods struggle with high-order atomic environment descriptors' encoded machine-learning many-body potentials. Herein we propose the strain perturbation method, a general framework that can efficiently compute high-resolution atomic virial stress. While remaining consistent with pairwise virial formulation, this method is broadly applicable and robust across many-body potentials with various atomic environment descriptors.

Highly polarized gamma rays with linear or circular polarization are essential light sources for nuclear and particle physics experiments, astronomical detector evaluations, and relativistic electron beam diagnostics. In this study, we demonstrate gamma-ray generation via Compton scattering with unique polarization states, termed axially symmetric polarization. To investigate this, we developed a polarimeter for Compton gamma-ray sources to measure their two-dimensional polarization distribution. We found two methods to generate gamma rays whose polarization axis follows the azimuthal direction. The first method exploits the inherent azimuthal polarization of gamma rays produced using a circularly polarized laser. In this configuration, the gamma rays along the central axis are circularly polarized, while the linear polarization components in the outer region of the beam cross section are aligned azimuthally. The second method utilizes azimuthal polarization that arises in the outer region of the beam due to the incoherent superposition of multiple linearly polarized gamma rays with varying polarization axes, generated by an axially symmetric polarized laser. Additionally, our calculations indicate the feasibility of generating gamma rays with polarization axes oriented along the radial direction. This radial polarization, observed near the beam axis, results from the incoherent superposition of second harmonic gamma rays produced through nonlinear interactions induced by an intense axially symmetric polarized laser.

Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a conserved density, require a notion of spatially local interactions. We study the transport of the energy, the most basic conserved density, in few-body and 1D chains of nearest-neighbor random matrix terms that square to one, which we dub the “Haar-Ising” local random matrix model. In the few-body but large local Hilbert space dimension case, we develop a mapping for the energy dynamics to a single-particle hopping picture. This allows for the computation of the energy density autocorrelators and an out-of-time-ordered correlator of the energy density. In the 1D chain, we numerically study the energy transport for a small local Hilbert space dimension. Throughout, we discuss the density of states and touch upon the relation to free probability theory.

We further develop a recently introduced phase-field model of far-from-equilibrium alloy solidification under additive manufacturing conditions [K. Ji et al., Phys. Rev. Lett. 130, 026203 (2023)]. This model utilizes enhanced solute diffusivity within the spatially diffuse interface region to quantitatively capture solute trapping with a larger interface width, thereby making simulations on experimentally relevant length and timescales computationally feasible. The main developments presented here include testing the robustness of different variational formulations, extending the model to concentrated alloys by incorporating solid and liquid free energies from thermodynamic databases, as illustrated for hypoeutectic Al-Ag alloys with CALPHAD, extending convergence tests as a function of interface width to 3D, and carrying out simulations in both 2D and 3D to examine existing theories of microstructure development. Our results indicate that the simplest variational formulation that interpolates the bulk free-energy density between its solid and liquid forms is the most robust. Remarkably, for hypoeutectic Al-Ag alloys, this formulation yields a high-velocity nonequilibrium phase diagram that is independent of interface width, thereby demonstrating that the framework of enhanced solute diffusivity can be nontrivially extended to concentrated alloys. Other variational formulations have restricted ranges of materials or processing parameters that can be reliably modeled. We use 2D simulations to construct high-velocity microstructure selection maps for dilute Al-Cu alloys. The results validate the important role of latent heat rejection at the interface and extend the limited predictions of linear stability analysis [A. Karma and A. Sarkissian, Phys. Rev. E 47, 513 (1993)] and sharp-interface 1D simulations to fully nonlinear regimes. Furthermore, 3D simulations, carried out using a computationally tractable axisymmetric cellular/dendritic interface shape, demonstrate a good convergence similar to that observed in 2D as a function of interface width. Full 3D simulations, in turn, reveal that the standard theory of absolute stability is a good predictor of the upper critical velocity beyond which steady-state growth becomes unstable, despite the different morphological manifestations of this instability in 2D and 3D.

We explore self-induced parametric coupling between a driven (low frequency) and an undriven (high frequency) mode, also called internal resonances, in a membrane micromechanical system. Specifically, we focus on the formation of a limit cycle (LC) manifesting as a phononic frequency comb. As the LC formation involves a Hopf bifurcation, we developed a dedicated pump-noisy-probe technique to investigate which mechanical sidebands merge at the bifurcation. We reveal that the sideband of the driven lower mode is up-converted via a cross-Duffing nonlinearity to hybridize with the undriven high mode. When the up-conversion is initially red detuned relative to the high mode, significant squeezing and bimodality in the high mode occurs. Crucially, only when the up-converted sideband is initially blue detuned relative to the high mode, the sideband is attracted to the high mode and merges to form the Hopf bifurcation. This process delineates the microscopic origin of frequency comb formation. Our study reveals a key instability mechanism in driven nonlinear systems with implications for advanced sensing technologies and phononic metamaterials.

The magnetic properties of EuAlSi, a compound comprising a honeycomb lattice of Al/Si atoms and a triangular lattice of Eu atoms, are presented. By means of single-crystal x-ray diffraction, we find that EuAlSi crystallizes in an ${\mathrm{AlB}}_2$-type structure with space group $P6$/mmm and unit cell parameters $a=4.2229\left(10\right)\AA$ and $c=4.5268\left(12\right)\AA$. Our magnetic measurements indicate that EuAlSi is a soft ferromagnetic material with $T_{\mathrm{Curie}}=25.8\mathrm{K}$. The susceptibility follows the Curie-Weiss law at high temperatures, which allowed us to determine the paramagnetic Curie temperature ${\theta }_P=36.2\left(1\right)\mathrm{K}$ and an effective magnetic moment ${\mu }_{\text{eff}}=8.07\left(1\right){\mu }_B/\mathrm{Eu}$. This value is in agreement with the theoretical value of $7.9{\mu }_B$ for ${\mathrm{Eu}}^{2+}$ free ion. Moreover, we have prepared the ${\mathrm{Eu}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution, where the atoms in the triangular lattice were systematically exchanged, in order to study the evolution of the collective quantum properties from the ferromagnetic EuAlSi toward the superconducting SrAlSi. Across the ${\mathrm{Eu}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution, the unit cell parameters change linearly, following Vegard’s law, and making the system reliable for studying composition dependence of the interplay between the crystal structure and physical properties. As the Sr content increases, i.e., $x$ increases, we note a consistent reduction of ${\mu }_{\mathrm{eff}}$ and $T_{\mathrm{Curie}}$. Long-range magnetic order in ${\mathrm{Eu}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ persists up to $x=0.95$, whereas superconductivity is only observed for samples with $x>0.97$.

Most vaccines require multiple doses, the first to induce recognition and antibody production and subsequent doses to boost the primary response and achieve optimal protection. We show that properly prioritizing the administration of first and second doses can shift the epidemic threshold, separating the disease-free from the endemic state and potentially preventing widespread outbreaks. Assuming homogeneous mixing, we prove that at a low vaccination rate, the best strategy is to give absolute priority to first doses. In contrast, for high vaccination rates, we propose a scheduling that outperforms a first-come first-served approach. We identify the threshold that separates these two scenarios and derive the optimal prioritization scheme and interdose interval. Agent-based simulations on real and synthetic contact networks validate our findings. We provide specific guidelines for effective resource allocation, showing that adjusting the timing between the primer and booster significantly impacts epidemic outcomes and can determine whether the disease persists or disappears.

Entanglement of qudit pairs, with single-particle Hilbert space dimension $d$, has important potential for quantum information processing, with applications in cryptography, algorithms, and error correction. For a pair of qudits of arbitrary even dimension $d$, we introduce a generalized Bell basis with definite symmetry under exchange of internal states between the two particles. We show that no complete exchange-symmetrized basis can exist for odd $d$. This framework extends prior work on exchange-symmetrized hyperentangled qubit bases, where $d$ is a power of 2. For our exchange-symmetrized basis, we show that measurement devices restricted to linear evolution and local measurement (LELM) can unambiguously distinguish $2d-1$ qudit Bell states for any even $d$. This achieves the upper bound in general for reliable Bell-state distinguishability via LELM and augments previously known limits for $d=2^n$ and $d=3$. This result is relevant to near-term realizations of quantum communication protocols.

Bacterial populations typically exhibit exponential growth under resource-rich conditions, yet individual cells often deviate from this pattern. Recent work has shown that the elongation rates of Escherichia coli and Caulobacter crescentus increase throughout the cell cycle (super-exponential growth), while Bacillus subtilis displays a midcycle minimum (convex growth), and Mycobacterium tuberculosis grows linearly. Here, we develop a single-cell model linking gene expression, proteome allocation, and mass growth to explain these diverse growth trajectories. By calibrating model parameters with experimental data, we show that DNA-proportional mRNA transcription produces near-exponential growth, whereas deviations from this proportionality yield the observed non-exponential growth patterns. Analysis of gene expression perturbations reveals that ribosome expression primarily controls dry mass growth rate, whereas cell envelope protein expression more strongly affects cell elongation rate. We show that cell-cycle-dependent transcription dynamics give rise to convex, super-exponential, and linear modes of cell elongation observed experimentally, demonstrating how the timing of cell envelope and ribosomal protein expressions drive cell-cycle-specific behaviors. These findings provide a mechanistic basis for non-exponential single-cell growth and offer insights into how bacterial cells dynamically regulate elongation rates within each generation.